ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SCT171+7 : 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 : n009.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 08:55:42 AM UTC 2026

% Result   : Theorem 8.47s 8.75s
% Output   : Proof 8.59s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OIIA_res,axiom,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
    file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OIIA_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OLin_res,axiom,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
    file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OLin_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OProf_res,axiom,
    ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
    file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OProf_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Oabove_res,axiom,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
    file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Oabove_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Obelow_res,axiom,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
    file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Obelow_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Odictator_res,axiom,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
    file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Odictator_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omkbot_res,axiom,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
    file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omkbot_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omktop_res,axiom,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
    file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omktop_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Ounanimity_res,axiom,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
    file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Ounanimity_res) ).

fof(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co1399186613setsum(X_a,X_b)) = big_co1399186613setsum(X_a,X_b) ),
    file('theBenchmark.p',tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) ).

fof(tsy_c_COMBB_res,axiom,
    ! [X_b,X_c,X_a] : ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a),
    file('theBenchmark.p',tsy_c_COMBB_res) ).

fof(tsy_c_COMBC_res,axiom,
    ! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c),
    file('theBenchmark.p',tsy_c_COMBC_res) ).

fof(tsy_c_COMBI_res,axiom,
    ! [X_a] : ti(fun(X_a,X_a),combi(X_a)) = combi(X_a),
    file('theBenchmark.p',tsy_c_COMBI_res) ).

fof(tsy_c_COMBK_res,axiom,
    ! [X_a,X_b] : ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b),
    file('theBenchmark.p',tsy_c_COMBK_res) ).

fof(tsy_c_COMBS_res,axiom,
    ! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c),
    file('theBenchmark.p',tsy_c_COMBS_res) ).

fof(tsy_c_Finite__Set_Ocard_res,axiom,
    ! [X_a] : ti(fun(fun(X_a,bool),nat),finite_card(X_a)) = finite_card(X_a),
    file('theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).

fof(tsy_c_Finite__Set_Ofinite_res,axiom,
    ! [X_b] : ti(fun(fun(X_b,bool),bool),finite_finite_1(X_b)) = finite_finite_1(X_b),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).

fof(tsy_c_Finite__Set_Ofold__image_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)))),finite_fold_image(X_a,X_b)) = finite_fold_image(X_a,X_b),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofold__image_res) ).

fof(tsy_c_Finite__Set_Ofolding__idem_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool)),finite_folding_idem(X_a,X_b)) = finite_folding_idem(X_a,X_b),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofolding__idem_res) ).

fof(tsy_c_Finite__Set_Ofolding__image_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool))),finite_folding_image(X_a,X_b)) = finite_folding_image(X_a,X_b),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofolding__image_res) ).

fof(tsy_c_Finite__Set_Ofolding__image__simple__idem_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)))),finite908156982e_idem(X_a,X_b)) = finite908156982e_idem(X_a,X_b),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple__idem_res) ).

fof(tsy_c_FunDef_Oin__rel_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b)) = in_rel(X_a,X_b),
    file('theBenchmark.p',tsy_c_FunDef_Oin__rel_res) ).

fof(tsy_c_Fun_Ocomp_res,axiom,
    ! [X_a,X_c,X_b] : ti(fun(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c))),comp(X_a,X_c,X_b)) = comp(X_a,X_c,X_b),
    file('theBenchmark.p',tsy_c_Fun_Ocomp_res) ).

fof(tsy_c_Fun_Oinj__on_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),inj_on(X_a,X_b)) = inj_on(X_a,X_b),
    file('theBenchmark.p',tsy_c_Fun_Oinj__on_res) ).

fof(tsy_c_Fun_Othe__inv__into_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a))),the_inv_into(X_a,X_b)) = the_inv_into(X_a,X_b),
    file('theBenchmark.p',tsy_c_Fun_Othe__inv__into_res) ).

fof(tsy_c_FuncSet_OPi_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool))),pi(X_a,X_b)) = pi(X_a,X_b),
    file('theBenchmark.p',tsy_c_FuncSet_OPi_res) ).

fof(tsy_c_FuncSet_Ocompose_res,axiom,
    ! [X_a,X_c,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)))),compose(X_a,X_c,X_b)) = compose(X_a,X_c,X_b),
    file('theBenchmark.p',tsy_c_FuncSet_Ocompose_res) ).

fof(tsy_c_FuncSet_Oextensional_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,X_b),bool)),extensional(X_a,X_b)) = extensional(X_a,X_b),
    file('theBenchmark.p',tsy_c_FuncSet_Oextensional_res) ).

fof(tsy_c_FuncSet_Orestrict_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),restrict(X_a,X_b)) = restrict(X_a,X_b),
    file('theBenchmark.p',tsy_c_FuncSet_Orestrict_res) ).

fof(tsy_c_Groups_Oone__class_Oone_res,axiom,
    ! [X_a] :
      ( one(X_a)
     => ti(X_a,one_one(X_a)) = one_one(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_0_res,axiom,
    ! [X_a] :
      ( monoid_add(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_1_res,axiom,
    ! [X_a] :
      ( ab_semigroup_add(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_2_res,axiom,
    ! [X_a] :
      ( cancel_semigroup_add(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_0_res,axiom,
    ! [X_a] :
      ( semiring(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_1_res,axiom,
    ! [X_a] :
      ( monoid_mult(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_2_res,axiom,
    ! [X_a] :
      ( ab_semigroup_mult(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_3_res,axiom,
    ! [X_a] :
      ( mult_zero(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_4_res,axiom,
    ! [X_a] :
      ( no_zero_divisors(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_res) ).

fof(tsy_c_Groups_Ozero__class_Ozero_res,axiom,
    ! [X_a] :
      ( zero(X_a)
     => ti(X_a,zero_zero(X_a)) = zero_zero(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_res) ).

fof(tsy_c_HOL_Obool_Obool__size_res,axiom,
    ti(fun(bool,nat),bool_size) = bool_size,
    file('theBenchmark.p',tsy_c_HOL_Obool_Obool__size_res) ).

fof(tsy_c_HOL_Oundefined_res,axiom,
    ! [X_a] : ti(X_a,undefined(X_a)) = undefined(X_a),
    file('theBenchmark.p',tsy_c_HOL_Oundefined_res) ).

fof(tsy_c_Hilbert__Choice_Oinv__into_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a))),hilbert_inv_into(X_a,X_b)) = hilbert_inv_into(X_a,X_b),
    file('theBenchmark.p',tsy_c_Hilbert__Choice_Oinv__into_res) ).

fof(tsy_c_If_res,axiom,
    ! [X_a] : ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a),
    file('theBenchmark.p',tsy_c_If_res) ).

fof(tsy_c_Int_Oring__1__class_OInts_res,axiom,
    ! [X_a] :
      ( ring_1(X_a)
     => ti(fun(X_a,bool),ring_1_Ints(X_a)) = ring_1_Ints(X_a) ),
    file('theBenchmark.p',tsy_c_Int_Oring__1__class_OInts_res) ).

fof(tsy_c_Lattices_Osemilattice__inf__class_Oinf_res,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),semilattice_inf_inf(X_a)) = semilattice_inf_inf(X_a) ),
    file('theBenchmark.p',tsy_c_Lattices_Osemilattice__inf__class_Oinf_res) ).

fof(tsy_c_Lattices_Osemilattice__sup__class_Osup_res,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),semilattice_sup_sup(X_a)) = semilattice_sup_sup(X_a) ),
    file('theBenchmark.p',tsy_c_Lattices_Osemilattice__sup__class_Osup_res) ).

fof(tsy_c_Nat_OSuc_res,axiom,
    ti(fun(nat,nat),suc) = suc,
    file('theBenchmark.p',tsy_c_Nat_OSuc_res) ).

fof(tsy_c_Nat_Onat_Onat__case_res,axiom,
    ! [X_a] : ti(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),nat_case(X_a)) = nat_case(X_a),
    file('theBenchmark.p',tsy_c_Nat_Onat_Onat__case_res) ).

fof(tsy_c_Nat_Onat_Onat__size_res,axiom,
    ti(fun(nat,nat),nat_size) = nat_size,
    file('theBenchmark.p',tsy_c_Nat_Onat_Onat__size_res) ).

fof(tsy_c_Nat_Osize__class_Osize_res,axiom,
    ti(fun(nat,nat),size_size(nat)) = size_size(nat),
    file('theBenchmark.p',tsy_c_Nat_Osize__class_Osize_res) ).

fof(tsy_c_Orderings_Oord__class_Oless_res,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a) ),
    file('theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_res) ).

fof(tsy_c_Orderings_Oord__class_Oless__eq_res,axiom,
    ! [X_b] :
      ( ord(X_b)
     => ti(fun(X_b,fun(X_b,bool)),ord_less_eq(X_b)) = ord_less_eq(X_b) ),
    file('theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).

fof(tsy_c_Orderings_Otop__class_Otop_res,axiom,
    ! [X_a] :
      ( top(X_a)
     => ti(X_a,top_top(X_a)) = top_top(X_a) ),
    file('theBenchmark.p',tsy_c_Orderings_Otop__class_Otop_res) ).

fof(tsy_c_Product__Type_OPair_res,axiom,
    ! [X_a,X_b] : ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b)) = product_Pair(X_a,X_b),
    file('theBenchmark.p',tsy_c_Product__Type_OPair_res) ).

fof(tsy_c_Product__Type_Oprod_Oprod__rec_res,axiom,
    ! [X_b,X_c,X_a] : ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a)) = product_prod_rec(X_b,X_c,X_a),
    file('theBenchmark.p',tsy_c_Product__Type_Oprod_Oprod__rec_res) ).

fof(tsy_c_SetInterval_Oord__class_OatLeast_res,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ti(fun(X_a,fun(X_a,bool)),ord_atLeast(X_a)) = ord_atLeast(X_a) ),
    file('theBenchmark.p',tsy_c_SetInterval_Oord__class_OatLeast_res) ).

fof(tsy_c_SetInterval_Oord__class_OatLeastAtMost_res,axiom,
    ! [X_a] :
      ( order(X_a)
     => ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastAtMost(X_a)) = ord_atLeastAtMost(X_a) ),
    file('theBenchmark.p',tsy_c_SetInterval_Oord__class_OatLeastAtMost_res) ).

fof(tsy_c_SetInterval_Oord__class_OatLeastLessThan_res,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastLessThan(X_a)) = ord_atLeastLessThan(X_a) ),
    file('theBenchmark.p',tsy_c_SetInterval_Oord__class_OatLeastLessThan_res) ).

fof(tsy_c_SetInterval_Oord__class_OgreaterThan_res,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ti(fun(X_a,fun(X_a,bool)),ord_greaterThan(X_a)) = ord_greaterThan(X_a) ),
    file('theBenchmark.p',tsy_c_SetInterval_Oord__class_OgreaterThan_res) ).

fof(tsy_c_SetInterval_Oord__class_OgreaterThanAtMost_res,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr1471790799AtMost(X_a)) = ord_gr1471790799AtMost(X_a) ),
    file('theBenchmark.p',tsy_c_SetInterval_Oord__class_OgreaterThanAtMost_res) ).

fof(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_res,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)) = ord_gr676655987ssThan(X_a) ),
    file('theBenchmark.p',tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_res) ).

fof(tsy_c_Set_OCollect_res,axiom,
    ! [X_a] : ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a),
    file('theBenchmark.p',tsy_c_Set_OCollect_res) ).

fof(tsy_c_Set_Oimage_res,axiom,
    ! [X_b,X_a] : ti(fun(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool))),image(X_b,X_a)) = image(X_b,X_a),
    file('theBenchmark.p',tsy_c_Set_Oimage_res) ).

fof(tsy_c_Sum__Type_OPlus_res,axiom,
    ! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool))),sum_Plus(X_a,X_b)) = sum_Plus(X_a,X_b),
    file('theBenchmark.p',tsy_c_Sum__Type_OPlus_res) ).

fof(tsy_c_Wellfounded_Ofinite__psubset_res,axiom,
    ! [X_a] : ti(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),finite_psubset(X_a)) = finite_psubset(X_a),
    file('theBenchmark.p',tsy_c_Wellfounded_Ofinite__psubset_res) ).

fof(tsy_c_Wellfounded_Omeasure_res,axiom,
    ! [X_a] : ti(fun(fun(X_a,nat),fun(product_prod(X_a,X_a),bool)),measure(X_a)) = measure(X_a),
    file('theBenchmark.p',tsy_c_Wellfounded_Omeasure_res) ).

fof(tsy_c_Wellfounded_Omlex__prod_res,axiom,
    ! [X_a] : ti(fun(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool))),mlex_prod(X_a)) = mlex_prod(X_a),
    file('theBenchmark.p',tsy_c_Wellfounded_Omlex__prod_res) ).

fof(tsy_c_fFalse_res,axiom,
    ti(bool,fFalse) = fFalse,
    file('theBenchmark.p',tsy_c_fFalse_res) ).

fof(tsy_c_fNot_res,axiom,
    ti(fun(bool,bool),fNot) = fNot,
    file('theBenchmark.p',tsy_c_fNot_res) ).

fof(tsy_c_fTrue_res,axiom,
    ti(bool,fTrue) = fTrue,
    file('theBenchmark.p',tsy_c_fTrue_res) ).

fof(tsy_c_fconj_res,axiom,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    file('theBenchmark.p',tsy_c_fconj_res) ).

fof(tsy_c_fdisj_res,axiom,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    file('theBenchmark.p',tsy_c_fdisj_res) ).

fof(tsy_c_fequal_res,axiom,
    ! [X_a] : ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a),
    file('theBenchmark.p',tsy_c_fequal_res) ).

fof(tsy_c_hAPP_arg1,axiom,
    ! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1),
    file('theBenchmark.p',tsy_c_hAPP_arg1) ).

fof(tsy_c_hAPP_arg2,axiom,
    ! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
    file('theBenchmark.p',tsy_c_hAPP_arg2) ).

fof(tsy_c_hAPP_res,axiom,
    ! [X_c,X_a,B_1_1,B_2_1] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
    file('theBenchmark.p',tsy_c_hAPP_res) ).

fof(tsy_c_hBOOL_arg1,hypothesis,
    ! [B_1_1] :
      ( hBOOL(ti(bool,B_1_1))
    <=> hBOOL(B_1_1) ),
    file('theBenchmark.p',tsy_c_hBOOL_arg1) ).

fof(tsy_c_member_res,axiom,
    ! [X_a] : ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a),
    file('theBenchmark.p',tsy_c_member_res) ).

fof(tsy_v_F_res,hypothesis,
    ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),f) = f,
    file('theBenchmark.p',tsy_v_F_res) ).

fof(tsy_v_Lab_____res,axiom,
    ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
    file('theBenchmark.p',tsy_v_Lab_____res) ).

fof(tsy_v_Lba_____res,axiom,
    ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
    file('theBenchmark.p',tsy_v_Lba_____res) ).

fof(tsy_v_P_____res,hypothesis,
    ti(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),p) = p,
    file('theBenchmark.p',tsy_v_P_____res) ).

fof(tsy_v_a_____res,axiom,
    ti(arrow_2142409994le_alt,a) = a,
    file('theBenchmark.p',tsy_v_a_____res) ).

fof(tsy_v_b_____res,axiom,
    ti(arrow_2142409994le_alt,b) = b,
    file('theBenchmark.p',tsy_v_b_____res) ).

fof(tsy_v_c_____res,hypothesis,
    ti(arrow_2142409994le_alt,c) = c,
    file('theBenchmark.p',tsy_v_c_____res) ).

fof(tsy_v_d_____res,hypothesis,
    ti(arrow_2142409994le_alt,d) = d,
    file('theBenchmark.p',tsy_v_d_____res) ).

fof(tsy_v_e_____res,axiom,
    ti(arrow_2142409994le_alt,e) = e,
    file('theBenchmark.p',tsy_v_e_____res) ).

fof(tsy_v_h_____res,axiom,
    ti(fun(arrow_1998540521e_indi,nat),h) = h,
    file('theBenchmark.p',tsy_v_h_____res) ).

fof(tsy_v_n_____res,axiom,
    ti(nat,n) = n,
    file('theBenchmark.p',tsy_v_n_____res) ).

fof(fact_0_assms_I3_J,axiom,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
    file('theBenchmark.p',fact_0_assms_I3_J) ).

fof(fact_1_u,axiom,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,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(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
    file('theBenchmark.p',fact_3__096P_A_058_AProf_096) ).

fof(fact_4_in__mkbot,axiom,
    ! [X_2,Y_1,L_3,Z_1] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,L_3),Z_1)))
    <=> ( ( ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Z_1)
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3)) )
        & ( ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Z_1)
         => ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1) )
        & ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Z_1) ) ),
    file('theBenchmark.p',fact_4_in__mkbot) ).

fof(fact_5_in__mktop,axiom,
    ! [X_2,Y_1,L_3,Z_1] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,L_3),Z_1)))
    <=> ( ( ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Z_1)
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3)) )
        & ( ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Z_1)
         => ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1) )
        & ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Z_1) ) ),
    file('theBenchmark.p',fact_5_in__mktop) ).

fof(fact_6__C2_C,axiom,
    ! [P_2,Pa,A_5,B_4,Aa,Ba] :
      ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba)
     => ( ti(arrow_2142409994le_alt,A_5) != ti(arrow_2142409994le_alt,B_4)
       => ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,B_4)
         => ( ti(arrow_2142409994le_alt,Ba) != ti(arrow_2142409994le_alt,A_5)
           => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof))
             => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_2),arrow_301600364e_Prof))
               => ( ! [I_1] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2))) ) ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_6__C2_C) ).

fof(fact_7__C1_C,axiom,
    ! [P_2,Pa,A_5,B_4,Aa,Ba] :
      ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba)
     => ( ti(arrow_2142409994le_alt,A_5) != ti(arrow_2142409994le_alt,B_4)
       => ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,B_4)
         => ( ti(arrow_2142409994le_alt,Ba) != ti(arrow_2142409994le_alt,A_5)
           => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof))
             => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_2),arrow_301600364e_Prof))
               => ( ! [I_1] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa)))
                   => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2))) ) ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_7__C1_C) ).

fof(fact_8__C4_C,axiom,
    ! [P_2,Pa,Ca,Aa,Ba] :
      ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba)
     => ( ti(arrow_2142409994le_alt,Ba) != ti(arrow_2142409994le_alt,Ca)
       => ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ca)
         => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof))
           => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_2),arrow_301600364e_Prof))
             => ( ! [I_1] :
                    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Ca)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1))) )
               => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa)))
                <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Ca)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2))) ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_8__C4_C) ).

fof(fact_9_pairwise__neutrality,axiom,
    ! [P_2,Pa,A_5,B_4,Aa,Ba] :
      ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba)
     => ( ti(arrow_2142409994le_alt,A_5) != ti(arrow_2142409994le_alt,B_4)
       => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof))
         => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_2),arrow_301600364e_Prof))
           => ( ! [I_1] :
                  ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1)))
                <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1))) )
             => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa)))
              <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2))) ) ) ) ) ) ),
    file('theBenchmark.p',fact_9_pairwise__neutrality) ).

fof(fact_10__C3_C,axiom,
    ! [P_2,Pa,Aa,Ba] :
      ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba)
     => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof))
       => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_2),arrow_301600364e_Prof))
         => ( ! [I_1] :
                ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1)))
              <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Aa)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1))) )
           => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa)))
            <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Aa)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2))) ) ) ) ) ),
    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(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)))
    <=> ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n))
         => ( ( hAPP(arrow_1998540521e_indi,nat,h,I_1) != n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e))) )
            & ( hAPP(arrow_1998540521e_indi,nat,h,I_1) = n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),c),e))) ) ) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),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(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_indi,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(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
    file('theBenchmark.p',fact_14_PW) ).

fof(fact_15_split__paired__All,axiom,
    ! [X_a,X_b,Pa] :
      ( ! [X1] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))
    <=> ! [A_4,B_3] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3))) ),
    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(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_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(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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    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(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
    file('theBenchmark.p',fact_19_n_I1_J) ).

fof(fact_20_injh,axiom,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
    file('theBenchmark.p',fact_20_injh) ).

fof(fact_21_Pair__inject,axiom,
    ! [X_b,X_a,A_2,B_1,A_6,B_5] :
      ( hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_6),B_5)
     => ~ ( ti(X_a,A_2) = ti(X_a,A_6)
         => ti(X_b,B_1) != ti(X_b,B_5) ) ),
    file('theBenchmark.p',fact_21_Pair__inject) ).

fof(fact_22_Pair__eq,axiom,
    ! [X_b,X_a,Aa,Ba,A_5,B_4] :
      ( hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_4)
    <=> ( ti(X_b,Ba) = ti(X_b,B_4)
        & ti(X_a,Aa) = ti(X_a,A_5) ) ),
    file('theBenchmark.p',fact_22_Pair__eq) ).

fof(fact_23_IIA__def,axiom,
    ! [Fa] :
      ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,Fa))
    <=> ! [X_1] :
          ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof))
         => ! [Xa] :
              ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Xa),arrow_301600364e_Prof))
             => ! [A_4,B_3] :
                  ( ! [I_1] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I_1)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Xa,I_1))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,Xa))) ) ) ) ) ),
    file('theBenchmark.p',fact_23_IIA__def) ).

fof(fact_24_unanimity__def,axiom,
    ! [Fa] :
      ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,Fa))
    <=> ! [X_1] :
          ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof))
         => ! [A_4,B_3] :
              ( ! [I_1] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I_1)))
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1))) ) ) ),
    file('theBenchmark.p',fact_24_unanimity__def) ).

fof(fact_25_top1I,axiom,
    ! [X_a,X_2] : hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_2)),
    file('theBenchmark.p',fact_25_top1I) ).

fof(fact_26_UNIV__I,axiom,
    ! [X_a,X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool)))),
    file('theBenchmark.p',fact_26_UNIV__I) ).

fof(fact_27_iso__tuple__UNIV__I,axiom,
    ! [X_a,X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool)))),
    file('theBenchmark.p',fact_27_iso__tuple__UNIV__I) ).

fof(fact_28_prod_Orecs,axiom,
    ! [X_b,X_c,X_a,F1,Aa,Ba] : hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba),
    file('theBenchmark.p',fact_28_prod_Orecs) ).

fof(fact_29_top__apply,axiom,
    ! [X_b,X_a] :
      ( top(X_a)
     => ! [X_2] : hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_2) = top_top(X_a) ),
    file('theBenchmark.p',fact_29_top__apply) ).

fof(fact_30_not__top__less,axiom,
    ! [X_a] :
      ( top(X_a)
     => ! [A_2] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),top_top(X_a)),A_2)) ),
    file('theBenchmark.p',fact_30_not__top__less) ).

fof(fact_31_less__top,axiom,
    ! [X_a] :
      ( top(X_a)
     => ! [Aa] :
          ( ti(X_a,Aa) != top_top(X_a)
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),top_top(X_a))) ) ),
    file('theBenchmark.p',fact_31_less__top) ).

fof(fact_32_assms_I1_J,axiom,
    hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
    file('theBenchmark.p',fact_32_assms_I1_J) ).

fof(fact_33__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    file('theBenchmark.p',fact_33__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_34_dictator__def,axiom,
    ! [Fa,I] :
      ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,Fa),I))
    <=> ! [X_1] :
          ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof))
         => hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I) ) ),
    file('theBenchmark.p',fact_34_dictator__def) ).

fof(fact_35__096Lab_A_058_ALin_096,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
    file('theBenchmark.p',fact_35__096Lab_A_058_ALin_096) ).

fof(fact_36__096Lba_A_058_ALin_096,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
    file('theBenchmark.p',fact_36__096Lba_A_058_ALin_096) ).

fof(fact_37__096a_A_126_061_Ab_096,axiom,
    a != b,
    file('theBenchmark.p',fact_37__096a_A_126_061_Ab_096) ).

fof(fact_38__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
    file('theBenchmark.p',fact_38__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

fof(fact_39__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
    file('theBenchmark.p',fact_39__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

fof(fact_40__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
    file('theBenchmark.p',fact_40__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

fof(fact_41__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
    file('theBenchmark.p',fact_41__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

fof(fact_42_PiProf,axiom,
    ! [Na] : hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),Na))),lab)),lba)),arrow_301600364e_Prof)),
    file('theBenchmark.p',fact_42_PiProf) ).

fof(fact_43__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
    ~ ! [Lab] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),Lab))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),Lab),arrow_1568854078le_Lin)) ),
    file('theBenchmark.p',fact_43__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

fof(fact_44__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
    ~ ! [Lba] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),Lba))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),Lba),arrow_1568854078le_Lin)) ),
    file('theBenchmark.p',fact_44__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

fof(fact_45__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(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n))
         => ( ( hAPP(arrow_1998540521e_indi,nat,h,I_1) != n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e))) )
            & ( hAPP(arrow_1998540521e_indi,nat,h,I_1) = n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),c),e))) ) ) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e))) ) )
    <=> ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ) ) ),
    file('theBenchmark.p',fact_45__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_46_n_I2_J,axiom,
    ! [M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),n))
     => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),M_1))),lab)),lba)))) ),
    file('theBenchmark.p',fact_46_n_I2_J) ).

fof(fact_47_notin__Lin__iff,axiom,
    ! [X_2,Y_1,L_3] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
     => ( ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1)
       => ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3))
        <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Y_1),X_2)),L_3)) ) ) ),
    file('theBenchmark.p',fact_47_notin__Lin__iff) ).

fof(fact_48_Lin__irrefl,axiom,
    ! [Aa,Ba,L_3] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
     => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),L_3))
       => ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Aa)),L_3)) ) ),
    file('theBenchmark.p',fact_48_Lin__irrefl) ).

fof(fact_49_mktop__Lin,axiom,
    ! [X_2,L_3] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
     => hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,L_3),X_2)),arrow_1568854078le_Lin)) ),
    file('theBenchmark.p',fact_49_mktop__Lin) ).

fof(fact_50_mkbot__Lin,axiom,
    ! [X_2,L_3] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
     => hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,L_3),X_2)),arrow_1568854078le_Lin)) ),
    file('theBenchmark.p',fact_50_mkbot__Lin) ).

fof(fact_51_above__Lin,axiom,
    ! [L_3,X_2,Y_1] :
      ( ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
       => hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,L_3),X_2),Y_1)),arrow_1568854078le_Lin)) ) ),
    file('theBenchmark.p',fact_51_above__Lin) ).

fof(fact_52_const__Lin__Prof,axiom,
    ! [L_3] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
     => hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),L_3)),arrow_301600364e_Prof)) ),
    file('theBenchmark.p',fact_52_const__Lin__Prof) ).

fof(fact_53_linorder__cases,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ( ti(X_a,X) != ti(X_a,Y)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ),
    file('theBenchmark.p',fact_53_linorder__cases) ).

fof(fact_54_order__less__asym,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_54_order__less__asym) ).

fof(fact_55_xt1_I10_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)) ) ) ),
    file('theBenchmark.p',fact_55_xt1_I10_J) ).

fof(fact_56_order__less__trans,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)) ) ) ),
    file('theBenchmark.p',fact_56_order__less__trans) ).

fof(fact_57_xt1_I2_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))
         => ( ti(X_a,B_1) = ti(X_a,C_1)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2)) ) ) ),
    file('theBenchmark.p',fact_57_xt1_I2_J) ).

fof(fact_58_ord__less__eq__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => ( B_1 = C_1
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_1)) ) ) ),
    file('theBenchmark.p',fact_58_ord__less__eq__trans) ).

fof(fact_59_xt1_I1_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C_1,A_2,B_1] :
          ( ti(X_a,A_2) = ti(X_a,B_1)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2)) ) ) ),
    file('theBenchmark.p',fact_59_xt1_I1_J) ).

fof(fact_60_ord__eq__less__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C_1,A_2,B_1] :
          ( A_2 = B_1
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_1)) ) ) ),
    file('theBenchmark.p',fact_60_ord__eq__less__trans) ).

fof(fact_61_xt1_I9_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ),
    file('theBenchmark.p',fact_61_xt1_I9_J) ).

fof(fact_62_order__less__asym_H,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) ) ),
    file('theBenchmark.p',fact_62_order__less__asym_H) ).

fof(fact_63_order__less__imp__triv,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [Pa,X_2,Y_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
           => hBOOL(Pa) ) ) ),
    file('theBenchmark.p',fact_63_order__less__imp__triv) ).

fof(fact_64_order__less__imp__not__eq2,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ti(X_a,Y) != ti(X_a,X) ) ),
    file('theBenchmark.p',fact_64_order__less__imp__not__eq2) ).

fof(fact_65_order__less__imp__not__eq,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ti(X_a,X) != ti(X_a,Y) ) ),
    file('theBenchmark.p',fact_65_order__less__imp__not__eq) ).

fof(fact_66_order__less__imp__not__less,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_66_order__less__imp__not__less) ).

fof(fact_67_order__less__not__sym,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_67_order__less__not__sym) ).

fof(fact_68_less__imp__neq,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ti(X_a,X) != ti(X_a,Y) ) ),
    file('theBenchmark.p',fact_68_less__imp__neq) ).

fof(fact_69_linorder__neqE,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( ti(X_a,X) != ti(X_a,Y)
         => ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ),
    file('theBenchmark.p',fact_69_linorder__neqE) ).

fof(fact_70_linorder__antisym__conv3,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [Y_1,X_2] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
         => ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
          <=> ti(X_a,X_2) = ti(X_a,Y_1) ) ) ),
    file('theBenchmark.p',fact_70_linorder__antisym__conv3) ).

fof(fact_71_linorder__less__linear,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ti(X_a,X) = ti(X_a,Y)
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_71_linorder__less__linear) ).

fof(fact_72_not__less__iff__gr__or__eq,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X_2,Y_1] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
        <=> ( ti(X_a,X_2) = ti(X_a,Y_1)
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) ) ) ),
    file('theBenchmark.p',fact_72_not__less__iff__gr__or__eq) ).

fof(fact_73_linorder__neq__iff,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X_2,Y_1] :
          ( ti(X_a,X_2) != ti(X_a,Y_1)
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) ) ),
    file('theBenchmark.p',fact_73_linorder__neq__iff) ).

fof(fact_74_order__less__irrefl,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X)) ),
    file('theBenchmark.p',fact_74_order__less__irrefl) ).

fof(fact_75_ext,axiom,
    ! [X_a,X_b,F,G] :
      ( ! [X_1] : hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1)
     => ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G) ),
    file('theBenchmark.p',fact_75_ext) ).

fof(fact_76_mem__def,axiom,
    ! [X_a,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
    <=> hBOOL(hAPP(X_a,bool,A_1,X_2)) ),
    file('theBenchmark.p',fact_76_mem__def) ).

fof(fact_77_Collect__def,axiom,
    ! [X_a,Pa] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = ti(fun(X_a,bool),Pa),
    file('theBenchmark.p',fact_77_Collect__def) ).

fof(fact_78_UNIV__def,axiom,
    ! [X_a] : top_top(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fTrue)),
    file('theBenchmark.p',fact_78_UNIV__def) ).

fof(fact_79_in__above,axiom,
    ! [X_2,Y_1,L_3,Aa,Ba] :
      ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
       => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,L_3),Aa),Ba)))
        <=> ( ( ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Ba)
             => ( ( ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Ba)
                 => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3)) )
                & ( ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Ba)
                 => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Aa)),L_3))
                    | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Aa) ) ) ) )
            & ( ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Ba)
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Y_1)),L_3)) )
            & ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1) ) ) ) ),
    file('theBenchmark.p',fact_79_in__above) ).

fof(fact_80_pred__equals__eq2,axiom,
    ! [X_a,X_b,S,R_2] :
      ( ! [X_1,Xa] :
          ( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),R_2))
        <=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),S)) )
    <=> ti(fun(product_prod(X_a,X_b),bool),R_2) = ti(fun(product_prod(X_a,X_b),bool),S) ),
    file('theBenchmark.p',fact_80_pred__equals__eq2) ).

fof(fact_81_dictatorI,axiom,
    ! [I,Fa] :
      ( hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Fa),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
     => ( ! [X_1] :
            ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof))
           => ! [A_4,B_3] :
                ( ti(arrow_2142409994le_alt,A_4) != ti(arrow_2142409994le_alt,B_3)
               => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I)))
                 => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1))) ) ) )
       => hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,Fa),I)) ) ),
    file('theBenchmark.p',fact_81_dictatorI) ).

fof(fact_82_n_I3_J,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_82_n_I3_J) ).

fof(fact_83__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_83__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_84__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ! [I_1] :
      ( ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n))
         => ( ( hAPP(arrow_1998540521e_indi,nat,h,I_1) != n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e))) )
            & ( hAPP(arrow_1998540521e_indi,nat,h,I_1) = n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),c),e))) ) ) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e))) ) )
    <=> ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ) ) ),
    file('theBenchmark.p',fact_84__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_85_inv__f__eq,axiom,
    ! [X_a,X_b,X_2,Y_1,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => ( hAPP(X_a,X_b,F,X_2) = ti(X_b,Y_1)
       => hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),Y_1) = ti(X_a,X_2) ) ),
    file('theBenchmark.p',fact_85_inv__f__eq) ).

fof(fact_86_inv__f__f,axiom,
    ! [X_a,X_b,X_2,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2) ),
    file('theBenchmark.p',fact_86_inv__f__f) ).

fof(fact_87_PiE,axiom,
    ! [X_a,X_b,X_2,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
     => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2)))
       => ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ) ),
    file('theBenchmark.p',fact_87_PiE) ).

fof(fact_88_complete__Lin,axiom,
    ! [Aa,Ba] :
      ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba)
     => ? [X_1] :
          ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),X_1))
          & hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X_1),arrow_1568854078le_Lin)) ) ),
    file('theBenchmark.p',fact_88_complete__Lin) ).

fof(fact_89_Pi__UNIV,axiom,
    ! [X_a,X_b,A_1] : hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),top_top(fun(X_b,bool)))) = top_top(fun(fun(X_a,X_b),bool)),
    file('theBenchmark.p',fact_89_Pi__UNIV) ).

fof(fact_90_inj__fun,axiom,
    ! [X_c,X_a,X_b,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,fun(X_c,X_b)),fun(fun(X_a,bool),bool),inj_on(X_a,fun(X_c,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_c,X_b)),hAPP(fun(X_b,fun(X_c,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_c,X_b))),combb(X_b,fun(X_c,X_b),X_a),combk(X_b,X_c)),F)),top_top(fun(X_a,bool)))) ),
    file('theBenchmark.p',fact_90_inj__fun) ).

fof(fact_91_in__below,axiom,
    ! [X_2,Y_1,L_3,Aa,Ba] :
      ( ti(arrow_2142409994le_alt,Aa) != ti(arrow_2142409994le_alt,Ba)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
       => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,L_3),Aa),Ba)))
        <=> ( ( ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Aa)
             => ( ( ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Aa)
                 => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3)) )
                & ( ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Aa)
                 => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Y_1)),L_3))
                    | ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Ba) ) ) ) )
            & ( ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Aa)
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Ba)),L_3)) )
            & ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1) ) ) ) ),
    file('theBenchmark.p',fact_91_in__below) ).

fof(fact_92_order__refl,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X)) ),
    file('theBenchmark.p',fact_92_order__refl) ).

fof(fact_93__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_,axiom,
    ? [N_2] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),one_one(nat))))),lab)),lba))))
      & ! [M_1] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),M_1))),lab)),lba)))) )
      & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))) ),
    file('theBenchmark.p',fact_93__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_) ).

fof(fact_94__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O,axiom,
    ~ ! [N_2] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
       => ( ! [M_1] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2))
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),M_1))),lab)),lba)))) )
         => ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),one_one(nat))))),lab)),lba)))) ) ),
    file('theBenchmark.p',fact_94__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O) ).

fof(fact_95_linorder__le__cases,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_95_linorder__le__cases) ).

fof(fact_96_le__funE,axiom,
    ! [X_a,X_b] :
      ( ord(X_b)
     => ! [X_2,F,G] :
          ( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G))
         => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))) ) ),
    file('theBenchmark.p',fact_96_le__funE) ).

fof(fact_97_xt1_I6_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X)) ) ) ),
    file('theBenchmark.p',fact_97_xt1_I6_J) ).

fof(fact_98_xt1_I5_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
           => ti(X_a,X) = ti(X_a,Y) ) ) ),
    file('theBenchmark.p',fact_98_xt1_I5_J) ).

fof(fact_99_order__trans,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z)) ) ) ),
    file('theBenchmark.p',fact_99_order__trans) ).

fof(fact_100_order__antisym,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
           => ti(X_a,X) = ti(X_a,Y) ) ) ),
    file('theBenchmark.p',fact_100_order__antisym) ).

fof(fact_101_xt1_I4_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
         => ( ti(X_a,B_1) = ti(X_a,C_1)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) ) ) ),
    file('theBenchmark.p',fact_101_xt1_I4_J) ).

fof(fact_102_ord__le__eq__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => ( B_1 = C_1
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1)) ) ) ),
    file('theBenchmark.p',fact_102_ord__le__eq__trans) ).

fof(fact_103_xt1_I3_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C_1,A_2,B_1] :
          ( ti(X_a,A_2) = ti(X_a,B_1)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) ) ) ),
    file('theBenchmark.p',fact_103_xt1_I3_J) ).

fof(fact_104_ord__eq__le__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C_1,A_2,B_1] :
          ( A_2 = B_1
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1)) ) ) ),
    file('theBenchmark.p',fact_104_ord__eq__le__trans) ).

fof(fact_105_order__antisym__conv,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Y_1,X_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
          <=> ti(X_a,X_2) = ti(X_a,Y_1) ) ) ),
    file('theBenchmark.p',fact_105_order__antisym__conv) ).

fof(fact_106_le__funD,axiom,
    ! [X_a,X_b] :
      ( ord(X_b)
     => ! [X_2,F,G] :
          ( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G))
         => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))) ) ),
    file('theBenchmark.p',fact_106_le__funD) ).

fof(fact_107_order__eq__refl,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X,Y] :
          ( X = Y
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_107_order__eq__refl) ).

fof(fact_108_order__eq__iff,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X_2,Y_1] :
          ( ti(X_a,X_2) = ti(X_a,Y_1)
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2))
            & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) ) ) ),
    file('theBenchmark.p',fact_108_order__eq__iff) ).

fof(fact_109_linorder__linear,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_109_linorder__linear) ).

fof(fact_110_le__fun__def,axiom,
    ! [X_a,X_b] :
      ( ord(X_b)
     => ! [F,G] :
          ( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G))
        <=> ! [X_1] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))) ) ),
    file('theBenchmark.p',fact_110_le__fun__def) ).

fof(fact_111_linorder__not__less,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X_2,Y_1] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2)) ) ),
    file('theBenchmark.p',fact_111_linorder__not__less) ).

fof(fact_112_linorder__not__le,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X_2,Y_1] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) ) ),
    file('theBenchmark.p',fact_112_linorder__not__le) ).

fof(fact_113_linorder__le__less__linear,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_113_linorder__le__less__linear) ).

fof(fact_114_order__less__le,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X_2,Y_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
        <=> ( ti(X_a,X_2) != ti(X_a,Y_1)
            & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) ) ) ),
    file('theBenchmark.p',fact_114_order__less__le) ).

fof(fact_115_less__le__not__le,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X_2,Y_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
        <=> ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2))
            & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) ) ) ),
    file('theBenchmark.p',fact_115_less__le__not__le) ).

fof(fact_116_order__le__less,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X_2,Y_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
        <=> ( ti(X_a,X_2) = ti(X_a,Y_1)
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) ) ),
    file('theBenchmark.p',fact_116_order__le__less) ).

fof(fact_117_leI,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_117_leI) ).

fof(fact_118_not__leE,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [Y,X] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_118_not__leE) ).

fof(fact_119_linorder__antisym__conv1,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X_2,Y_1] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
          <=> ti(X_a,X_2) = ti(X_a,Y_1) ) ) ),
    file('theBenchmark.p',fact_119_linorder__antisym__conv1) ).

fof(fact_120_order__neq__le__trans,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [A_2,B_1] :
          ( ti(X_a,A_2) != ti(X_a,B_1)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ),
    file('theBenchmark.p',fact_120_order__neq__le__trans) ).

fof(fact_121_xt1_I12_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [A_2,B_1] :
          ( ti(X_a,A_2) != ti(X_a,B_1)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) ) ) ),
    file('theBenchmark.p',fact_121_xt1_I12_J) ).

fof(fact_122_leD,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_122_leD) ).

fof(fact_123_order__less__imp__le,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_123_order__less__imp__le) ).

fof(fact_124_linorder__antisym__conv2,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X_2,Y_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
         => ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
          <=> ti(X_a,X_2) = ti(X_a,Y_1) ) ) ),
    file('theBenchmark.p',fact_124_linorder__antisym__conv2) ).

fof(fact_125_order__le__imp__less__or__eq,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => ( ti(X_a,X) = ti(X_a,Y)
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) ) ) ),
    file('theBenchmark.p',fact_125_order__le__imp__less__or__eq) ).

fof(fact_126_order__le__neq__trans,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => ( ti(X_a,A_2) != ti(X_a,B_1)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ),
    file('theBenchmark.p',fact_126_order__le__neq__trans) ).

fof(fact_127_xt1_I11_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
         => ( ti(X_a,A_2) != ti(X_a,B_1)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) ) ) ),
    file('theBenchmark.p',fact_127_xt1_I11_J) ).

fof(fact_128_order__less__le__trans,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)) ) ) ),
    file('theBenchmark.p',fact_128_order__less__le__trans) ).

fof(fact_129_xt1_I7_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)) ) ) ),
    file('theBenchmark.p',fact_129_xt1_I7_J) ).

fof(fact_130_order__le__less__trans,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)) ) ) ),
    file('theBenchmark.p',fact_130_order__le__less__trans) ).

fof(fact_131_xt1_I8_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)) ) ) ),
    file('theBenchmark.p',fact_131_xt1_I8_J) ).

fof(fact_132_top__greatest,axiom,
    ! [X_a] :
      ( top(X_a)
     => ! [A_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),top_top(X_a))) ),
    file('theBenchmark.p',fact_132_top__greatest) ).

fof(fact_133_top__unique,axiom,
    ! [X_a] :
      ( top(X_a)
     => ! [Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),Aa))
        <=> ti(X_a,Aa) = top_top(X_a) ) ),
    file('theBenchmark.p',fact_133_top__unique) ).

fof(fact_134_top__le,axiom,
    ! [X_a] :
      ( top(X_a)
     => ! [A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),A_2))
         => ti(X_a,A_2) = top_top(X_a) ) ),
    file('theBenchmark.p',fact_134_top__le) ).

fof(fact_135_inj__on__def,axiom,
    ! [X_a,X_b,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
    <=> ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => ! [Xa] :
              ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1))
             => ( hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Xa)
               => ti(X_a,X_1) = ti(X_a,Xa) ) ) ) ),
    file('theBenchmark.p',fact_135_inj__on__def) ).

fof(fact_136_inj__on__contraD,axiom,
    ! [X_a,X_b,X_2,Y_1,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( ti(X_a,X_2) != ti(X_a,Y_1)
       => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
           => hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1) ) ) ) ),
    file('theBenchmark.p',fact_136_inj__on__contraD) ).

fof(fact_137_inj__on__iff,axiom,
    ! [X_a,X_b,Y_1,X_2,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
       => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
         => ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
          <=> ti(X_a,X_2) = ti(X_a,Y_1) ) ) ) ),
    file('theBenchmark.p',fact_137_inj__on__iff) ).

fof(fact_138_inj__onD,axiom,
    ! [X_a,X_b,X_2,Y_1,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
       => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
           => ti(X_a,X_2) = ti(X_a,Y_1) ) ) ) ),
    file('theBenchmark.p',fact_138_inj__onD) ).

fof(fact_139_Pi__mem,axiom,
    ! [X_a,X_b,X_2,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2))) ) ),
    file('theBenchmark.p',fact_139_Pi__mem) ).

fof(fact_140_below__Lin,axiom,
    ! [L_3,X_2,Y_1] :
      ( ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
       => hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,L_3),X_2),Y_1)),arrow_1568854078le_Lin)) ) ),
    file('theBenchmark.p',fact_140_below__Lin) ).

fof(fact_141_Prof__def,axiom,
    arrow_301600364e_Prof = hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)),
    file('theBenchmark.p',fact_141_Prof__def) ).

fof(fact_142_inj__on__id2,axiom,
    ! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),combi(X_a)),A_1)),
    file('theBenchmark.p',fact_142_inj__on__id2) ).

fof(fact_143_funcset__mem,axiom,
    ! [X_a,X_b,X_2,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_143_funcset__mem) ).

fof(fact_144_funcset__id,axiom,
    ! [X_a,A_1] : hBOOL(hAPP(fun(fun(X_a,X_a),bool),bool,hAPP(fun(X_a,X_a),fun(fun(fun(X_a,X_a),bool),bool),member(fun(X_a,X_a)),combi(X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool)),pi(X_a,X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),combk(fun(X_a,bool),X_a),A_1)))),
    file('theBenchmark.p',fact_144_funcset__id) ).

fof(fact_145_inj__eq,axiom,
    ! [X_a,X_b,X_2,Y_1,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
      <=> ti(X_a,X_2) = ti(X_a,Y_1) ) ),
    file('theBenchmark.p',fact_145_inj__eq) ).

fof(fact_146_injD,axiom,
    ! [X_a,X_b,X_2,Y_1,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
       => ti(X_a,X_2) = ti(X_a,Y_1) ) ),
    file('theBenchmark.p',fact_146_injD) ).

fof(fact_147_inv__into__f__f,axiom,
    ! [X_a,X_b,X_2,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
       => hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2) ) ),
    file('theBenchmark.p',fact_147_inv__into__f__f) ).

fof(fact_148_inv__into__f__eq,axiom,
    ! [X_a,X_b,Y_1,X_2,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
       => ( hAPP(X_a,X_b,F,X_2) = ti(X_b,Y_1)
         => hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),Y_1) = ti(X_a,X_2) ) ) ),
    file('theBenchmark.p',fact_148_inv__into__f__eq) ).

fof(fact_149_Pi__I,axiom,
    ! [X_b,X_a,F,B,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1))) )
     => hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ),
    file('theBenchmark.p',fact_149_Pi__I) ).

fof(fact_150_inj__imp__inv__eq,axiom,
    ! [X_a,X_b,G,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => ( ! [X_1] : hAPP(X_a,X_b,F,hAPP(X_b,X_a,G,X_1)) = ti(X_b,X_1)
       => hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F) = ti(fun(X_b,X_a),G) ) ),
    file('theBenchmark.p',fact_150_inj__imp__inv__eq) ).

fof(fact_151_less__add__one,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [A_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),one_one(X_a)))) ),
    file('theBenchmark.p',fact_151_less__add__one) ).

fof(fact_152_add__less__le__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
    file('theBenchmark.p',fact_152_add__less__le__mono) ).

fof(fact_153_add__le__less__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
    file('theBenchmark.p',fact_153_add__le__less__mono) ).

fof(fact_154_injI,axiom,
    ! [X_a,X_b,F] :
      ( ! [X_1,Y_2] :
          ( hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2)
         => ti(X_a,X_1) = ti(X_a,Y_2) )
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    file('theBenchmark.p',fact_154_injI) ).

fof(fact_155_dense__le,axiom,
    ! [X_a] :
      ( dense_linorder(X_a)
     => ! [Z,Y] :
          ( ! [X_1] :
              ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)) )
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) ) ),
    file('theBenchmark.p',fact_155_dense__le) ).

fof(fact_156_dense__le__bounded,axiom,
    ! [X_a] :
      ( dense_linorder(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ( ! [W_1] :
                ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_1))
               => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_1),Y))
                 => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_1),Z)) ) )
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) ) ) ),
    file('theBenchmark.p',fact_156_dense__le__bounded) ).

fof(fact_157_xt5,axiom,
    ! [X_b,X_a] :
      ( ( order(X_b)
        & order(X_a) )
     => ! [Ca,F,Ba,Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),hAPP(X_a,X_b,F,Ba)))
           => ( ! [X_1,Y_2] :
                  ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))
                 => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_1))) )
             => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Aa))) ) ) ) ),
    file('theBenchmark.p',fact_157_xt5) ).

fof(fact_158_xt7,axiom,
    ! [X_b,X_a] :
      ( ( order(X_b)
        & order(X_a) )
     => ! [Ca,F,Ba,Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Ba)))
           => ( ! [X_1,Y_2] :
                  ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_1))
                 => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_1))) )
             => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Aa))) ) ) ) ),
    file('theBenchmark.p',fact_158_xt7) ).

fof(fact_159_less__fun__def,axiom,
    ! [X_a,X_b] :
      ( ord(X_b)
     => ! [F,G] :
          ( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G))
        <=> ( ~ hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F))
            & hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) ) ) ),
    file('theBenchmark.p',fact_159_less__fun__def) ).

fof(fact_160_Pi__anti__mono,axiom,
    ! [X_b,X_a,B,A_3,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),A_1))
     => hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(fun(X_a,X_b),bool),fun(fun(fun(X_a,X_b),bool),bool),ord_less_eq(fun(fun(X_a,X_b),bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_3),B))) ),
    file('theBenchmark.p',fact_160_Pi__anti__mono) ).

fof(fact_161_pred__subset__eq2,axiom,
    ! [X_a,X_b,R_2,S] :
      ( hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_2)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S)))
    <=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),bool),ord_less_eq(fun(product_prod(X_a,X_b),bool)),R_2),S)) ),
    file('theBenchmark.p',fact_161_pred__subset__eq2) ).

fof(fact_162_subset__UNIV,axiom,
    ! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),top_top(fun(X_a,bool)))),
    file('theBenchmark.p',fact_162_subset__UNIV) ).

fof(fact_163_subset__inj__on,axiom,
    ! [X_a,X_b,A_1,F,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ) ),
    file('theBenchmark.p',fact_163_subset__inj__on) ).

fof(fact_164_linorder__neqE__linordered__idom,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [X,Y] :
          ( ti(X_a,X) != ti(X_a,Y)
         => ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ),
    file('theBenchmark.p',fact_164_linorder__neqE__linordered__idom) ).

fof(fact_165_add__right__imp__eq,axiom,
    ! [X_a] :
      ( cancel_semigroup_add(X_a)
     => ! [B_1,A_2,C_1] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)
         => ti(X_a,B_1) = ti(X_a,C_1) ) ),
    file('theBenchmark.p',fact_165_add__right__imp__eq) ).

fof(fact_166_add__imp__eq,axiom,
    ! [X_a] :
      ( cancel146912293up_add(X_a)
     => ! [A_2,B_1,C_1] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)
         => ti(X_a,B_1) = ti(X_a,C_1) ) ),
    file('theBenchmark.p',fact_166_add__imp__eq) ).

fof(fact_167_add__left__imp__eq,axiom,
    ! [X_a] :
      ( cancel_semigroup_add(X_a)
     => ! [A_2,B_1,C_1] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)
         => ti(X_a,B_1) = ti(X_a,C_1) ) ),
    file('theBenchmark.p',fact_167_add__left__imp__eq) ).

fof(fact_168_add__right__cancel,axiom,
    ! [X_a] :
      ( cancel_semigroup_add(X_a)
     => ! [Ba,Aa,Ca] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)
        <=> ti(X_a,Ba) = ti(X_a,Ca) ) ),
    file('theBenchmark.p',fact_168_add__right__cancel) ).

fof(fact_169_add__left__cancel,axiom,
    ! [X_a] :
      ( cancel_semigroup_add(X_a)
     => ! [Aa,Ba,Ca] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)
        <=> ti(X_a,Ba) = ti(X_a,Ca) ) ),
    file('theBenchmark.p',fact_169_add__left__cancel) ).

fof(fact_170_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X_a] :
      ( ab_semigroup_add(X_a)
     => ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1)) ),
    file('theBenchmark.p',fact_170_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_171_one__reorient,axiom,
    ! [X_a] :
      ( one(X_a)
     => ! [X_2] :
          ( one_one(X_a) = ti(X_a,X_2)
        <=> ti(X_a,X_2) = one_one(X_a) ) ),
    file('theBenchmark.p',fact_171_one__reorient) ).

fof(fact_172_add__le__imp__le__left,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) ) ),
    file('theBenchmark.p',fact_172_add__le__imp__le__left) ).

fof(fact_173_add__le__imp__le__right,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [A_2,C_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) ) ),
    file('theBenchmark.p',fact_173_add__le__imp__le__right) ).

fof(fact_174_add__mono,axiom,
    ! [X_a] :
      ( ordere779506340up_add(X_a)
     => ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
    file('theBenchmark.p',fact_174_add__mono) ).

fof(fact_175_add__left__mono,axiom,
    ! [X_a] :
      ( ordere779506340up_add(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1))) ) ),
    file('theBenchmark.p',fact_175_add__left__mono) ).

fof(fact_176_add__right__mono,axiom,
    ! [X_a] :
      ( ordere779506340up_add(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))) ) ),
    file('theBenchmark.p',fact_176_add__right__mono) ).

fof(fact_177_add__le__cancel__left,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [Ca,Aa,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Ba)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) ),
    file('theBenchmark.p',fact_177_add__le__cancel__left) ).

fof(fact_178_add__le__cancel__right,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [Aa,Ca,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Ca)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) ),
    file('theBenchmark.p',fact_178_add__le__cancel__right) ).

fof(fact_179_add__less__imp__less__left,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ),
    file('theBenchmark.p',fact_179_add__less__imp__less__left) ).

fof(fact_180_add__less__imp__less__right,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [A_2,C_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ),
    file('theBenchmark.p',fact_180_add__less__imp__less__right) ).

fof(fact_181_add__strict__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
    file('theBenchmark.p',fact_181_add__strict__mono) ).

fof(fact_182_add__strict__left__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1))) ) ),
    file('theBenchmark.p',fact_182_add__strict__left__mono) ).

fof(fact_183_add__strict__right__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))) ) ),
    file('theBenchmark.p',fact_183_add__strict__right__mono) ).

fof(fact_184_add__less__cancel__left,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [Ca,Aa,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Ba)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) ) ),
    file('theBenchmark.p',fact_184_add__less__cancel__left) ).

fof(fact_185_add__less__cancel__right,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [Aa,Ca,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Ca)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) ) ),
    file('theBenchmark.p',fact_185_add__less__cancel__right) ).

fof(fact_186_le__funI,axiom,
    ! [X_a,X_b] :
      ( ord(X_b)
     => ! [F,G] :
          ( ! [X_1] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))
         => hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) ) ),
    file('theBenchmark.p',fact_186_le__funI) ).

fof(fact_187_xt6,axiom,
    ! [X_b,X_a] :
      ( ( ord(X_b)
        & order(X_a) )
     => ! [Ca,F,Ba,Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Ba)),Aa))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),Ba))
           => ( ! [X_1,Y_2] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1))
                 => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_1))) )
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ca)),Aa)) ) ) ) ),
    file('theBenchmark.p',fact_187_xt6) ).

fof(fact_188_xt4,axiom,
    ! [X_b,X_a] :
      ( ( order(X_b)
        & order(X_a) )
     => ! [Ca,F,Ba,Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ba)),Aa))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),Ba))
           => ( ! [X_1,Y_2] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1))
                 => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_1))) )
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ca)),Aa)) ) ) ) ),
    file('theBenchmark.p',fact_188_xt4) ).

fof(fact_189_order__le__less__subst1,axiom,
    ! [X_a,X_b] :
      ( ( order(X_a)
        & order(X_b) )
     => ! [Ca,Aa,F,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_b,X_a,F,Ba)))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),Ca))
           => ( ! [X_1,Y_2] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))
                 => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_2))) )
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ca))) ) ) ) ),
    file('theBenchmark.p',fact_189_order__le__less__subst1) ).

fof(fact_190_order__less__le__subst1,axiom,
    ! [X_a,X_b] :
      ( ( order(X_a)
        & order(X_b) )
     => ! [Ca,Aa,F,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ba)))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),Ca))
           => ( ! [X_1,Y_2] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))
                 => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_2))) )
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ca))) ) ) ) ),
    file('theBenchmark.p',fact_190_order__less__le__subst1) ).

fof(fact_191_order__le__less__subst2,axiom,
    ! [X_a,X_b] :
      ( ( order(X_a)
        & order(X_b) )
     => ! [F,Ca,Aa,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),Ca))
           => ( ! [X_1,Y_2] :
                  ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
                 => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_2))) )
             => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),Ca)) ) ) ) ),
    file('theBenchmark.p',fact_191_order__le__less__subst2) ).

fof(fact_192_order__less__le__subst2,axiom,
    ! [X_a,X_b] :
      ( ( order(X_a)
        & order(X_b) )
     => ! [F,Ca,Aa,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Ba)),Ca))
           => ( ! [X_1,Y_2] :
                  ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
                 => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_2))) )
             => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),Ca)) ) ) ) ),
    file('theBenchmark.p',fact_192_order__less__le__subst2) ).

fof(fact_193_add__leE,axiom,
    ! [M_3,K_2,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_2)),N))
     => ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
         => ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N)) ) ),
    file('theBenchmark.p',fact_193_add__leE) ).

fof(fact_194_equalityI,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
       => ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) ) ),
    file('theBenchmark.p',fact_194_equalityI) ).

fof(fact_195_subsetD,axiom,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B)) ) ),
    file('theBenchmark.p',fact_195_subsetD) ).

fof(fact_196_psubset__eq,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
    <=> ( ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B)
        & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ),
    file('theBenchmark.p',fact_196_psubset__eq) ).

fof(fact_197_subset__iff__psubset__eq,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
    <=> ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
        | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) ) ),
    file('theBenchmark.p',fact_197_subset__iff__psubset__eq) ).

fof(fact_198_psubset__imp__subset,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    file('theBenchmark.p',fact_198_psubset__imp__subset) ).

fof(fact_199_psubset__subset__trans,axiom,
    ! [X_a,C,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C)) ) ),
    file('theBenchmark.p',fact_199_psubset__subset__trans) ).

fof(fact_200_subset__psubset__trans,axiom,
    ! [X_a,C,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C)) ) ),
    file('theBenchmark.p',fact_200_subset__psubset__trans) ).

fof(fact_201_rev__predicate2D,axiom,
    ! [X_b,X_a,Q_1,Pa,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_2),Y_1))
     => ( hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1))
       => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_1)) ) ),
    file('theBenchmark.p',fact_201_rev__predicate2D) ).

fof(fact_202_equalityE,axiom,
    ! [X_a,A_1,B] :
      ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
     => ~ ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
         => ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) ) ),
    file('theBenchmark.p',fact_202_equalityE) ).

fof(fact_203_predicate2D,axiom,
    ! [X_a,X_b,X_2,Y_1,Pa,Q_1] :
      ( hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1))
     => ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_2),Y_1))
       => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_1)) ) ),
    file('theBenchmark.p',fact_203_predicate2D) ).

fof(fact_204_subset__trans,axiom,
    ! [X_a,C,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C)) ) ),
    file('theBenchmark.p',fact_204_subset__trans) ).

fof(fact_205_set__mp,axiom,
    ! [X_a,X_2,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) ) ),
    file('theBenchmark.p',fact_205_set__mp) ).

fof(fact_206_set__rev__mp,axiom,
    ! [X_a,B,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) ) ),
    file('theBenchmark.p',fact_206_set__rev__mp) ).

fof(fact_207_predicate1D,axiom,
    ! [X_a,X_2,Pa,Q_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1))
     => ( hBOOL(hAPP(X_a,bool,Pa,X_2))
       => hBOOL(hAPP(X_a,bool,Q_1,X_2)) ) ),
    file('theBenchmark.p',fact_207_predicate1D) ).

fof(fact_208_in__mono,axiom,
    ! [X_a,X_2,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) ) ),
    file('theBenchmark.p',fact_208_in__mono) ).

fof(fact_209_equalityD2,axiom,
    ! [X_a,A_1,B] :
      ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) ),
    file('theBenchmark.p',fact_209_equalityD2) ).

fof(fact_210_equalityD1,axiom,
    ! [X_a,A_1,B] :
      ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    file('theBenchmark.p',fact_210_equalityD1) ).

fof(fact_211_rev__predicate1D,axiom,
    ! [X_a,Q_1,Pa,X_2] :
      ( hBOOL(hAPP(X_a,bool,Pa,X_2))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1))
       => hBOOL(hAPP(X_a,bool,Q_1,X_2)) ) ),
    file('theBenchmark.p',fact_211_rev__predicate1D) ).

fof(fact_212_set__eq__subset,axiom,
    ! [X_a,A_1,B] :
      ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
    <=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
        & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ),
    file('theBenchmark.p',fact_212_set__eq__subset) ).

fof(fact_213_subset__refl,axiom,
    ! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),A_1)),
    file('theBenchmark.p',fact_213_subset__refl) ).

fof(fact_214_pred__subset__eq,axiom,
    ! [X_a,R_2,S] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))
    <=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_2),S)) ),
    file('theBenchmark.p',fact_214_pred__subset__eq) ).

fof(fact_215_less__not__refl,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    file('theBenchmark.p',fact_215_less__not__refl) ).

fof(fact_216_nat__neq__iff,axiom,
    ! [M,Na] :
      ( M != Na
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_216_nat__neq__iff) ).

fof(fact_217_linorder__neqE__nat,axiom,
    ! [X,Y] :
      ( X != Y
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X)) ) ),
    file('theBenchmark.p',fact_217_linorder__neqE__nat) ).

fof(fact_218_less__irrefl__nat,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    file('theBenchmark.p',fact_218_less__irrefl__nat) ).

fof(fact_219_less__not__refl2,axiom,
    ! [N,M_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_3))
     => M_3 != N ),
    file('theBenchmark.p',fact_219_less__not__refl2) ).

fof(fact_220_less__not__refl3,axiom,
    ! [S_1,T_4] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_4))
     => S_1 != T_4 ),
    file('theBenchmark.p',fact_220_less__not__refl3) ).

fof(fact_221_nat__less__cases,axiom,
    ! [Pa,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)) )
     => ( ( M = Na
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)) )
       => ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
           => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)) )
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)) ) ) ),
    file('theBenchmark.p',fact_221_nat__less__cases) ).

fof(fact_222_nat__add__commute,axiom,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_3),
    file('theBenchmark.p',fact_222_nat__add__commute) ).

fof(fact_223_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_223_nat__add__left__commute) ).

fof(fact_224_nat__add__assoc,axiom,
    ! [M_3,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_3),N)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_2)),
    file('theBenchmark.p',fact_224_nat__add__assoc) ).

fof(fact_225_nat__add__left__cancel,axiom,
    ! [K,M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)
    <=> M = Na ),
    file('theBenchmark.p',fact_225_nat__add__left__cancel) ).

fof(fact_226_nat__add__right__cancel,axiom,
    ! [M,K,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K)
    <=> M = Na ),
    file('theBenchmark.p',fact_226_nat__add__right__cancel) ).

fof(fact_227_le__refl,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N)),
    file('theBenchmark.p',fact_227_le__refl) ).

fof(fact_228_nat__le__linear,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_3))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    file('theBenchmark.p',fact_228_nat__le__linear) ).

fof(fact_229_eq__imp__le,axiom,
    ! [M_3,N] :
      ( M_3 = N
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    file('theBenchmark.p',fact_229_eq__imp__le) ).

fof(fact_230_le__trans,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),K_2))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_2)) ) ),
    file('theBenchmark.p',fact_230_le__trans) ).

fof(fact_231_le__antisym,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_3))
       => M_3 = N ) ),
    file('theBenchmark.p',fact_231_le__antisym) ).

fof(fact_232_inj__on__add__nat,axiom,
    ! [K,N_1] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),N_1)),
    file('theBenchmark.p',fact_232_inj__on__add__nat) ).

fof(fact_233_not__add__less1,axiom,
    ! [I_2,J_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_233_not__add__less1) ).

fof(fact_234_not__add__less2,axiom,
    ! [J_1,I_2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_234_not__add__less2) ).

fof(fact_235_nat__add__left__cancel__less,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ),
    file('theBenchmark.p',fact_235_nat__add__left__cancel__less) ).

fof(fact_236_trans__less__add1,axiom,
    ! [M_3,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),M_3))) ),
    file('theBenchmark.p',fact_236_trans__less__add1) ).

fof(fact_237_trans__less__add2,axiom,
    ! [M_3,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),J_1))) ),
    file('theBenchmark.p',fact_237_trans__less__add2) ).

fof(fact_238_add__less__mono1,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_238_add__less__mono1) ).

fof(fact_239_add__less__mono,axiom,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),L_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_239_add__less__mono) ).

fof(fact_240_less__add__eq__less,axiom,
    ! [M_3,N,K_2,L_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),L_1))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),L_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),N)
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ) ),
    file('theBenchmark.p',fact_240_less__add__eq__less) ).

fof(fact_241_add__lessD1,axiom,
    ! [I_2,J_1,K_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),I_2),K_2)) ),
    file('theBenchmark.p',fact_241_add__lessD1) ).

fof(fact_242_nat__less__le,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
    <=> ( M != Na
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_242_nat__less__le) ).

fof(fact_243_le__eq__less__or__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
    <=> ( M = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_243_le__eq__less__or__eq) ).

fof(fact_244_less__imp__le__nat,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    file('theBenchmark.p',fact_244_less__imp__le__nat) ).

fof(fact_245_le__neq__implies__less,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
     => ( M_3 != N
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ) ),
    file('theBenchmark.p',fact_245_le__neq__implies__less) ).

fof(fact_246_less__or__eq__imp__le,axiom,
    ! [M_3,N] :
      ( ( M_3 = N
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    file('theBenchmark.p',fact_246_less__or__eq__imp__le) ).

fof(fact_247_le__add2,axiom,
    ! [N,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N))),
    file('theBenchmark.p',fact_247_le__add2) ).

fof(fact_248_le__add1,axiom,
    ! [N,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_3))),
    file('theBenchmark.p',fact_248_le__add1) ).

fof(fact_249_le__iff__add,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
    <=> ? [K_1] : Na = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1) ),
    file('theBenchmark.p',fact_249_le__iff__add) ).

fof(fact_250_nat__add__left__cancel__le,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ),
    file('theBenchmark.p',fact_250_nat__add__left__cancel__le) ).

fof(fact_251_trans__le__add1,axiom,
    ! [M_3,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),M_3))) ),
    file('theBenchmark.p',fact_251_trans__le__add1) ).

fof(fact_252_trans__le__add2,axiom,
    ! [M_3,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),J_1))) ),
    file('theBenchmark.p',fact_252_trans__le__add2) ).

fof(fact_253_add__le__mono1,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_253_add__le__mono1) ).

fof(fact_254_add__le__mono,axiom,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),L_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_254_add__le__mono) ).

fof(fact_255_add__leD2,axiom,
    ! [M_3,K_2,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_2)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N)) ),
    file('theBenchmark.p',fact_255_add__leD2) ).

fof(fact_256_add__leD1,axiom,
    ! [M_3,K_2,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_2)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    file('theBenchmark.p',fact_256_add__leD1) ).

fof(fact_257_predicate2I,axiom,
    ! [X_b,X_a,Q_1,Pa] :
      ( ! [X_1,Y_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_2))
         => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_2)) )
     => hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1)) ),
    file('theBenchmark.p',fact_257_predicate2I) ).

fof(fact_258_Pi__mono,axiom,
    ! [X_b,X_a,B,C,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_a,fun(X_b,bool),B,X_1)),hAPP(X_a,fun(X_b,bool),C,X_1))) )
     => hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(fun(X_a,X_b),bool),fun(fun(fun(X_a,X_b),bool),bool),ord_less_eq(fun(fun(X_a,X_b),bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),C))) ),
    file('theBenchmark.p',fact_258_Pi__mono) ).

fof(fact_259_subsetI,axiom,
    ! [X_a,B,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) )
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    file('theBenchmark.p',fact_259_subsetI) ).

fof(fact_260_mono__nat__linear__lb,axiom,
    ! [M,K,F] :
      ( ! [M_1,N_2] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_1)),hAPP(nat,nat,F,N_2))) )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)))) ),
    file('theBenchmark.p',fact_260_mono__nat__linear__lb) ).

fof(fact_261_less__mono__imp__le__mono,axiom,
    ! [I,J,F] :
      ( ! [I_1,J_2] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_2))) )
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J))) ) ),
    file('theBenchmark.p',fact_261_less__mono__imp__le__mono) ).

fof(fact_262_termination__basic__simps_I3_J,axiom,
    ! [Z,X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))) ),
    file('theBenchmark.p',fact_262_termination__basic__simps_I3_J) ).

fof(fact_263_termination__basic__simps_I4_J,axiom,
    ! [Y,X,Z] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))) ),
    file('theBenchmark.p',fact_263_termination__basic__simps_I4_J) ).

fof(fact_264_termination__basic__simps_I5_J,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) ),
    file('theBenchmark.p',fact_264_termination__basic__simps_I5_J) ).

fof(fact_265_psubsetD,axiom,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B)) ) ),
    file('theBenchmark.p',fact_265_psubsetD) ).

fof(fact_266_psubset__trans,axiom,
    ! [X_a,C,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C)) ) ),
    file('theBenchmark.p',fact_266_psubset__trans) ).

fof(fact_267_termination__basic__simps_I2_J,axiom,
    ! [Y,X,Z] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))) ),
    file('theBenchmark.p',fact_267_termination__basic__simps_I2_J) ).

fof(fact_268_termination__basic__simps_I1_J,axiom,
    ! [Z,X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))) ),
    file('theBenchmark.p',fact_268_termination__basic__simps_I1_J) ).

fof(fact_269_in__rel__def,axiom,
    ! [X_b,X_a,R_2,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_2),X_2),Y_1))
    <=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_1)),R_2)) ),
    file('theBenchmark.p',fact_269_in__rel__def) ).

fof(fact_270_funcsetI,axiom,
    ! [X_b,X_a,F,B,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B)) )
     => hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
    file('theBenchmark.p',fact_270_funcsetI) ).

fof(fact_271_linear__alt,axiom,
    ? [L_2] : hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_2),arrow_1568854078le_Lin)),
    file('theBenchmark.p',fact_271_linear__alt) ).

fof(fact_272_Pi__cong,axiom,
    ! [X_b,X_a,B,F,G,A_1] :
      ( ! [W_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W_1),A_1))
         => hAPP(X_a,X_b,F,W_1) = hAPP(X_a,X_b,G,W_1) )
     => ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
      <=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ) ),
    file('theBenchmark.p',fact_272_Pi__cong) ).

fof(fact_273_Pi__I_H,axiom,
    ! [X_b,X_a,F,B,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1))) )
     => hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ),
    file('theBenchmark.p',fact_273_Pi__I_H) ).

fof(fact_274_card__inj,axiom,
    ! [X_a,X_b,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B))) ) ) ),
    file('theBenchmark.p',fact_274_card__inj) ).

fof(fact_275_inj__on__inverseI,axiom,
    ! [X_b,X_a,G,F,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => hAPP(X_b,X_a,G,hAPP(X_a,X_b,F,X_1)) = ti(X_a,X_1) )
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    file('theBenchmark.p',fact_275_inj__on__inverseI) ).

fof(fact_276_finite__indi,axiom,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    file('theBenchmark.p',fact_276_finite__indi) ).

fof(fact_277_card__bij,axiom,
    ! [X_a,X_b,G,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
       => ( hBOOL(hAPP(fun(fun(X_b,X_a),bool),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,X_a),bool),bool),member(fun(X_b,X_a)),G),hAPP(fun(X_b,fun(X_a,bool)),fun(fun(X_b,X_a),bool),hAPP(fun(X_b,bool),fun(fun(X_b,fun(X_a,bool)),fun(fun(X_b,X_a),bool)),pi(X_b,X_a),B),hAPP(fun(X_a,bool),fun(X_b,fun(X_a,bool)),combk(fun(X_a,bool),X_b),A_1))))
         => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),G),B))
           => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
             => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
               => hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_b,bool),nat,finite_card(X_b),B) ) ) ) ) ) ),
    file('theBenchmark.p',fact_277_card__bij) ).

fof(fact_278_finite__Collect__subsets,axiom,
    ! [X_a,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_1)))) ),
    file('theBenchmark.p',fact_278_finite__Collect__subsets) ).

fof(fact_279_card__psubset,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)))
         => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) ) ) ),
    file('theBenchmark.p',fact_279_card__psubset) ).

fof(fact_280_psubset__card__mono,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B))) ) ),
    file('theBenchmark.p',fact_280_psubset__card__mono) ).

fof(fact_281_card__seteq,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)))
         => ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) ) ) ),
    file('theBenchmark.p',fact_281_card__seteq) ).

fof(fact_282_card__mono,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B))) ) ),
    file('theBenchmark.p',fact_282_card__mono) ).

fof(fact_283_finite__Collect__le__nat,axiom,
    ! [K] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K)))),
    file('theBenchmark.p',fact_283_finite__Collect__le__nat) ).

fof(fact_284_finite__Collect__conjI,axiom,
    ! [X_a,Q_1,Pa] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
        | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa))) )
     => hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),Pa)),Q_1)))) ),
    file('theBenchmark.p',fact_284_finite__Collect__conjI) ).

fof(fact_285_finite__Collect__less__nat,axiom,
    ! [K] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K)))),
    file('theBenchmark.p',fact_285_finite__Collect__less__nat) ).

fof(fact_286_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    file('theBenchmark.p',fact_286_infinite__UNIV__nat) ).

fof(fact_287_finite__code,axiom,
    ! [X_a] :
      ( finite_finite(X_a)
     => ! [A_1] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    file('theBenchmark.p',fact_287_finite__code) ).

fof(fact_288_finite,axiom,
    ! [X_a] :
      ( finite_finite(X_a)
     => ! [A_1] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    file('theBenchmark.p',fact_288_finite) ).

fof(fact_289_card__UNIV__unit,axiom,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    file('theBenchmark.p',fact_289_card__UNIV__unit) ).

fof(fact_290_finite__Collect__disjI,axiom,
    ! [X_a,Pa,Q_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),Pa)),Q_1))))
    <=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
        & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa))) ) ),
    file('theBenchmark.p',fact_290_finite__Collect__disjI) ).

fof(fact_291_card__Collect__less__nat,axiom,
    ! [Na] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na))) = Na,
    file('theBenchmark.p',fact_291_card__Collect__less__nat) ).

fof(fact_292_rev__finite__subset,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
       => hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ),
    file('theBenchmark.p',fact_292_rev__finite__subset) ).

fof(fact_293_finite__subset,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
       => hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ),
    file('theBenchmark.p',fact_293_finite__subset) ).

fof(fact_294_finite__option__UNIV,axiom,
    ! [X_a] :
      ( hBOOL(hAPP(fun(option(X_a),bool),bool,finite_finite_1(option(X_a)),top_top(fun(option(X_a),bool))))
    <=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ),
    file('theBenchmark.p',fact_294_finite__option__UNIV) ).

fof(fact_295_finite__Plus__UNIV__iff,axiom,
    ! [X_a,X_b] :
      ( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),top_top(fun(sum_sum(X_a,X_b),bool))))
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),top_top(fun(X_b,bool))))
        & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ) ),
    file('theBenchmark.p',fact_295_finite__Plus__UNIV__iff) ).

fof(fact_296_finite__Prod__UNIV,axiom,
    ! [X_b,X_a] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),top_top(fun(X_b,bool))))
       => hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,finite_finite_1(product_prod(X_a,X_b)),top_top(fun(product_prod(X_a,X_b),bool)))) ) ),
    file('theBenchmark.p',fact_296_finite__Prod__UNIV) ).

fof(fact_297_finite__UNIV,axiom,
    ! [X_a] :
      ( finite_finite(X_a)
     => hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ),
    file('theBenchmark.p',fact_297_finite__UNIV) ).

fof(fact_298_finite__Collect__not,axiom,
    ! [X_a,Pa] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),Pa))))
      <=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ) ),
    file('theBenchmark.p',fact_298_finite__Collect__not) ).

fof(fact_299_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [X_a,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
     => ( hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_a,bool),nat,finite_card(X_a),top_top(fun(X_a,bool)))
       => ti(fun(X_a,bool),A_1) = top_top(fun(X_a,bool)) ) ),
    file('theBenchmark.p',fact_299_card__eq__UNIV__imp__eq__UNIV) ).

fof(fact_300_finite__fun__UNIVD2,axiom,
    ! [X_a,X_b] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,finite_finite_1(fun(X_a,X_b)),top_top(fun(fun(X_a,X_b),bool))))
     => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),top_top(fun(X_b,bool)))) ),
    file('theBenchmark.p',fact_300_finite__fun__UNIVD2) ).

fof(fact_301_finite__M__bounded__by__nat,axiom,
    ! [Pa,I] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I))))),
    file('theBenchmark.p',fact_301_finite__M__bounded__by__nat) ).

fof(fact_302_ex__new__if__finite,axiom,
    ! [X_a,A_1] :
      ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
       => ? [A_4] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),A_1)) ) ),
    file('theBenchmark.p',fact_302_ex__new__if__finite) ).

fof(fact_303_finite__nat__set__iff__bounded__le,axiom,
    ! [N_1] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_1))
    <=> ? [M_1] :
        ! [X_1] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_1))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),M_1)) ) ),
    file('theBenchmark.p',fact_303_finite__nat__set__iff__bounded__le) ).

fof(fact_304_finite__nat__set__iff__bounded,axiom,
    ! [N_1] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_1))
    <=> ? [M_1] :
        ! [X_1] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_1))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),M_1)) ) ),
    file('theBenchmark.p',fact_304_finite__nat__set__iff__bounded) ).

fof(fact_305_card__Plus,axiom,
    ! [X_b,X_a,B,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
       => hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)) ) ),
    file('theBenchmark.p',fact_305_card__Plus) ).

fof(fact_306_folding__image__simple__idem_Osubset__idem,axiom,
    ! [X_b,X_a,B,A_1,F,Z_1,G,Fa] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),Fa))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1))
         => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,B)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1) ) ) ),
    file('theBenchmark.p',fact_306_folding__image__simple__idem_Osubset__idem) ).

fof(fact_307_folding__image__simple__idem_Oidem,axiom,
    ! [X_b,X_a,X_2,F,Z_1,G,Fa] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),Fa))
     => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),X_2) = ti(X_a,X_2) ),
    file('theBenchmark.p',fact_307_folding__image__simple__idem_Oidem) ).

fof(fact_308_finite__PlusD_I2_J,axiom,
    ! [X_a,X_b,A_1,B] :
      ( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)))
     => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) ),
    file('theBenchmark.p',fact_308_finite__PlusD_I2_J) ).

fof(fact_309_finite__PlusD_I1_J,axiom,
    ! [X_a,X_b,A_1,B] :
      ( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)))
     => hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    file('theBenchmark.p',fact_309_finite__PlusD_I1_J) ).

fof(fact_310_finite__Plus,axiom,
    ! [X_b,X_a,B,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
       => hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B))) ) ),
    file('theBenchmark.p',fact_310_finite__Plus) ).

fof(fact_311_finite__Plus__iff,axiom,
    ! [X_a,X_b,A_1,B] :
      ( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)))
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
        & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ),
    file('theBenchmark.p',fact_311_finite__Plus__iff) ).

fof(fact_312_folding__image__simple__idem_Oin__idem,axiom,
    ! [X_b,X_a,X_2,A_1,F,Z_1,G,Fa] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),Fa))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
         => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1) ) ) ),
    file('theBenchmark.p',fact_312_folding__image__simple__idem_Oin__idem) ).

fof(fact_313_UNIV__Plus__UNIV,axiom,
    ! [X_b,X_a] : hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),top_top(fun(X_a,bool))),top_top(fun(X_b,bool))) = top_top(fun(sum_sum(X_a,X_b),bool)),
    file('theBenchmark.p',fact_313_UNIV__Plus__UNIV) ).

fof(fact_314_finite__less__ub,axiom,
    ! [U,F] :
      ( ! [N_2] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,F,N_2)))
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U)))) ),
    file('theBenchmark.p',fact_314_finite__less__ub) ).

fof(fact_315_bounded__nat__set__is__finite,axiom,
    ! [Na,N_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_1))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Na)) )
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_1)) ),
    file('theBenchmark.p',fact_315_bounded__nat__set__is__finite) ).

fof(fact_316_card__Plus__conv__if,axiom,
    ! [X_b,X_a,B,A_1] :
      ( ( ~ ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
            & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
       => hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)) = zero_zero(nat) )
      & ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
          & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
       => hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)) ) ),
    file('theBenchmark.p',fact_316_card__Plus__conv__if) ).

fof(fact_317_inj__onI,axiom,
    ! [X_b,X_a,F,A_1] :
      ( ! [X_1,Y_2] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1))
           => ( hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2)
             => ti(X_a,X_1) = ti(X_a,Y_2) ) ) )
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    file('theBenchmark.p',fact_317_inj__onI) ).

fof(fact_318_inj__on__cong,axiom,
    ! [X_b,X_a,F,G,A_1] :
      ( ! [A_4] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),A_1))
         => hAPP(X_a,X_b,F,A_4) = hAPP(X_a,X_b,G,A_4) )
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
      <=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),A_1)) ) ),
    file('theBenchmark.p',fact_318_inj__on__cong) ).

fof(fact_319_less__zeroE,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    file('theBenchmark.p',fact_319_less__zeroE) ).

fof(fact_320_le0,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N)),
    file('theBenchmark.p',fact_320_le0) ).

fof(fact_321_zero__reorient,axiom,
    ! [X_a] :
      ( zero(X_a)
     => ! [X_2] :
          ( zero_zero(X_a) = ti(X_a,X_2)
        <=> ti(X_a,X_2) = zero_zero(X_a) ) ),
    file('theBenchmark.p',fact_321_zero__reorient) ).

fof(fact_322_add_Ocomm__neutral,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_322_add_Ocomm__neutral) ).

fof(fact_323_add__0__right,axiom,
    ! [X_a] :
      ( monoid_add(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_323_add__0__right) ).

fof(fact_324_double__zero__sym,axiom,
    ! [X_a] :
      ( linord219039673up_add(X_a)
     => ! [Aa] :
          ( zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)
        <=> ti(X_a,Aa) = zero_zero(X_a) ) ),
    file('theBenchmark.p',fact_324_double__zero__sym) ).

fof(fact_325_add__0,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_325_add__0) ).

fof(fact_326_add__0__left,axiom,
    ! [X_a] :
      ( monoid_add(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_326_add__0__left) ).

fof(fact_327_zero__neq__one,axiom,
    ! [X_a] :
      ( zero_neq_one(X_a)
     => zero_zero(X_a) != one_one(X_a) ),
    file('theBenchmark.p',fact_327_zero__neq__one) ).

fof(fact_328_one__neq__zero,axiom,
    ! [X_a] :
      ( zero_neq_one(X_a)
     => one_one(X_a) != zero_zero(X_a) ),
    file('theBenchmark.p',fact_328_one__neq__zero) ).

fof(fact_329_not__less0,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    file('theBenchmark.p',fact_329_not__less0) ).

fof(fact_330_neq0__conv,axiom,
    ! [Na] :
      ( Na != zero_zero(nat)
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) ),
    file('theBenchmark.p',fact_330_neq0__conv) ).

fof(fact_331_less__nat__zero__code,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    file('theBenchmark.p',fact_331_less__nat__zero__code) ).

fof(fact_332_gr__implies__not0,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
     => N != zero_zero(nat) ),
    file('theBenchmark.p',fact_332_gr__implies__not0) ).

fof(fact_333_gr0I,axiom,
    ! [N] :
      ( N != zero_zero(nat)
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) ),
    file('theBenchmark.p',fact_333_gr0I) ).

fof(fact_334_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_334_plus__nat_Oadd__0) ).

fof(fact_335_Nat_Oadd__0__right,axiom,
    ! [M_3] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),zero_zero(nat)) = M_3,
    file('theBenchmark.p',fact_335_Nat_Oadd__0__right) ).

fof(fact_336_add__is__0,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) = zero_zero(nat)
    <=> ( Na = zero_zero(nat)
        & M = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_336_add__is__0) ).

fof(fact_337_add__eq__self__zero,axiom,
    ! [M_3,N] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N) = M_3
     => N = zero_zero(nat) ),
    file('theBenchmark.p',fact_337_add__eq__self__zero) ).

fof(fact_338_le__0__eq,axiom,
    ! [Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat)))
    <=> Na = zero_zero(nat) ),
    file('theBenchmark.p',fact_338_le__0__eq) ).

fof(fact_339_less__eq__nat_Osimps_I1_J,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N)),
    file('theBenchmark.p',fact_339_less__eq__nat_Osimps_I1_J) ).

fof(fact_340_add__nonpos__nonpos,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_340_add__nonpos__nonpos) ).

fof(fact_341_add__increasing2,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_2,C_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1))) ) ) ),
    file('theBenchmark.p',fact_341_add__increasing2) ).

fof(fact_342_add__increasing,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,C_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1))) ) ) ),
    file('theBenchmark.p',fact_342_add__increasing) ).

fof(fact_343_add__nonneg__eq__0__iff,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [Y_1,X_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y_1))
           => ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Y_1) = zero_zero(X_a)
            <=> ( ti(X_a,Y_1) = zero_zero(X_a)
                & ti(X_a,X_2) = zero_zero(X_a) ) ) ) ) ),
    file('theBenchmark.p',fact_343_add__nonneg__eq__0__iff) ).

fof(fact_344_add__nonneg__nonneg,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))) ) ) ),
    file('theBenchmark.p',fact_344_add__nonneg__nonneg) ).

fof(fact_345_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X_a] :
      ( linord219039673up_add(X_a)
     => ! [Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) ) ),
    file('theBenchmark.p',fact_345_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_346_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [X_a] :
      ( linord219039673up_add(X_a)
     => ! [Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) ) ),
    file('theBenchmark.p',fact_346_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_347_add__neg__neg,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_347_add__neg__neg) ).

fof(fact_348_pos__add__strict,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [B_1,C_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1))) ) ) ),
    file('theBenchmark.p',fact_348_pos__add__strict) ).

fof(fact_349_add__pos__pos,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))) ) ) ),
    file('theBenchmark.p',fact_349_add__pos__pos) ).

fof(fact_350_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X_a] :
      ( linord219039673up_add(X_a)
     => ! [Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) ) ),
    file('theBenchmark.p',fact_350_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_351_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [X_a] :
      ( linord219039673up_add(X_a)
     => ! [Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)) ) ),
    file('theBenchmark.p',fact_351_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_352_zero__le__one,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a))) ),
    file('theBenchmark.p',fact_352_zero__le__one) ).

fof(fact_353_not__one__le__zero,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a))) ),
    file('theBenchmark.p',fact_353_not__one__le__zero) ).

fof(fact_354_zero__less__one,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))) ),
    file('theBenchmark.p',fact_354_zero__less__one) ).

fof(fact_355_not__one__less__zero,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))) ),
    file('theBenchmark.p',fact_355_not__one__less__zero) ).

fof(fact_356_add__gr__0,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) ) ),
    file('theBenchmark.p',fact_356_add__gr__0) ).

fof(fact_357_card__infinite,axiom,
    ! [X_a,A_1] :
      ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = zero_zero(nat) ),
    file('theBenchmark.p',fact_357_card__infinite) ).

fof(fact_358_add__nonpos__neg,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_358_add__nonpos__neg) ).

fof(fact_359_add__neg__nonpos,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_359_add__neg__nonpos) ).

fof(fact_360_add__strict__increasing2,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,C_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1))) ) ) ),
    file('theBenchmark.p',fact_360_add__strict__increasing2) ).

fof(fact_361_add__strict__increasing,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,C_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1))) ) ) ),
    file('theBenchmark.p',fact_361_add__strict__increasing) ).

fof(fact_362_add__nonneg__pos,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))) ) ) ),
    file('theBenchmark.p',fact_362_add__nonneg__pos) ).

fof(fact_363_add__pos__nonneg,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))) ) ) ),
    file('theBenchmark.p',fact_363_add__pos__nonneg) ).

fof(fact_364_zero__less__two,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))) ),
    file('theBenchmark.p',fact_364_zero__less__two) ).

fof(fact_365_card__ge__0__finite,axiom,
    ! [X_a,A_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)))
     => hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    file('theBenchmark.p',fact_365_card__ge__0__finite) ).

fof(fact_366_finite__UNIV__card__ge__0,axiom,
    ! [X_a] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,finite_card(X_a),top_top(fun(X_a,bool))))) ),
    file('theBenchmark.p',fact_366_finite__UNIV__card__ge__0) ).

fof(fact_367_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(nat,fun(nat,bool),ord_less_eq(nat),I_1),K_1))
               => ~ hBOOL(hAPP(nat,bool,Pa,I_1)) )
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),Na)) ) ) ),
    file('theBenchmark.p',fact_367_ex__least__nat__less) ).

fof(fact_368_card_Oneutral,axiom,
    ! [X_a,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( ( ? [X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => one_one(nat) = zero_zero(nat) )
       => hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_368_card_Oneutral) ).

fof(fact_369_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(nat,fun(nat,bool),ord_less(nat),I_1),K_1))
               => ~ hBOOL(hAPP(nat,bool,Pa,I_1)) )
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),Na)) ) ) ),
    file('theBenchmark.p',fact_369_ex__least__nat__le) ).

fof(fact_370_less__imp__add__positive,axiom,
    ! [I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) ) ),
    file('theBenchmark.p',fact_370_less__imp__add__positive) ).

fof(fact_371_even__less__0__iff,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) ) ),
    file('theBenchmark.p',fact_371_even__less__0__iff) ).

fof(fact_372_finite__fun__UNIVD1,axiom,
    ! [X_a,X_b] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,finite_finite_1(fun(X_a,X_b)),top_top(fun(fun(X_a,X_b),bool))))
     => ( hAPP(fun(X_b,bool),nat,finite_card(X_b),top_top(fun(X_b,bool))) != hAPP(nat,nat,suc,zero_zero(nat))
       => hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ) ),
    file('theBenchmark.p',fact_372_finite__fun__UNIVD1) ).

fof(fact_373_lessI,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N))),
    file('theBenchmark.p',fact_373_lessI) ).

fof(fact_374_Suc__mono,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_374_Suc__mono) ).

fof(fact_375_zero__less__Suc,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))),
    file('theBenchmark.p',fact_375_zero__less__Suc) ).

fof(fact_376_Suc__inject,axiom,
    ! [X,Y] :
      ( hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y)
     => X = Y ),
    file('theBenchmark.p',fact_376_Suc__inject) ).

fof(fact_377_nat_Oinject,axiom,
    ! [Nat_1,Nat_5] :
      ( hAPP(nat,nat,suc,Nat_1) = hAPP(nat,nat,suc,Nat_5)
    <=> Nat_1 = Nat_5 ),
    file('theBenchmark.p',fact_377_nat_Oinject) ).

fof(fact_378_Suc__n__not__n,axiom,
    ! [N] : hAPP(nat,nat,suc,N) != N,
    file('theBenchmark.p',fact_378_Suc__n__not__n) ).

fof(fact_379_n__not__Suc__n,axiom,
    ! [N] : N != hAPP(nat,nat,suc,N),
    file('theBenchmark.p',fact_379_n__not__Suc__n) ).

fof(fact_380_Suc__neq__Zero,axiom,
    ! [M_3] : hAPP(nat,nat,suc,M_3) != zero_zero(nat),
    file('theBenchmark.p',fact_380_Suc__neq__Zero) ).

fof(fact_381_Zero__neq__Suc,axiom,
    ! [M_3] : zero_zero(nat) != hAPP(nat,nat,suc,M_3),
    file('theBenchmark.p',fact_381_Zero__neq__Suc) ).

fof(fact_382_nat_Osimps_I3_J,axiom,
    ! [Nat_4] : hAPP(nat,nat,suc,Nat_4) != zero_zero(nat),
    file('theBenchmark.p',fact_382_nat_Osimps_I3_J) ).

fof(fact_383_Suc__not__Zero,axiom,
    ! [M_3] : hAPP(nat,nat,suc,M_3) != zero_zero(nat),
    file('theBenchmark.p',fact_383_Suc__not__Zero) ).

fof(fact_384_nat_Osimps_I2_J,axiom,
    ! [Nat_3] : zero_zero(nat) != hAPP(nat,nat,suc,Nat_3),
    file('theBenchmark.p',fact_384_nat_Osimps_I2_J) ).

fof(fact_385_Zero__not__Suc,axiom,
    ! [M_3] : zero_zero(nat) != hAPP(nat,nat,suc,M_3),
    file('theBenchmark.p',fact_385_Zero__not__Suc) ).

fof(fact_386_Suc__less__SucD,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),hAPP(nat,nat,suc,N)))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ),
    file('theBenchmark.p',fact_386_Suc__less__SucD) ).

fof(fact_387_Suc__lessD,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ),
    file('theBenchmark.p',fact_387_Suc__lessD) ).

fof(fact_388_less__SucE,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
       => M_3 = N ) ),
    file('theBenchmark.p',fact_388_less__SucE) ).

fof(fact_389_less__trans__Suc,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_2))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_2)) ) ),
    file('theBenchmark.p',fact_389_less__trans__Suc) ).

fof(fact_390_Suc__lessI,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
     => ( hAPP(nat,nat,suc,M_3) != N
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),N)) ) ),
    file('theBenchmark.p',fact_390_Suc__lessI) ).

fof(fact_391_less__SucI,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_391_less__SucI) ).

fof(fact_392_less__antisym,axiom,
    ! [N,M_3] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_3))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M_3)))
       => M_3 = N ) ),
    file('theBenchmark.p',fact_392_less__antisym) ).

fof(fact_393_not__less__less__Suc__eq,axiom,
    ! [Na,M] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))
      <=> Na = M ) ),
    file('theBenchmark.p',fact_393_not__less__less__Suc__eq) ).

fof(fact_394_Suc__less__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ),
    file('theBenchmark.p',fact_394_Suc__less__eq) ).

fof(fact_395_less__Suc__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
    <=> ( M = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_395_less__Suc__eq) ).

fof(fact_396_not__less__eq,axiom,
    ! [M,Na] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))) ),
    file('theBenchmark.p',fact_396_not__less__eq) ).

fof(fact_397_add__Suc__shift,axiom,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,suc,N)),
    file('theBenchmark.p',fact_397_add__Suc__shift) ).

fof(fact_398_add__Suc,axiom,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N)),
    file('theBenchmark.p',fact_398_add__Suc) ).

fof(fact_399_add__Suc__right,axiom,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N)),
    file('theBenchmark.p',fact_399_add__Suc__right) ).

fof(fact_400_Suc__leD,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    file('theBenchmark.p',fact_400_Suc__leD) ).

fof(fact_401_le__SucE,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,N)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
       => M_3 = hAPP(nat,nat,suc,N) ) ),
    file('theBenchmark.p',fact_401_le__SucE) ).

fof(fact_402_le__SucI,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_402_le__SucI) ).

fof(fact_403_Suc__le__mono,axiom,
    ! [Na,M] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M)) ),
    file('theBenchmark.p',fact_403_Suc__le__mono) ).

fof(fact_404_le__Suc__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,Na)))
    <=> ( M = hAPP(nat,nat,suc,Na)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_404_le__Suc__eq) ).

fof(fact_405_not__less__eq__eq,axiom,
    ! [M,Na] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M)) ),
    file('theBenchmark.p',fact_405_not__less__eq__eq) ).

fof(fact_406_Suc__n__not__le__n,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N)),
    file('theBenchmark.p',fact_406_Suc__n__not__le__n) ).

fof(fact_407_inj__Suc,axiom,
    ! [N_1] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),N_1)),
    file('theBenchmark.p',fact_407_inj__Suc) ).

fof(fact_408_gr0__conv__Suc,axiom,
    ! [Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
    <=> ? [M_1] : Na = hAPP(nat,nat,suc,M_1) ),
    file('theBenchmark.p',fact_408_gr0__conv__Suc) ).

fof(fact_409_less__Suc0,axiom,
    ! [Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))
    <=> Na = zero_zero(nat) ),
    file('theBenchmark.p',fact_409_less__Suc0) ).

fof(fact_410_less__Suc__eq__0__disj,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
    <=> ( ? [J_2] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),Na))
            & M = hAPP(nat,nat,suc,J_2) )
        | M = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_410_less__Suc__eq__0__disj) ).

fof(fact_411_add__is__1,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) = hAPP(nat,nat,suc,zero_zero(nat))
    <=> ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('theBenchmark.p',fact_411_add__is__1) ).

fof(fact_412_one__is__add,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)
    <=> ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('theBenchmark.p',fact_412_one__is__add) ).

fof(fact_413_less__add__Suc1,axiom,
    ! [I_2,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),M_3)))),
    file('theBenchmark.p',fact_413_less__add__Suc1) ).

fof(fact_414_less__add__Suc2,axiom,
    ! [I_2,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),I_2)))),
    file('theBenchmark.p',fact_414_less__add__Suc2) ).

fof(fact_415_less__iff__Suc__add,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
    <=> ? [K_1] : Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1)) ),
    file('theBenchmark.p',fact_415_less__iff__Suc__add) ).

fof(fact_416_less__eq__Suc__le,axiom,
    ! [Na,M] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M)) ),
    file('theBenchmark.p',fact_416_less__eq__Suc__le) ).

fof(fact_417_less__Suc__eq__le,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ),
    file('theBenchmark.p',fact_417_less__Suc__eq__le) ).

fof(fact_418_Suc__le__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ),
    file('theBenchmark.p',fact_418_Suc__le__eq) ).

fof(fact_419_le__imp__less__Suc,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_419_le__imp__less__Suc) ).

fof(fact_420_Suc__leI,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N)) ),
    file('theBenchmark.p',fact_420_Suc__leI) ).

fof(fact_421_le__less__Suc__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))
      <=> Na = M ) ),
    file('theBenchmark.p',fact_421_le__less__Suc__eq) ).

fof(fact_422_Suc__le__lessD,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ),
    file('theBenchmark.p',fact_422_Suc__le__lessD) ).

fof(fact_423_One__nat__def,axiom,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    file('theBenchmark.p',fact_423_One__nat__def) ).

fof(fact_424_less__eq__Suc__le__raw,axiom,
    ! [X_1] : hAPP(nat,fun(nat,bool),ord_less(nat),X_1) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_1)),
    file('theBenchmark.p',fact_424_less__eq__Suc__le__raw) ).

fof(fact_425_card__Collect__le__nat,axiom,
    ! [Na] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),Na))) = hAPP(nat,nat,suc,Na),
    file('theBenchmark.p',fact_425_card__Collect__le__nat) ).

fof(fact_426_card__less__Suc,axiom,
    ! [I,M_2] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_2))
     => hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))) ),
    file('theBenchmark.p',fact_426_card__less__Suc) ).

fof(fact_427_card__less,axiom,
    ! [I,M_2] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_2))
     => hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))) != zero_zero(nat) ),
    file('theBenchmark.p',fact_427_card__less) ).

fof(fact_428_card__less__Suc2,axiom,
    ! [I,M_2] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_2))
     => hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))) ),
    file('theBenchmark.p',fact_428_card__less__Suc2) ).

fof(fact_429_double__eq__0__iff,axiom,
    ! [X_a] :
      ( linord219039673up_add(X_a)
     => ! [Aa] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a)
        <=> ti(X_a,Aa) = zero_zero(X_a) ) ),
    file('theBenchmark.p',fact_429_double__eq__0__iff) ).

fof(fact_430_inc__induct,axiom,
    ! [Pa,I,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J))
     => ( hBOOL(hAPP(nat,bool,Pa,J))
       => ( ! [I_1] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_430_inc__induct) ).

fof(fact_431_less__imp__Suc__add,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
     => ? [K_1] : N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_1)) ),
    file('theBenchmark.p',fact_431_less__imp__Suc__add) ).

fof(fact_432_gr0__implies__Suc,axiom,
    ! [N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))
     => ? [M_1] : N = hAPP(nat,nat,suc,M_1) ),
    file('theBenchmark.p',fact_432_gr0__implies__Suc) ).

fof(fact_433_lift__Suc__mono__le,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Na,N_3,F] :
          ( ! [N_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_3))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,N_3))) ) ) ),
    file('theBenchmark.p',fact_433_lift__Suc__mono__le) ).

fof(fact_434_lift__Suc__mono__less__iff,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Na,M,F] :
          ( ! [N_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,M)))
          <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) ) ) ),
    file('theBenchmark.p',fact_434_lift__Suc__mono__less__iff) ).

fof(fact_435_lift__Suc__mono__less,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Na,N_3,F] :
          ( ! [N_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_3))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,N_3))) ) ) ),
    file('theBenchmark.p',fact_435_lift__Suc__mono__less) ).

fof(fact_436_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_436_Suc__eq__plus1) ).

fof(fact_437_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_437_Suc__eq__plus1__left) ).

fof(fact_438_Suc__le__D,axiom,
    ! [N,M_4] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M_4))
     => ? [M_1] : M_4 = hAPP(nat,nat,suc,M_1) ),
    file('theBenchmark.p',fact_438_Suc__le__D) ).

fof(fact_439_lessE,axiom,
    ! [I_2,K_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_2))
     => ( K_2 != hAPP(nat,nat,suc,I_2)
       => ~ ! [J_2] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))
             => K_2 != hAPP(nat,nat,suc,J_2) ) ) ),
    file('theBenchmark.p',fact_439_lessE) ).

fof(fact_440_Suc__lessE,axiom,
    ! [I_2,K_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_2))
     => ~ ! [J_2] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))
           => K_2 != hAPP(nat,nat,suc,J_2) ) ),
    file('theBenchmark.p',fact_440_Suc__lessE) ).

fof(fact_441_not0__implies__Suc,axiom,
    ! [N] :
      ( N != zero_zero(nat)
     => ? [M_1] : N = hAPP(nat,nat,suc,M_1) ),
    file('theBenchmark.p',fact_441_not0__implies__Suc) ).

fof(fact_442_nat_Oexhaust,axiom,
    ! [Y] :
      ( Y != zero_zero(nat)
     => ~ ! [Nat_2] : Y != hAPP(nat,nat,suc,Nat_2) ),
    file('theBenchmark.p',fact_442_nat_Oexhaust) ).

fof(fact_443_zero__induct,axiom,
    ! [Pa,K] :
      ( hBOOL(hAPP(nat,bool,Pa,K))
     => ( ! [N_2] :
            ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_2)))
           => hBOOL(hAPP(nat,bool,Pa,N_2)) )
       => hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ) ),
    file('theBenchmark.p',fact_443_zero__induct) ).

fof(fact_444_nat__induct,axiom,
    ! [Na,Pa] :
      ( hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
     => ( ! [N_2] :
            ( hBOOL(hAPP(nat,bool,Pa,N_2))
           => hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_2))) )
       => hBOOL(hAPP(nat,bool,Pa,Na)) ) ),
    file('theBenchmark.p',fact_444_nat__induct) ).

fof(fact_445_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_445_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_446_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2) ),
    file('theBenchmark.p',fact_446_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_447_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2,C_1,D] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),D)) ),
    file('theBenchmark.p',fact_447_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_448_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2,C_1,D] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),D) ),
    file('theBenchmark.p',fact_448_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_449_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1)) ),
    file('theBenchmark.p',fact_449_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_450_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),B_1) ),
    file('theBenchmark.p',fact_450_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_451_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2,B_1,C_1,D] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)) ),
    file('theBenchmark.p',fact_451_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_452_add__0__iff,axiom,
    ! [X_a] :
      ( semiri456707255roduct(X_a)
     => ! [Ba,Aa] :
          ( ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)
        <=> ti(X_a,Aa) = zero_zero(X_a) ) ),
    file('theBenchmark.p',fact_452_add__0__iff) ).

fof(fact_453_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_453_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_454_field__le__epsilon,axiom,
    ! [X_a] :
      ( linordered_field(X_a)
     => ! [X,Y] :
          ( ! [E_1] :
              ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E_1))
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E_1))) )
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_454_field__le__epsilon) ).

fof(fact_455_card__def,axiom,
    ! [X_a,A_1] :
      ( ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
       => hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = zero_zero(nat) )
      & ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
       => hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_a,bool),nat,hAPP(nat,fun(fun(X_a,bool),nat),hAPP(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat))),finite_fold_image(nat,X_a),plus_plus(nat)),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),zero_zero(nat)),A_1) ) ),
    file('theBenchmark.p',fact_455_card__def) ).

fof(fact_456_card_Oeq__fold__g,axiom,
    ! [X_a,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_a,bool),nat,hAPP(nat,fun(fun(X_a,bool),nat),hAPP(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat))),finite_fold_image(nat,X_a),plus_plus(nat)),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),zero_zero(nat)),A_1) ),
    file('theBenchmark.p',fact_456_card_Oeq__fold__g) ).

fof(fact_457_surjh,axiom,
    hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    file('theBenchmark.p',fact_457_surjh) ).

fof(fact_458_image__eqI,axiom,
    ! [X_a,X_b,A_1,Ba,F,X_2] :
      ( ti(X_a,Ba) = hAPP(X_b,X_a,F,X_2)
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ) ),
    file('theBenchmark.p',fact_458_image__eqI) ).

fof(fact_459_finite__imageI,axiom,
    ! [X_b,X_a,Ha,Fa] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa))
     => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),Ha),Fa))) ),
    file('theBenchmark.p',fact_459_finite__imageI) ).

fof(fact_460_finite__atLeastLessThan,axiom,
    ! [L,U] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),U))),
    file('theBenchmark.p',fact_460_finite__atLeastLessThan) ).

fof(fact_461__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123,axiom,
    ~ ! [H] :
        ( hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),H),top_top(fun(arrow_1998540521e_indi,bool))))
       => hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),H),top_top(fun(arrow_1998540521e_indi,bool))) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))) ),
    file('theBenchmark.p',fact_461__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123) ).

fof(fact_462_image__mono,axiom,
    ! [X_b,X_a,F,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B))) ),
    file('theBenchmark.p',fact_462_image__mono) ).

fof(fact_463_subset__image__iff,axiom,
    ! [X_a,X_b,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
    <=> ? [AA] :
          ( ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA)
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_1)) ) ),
    file('theBenchmark.p',fact_463_subset__image__iff) ).

fof(fact_464_rangeI,axiom,
    ! [X_a,X_b,F,X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))))),
    file('theBenchmark.p',fact_464_rangeI) ).

fof(fact_465_range__eqI,axiom,
    ! [X_a,X_b,Ba,F,X_2] :
      ( ti(X_a,Ba) = hAPP(X_b,X_a,F,X_2)
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))))) ),
    file('theBenchmark.p',fact_465_range__eqI) ).

fof(fact_466_image__ident,axiom,
    ! [X_a,Y_3] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_3) = ti(fun(X_a,bool),Y_3),
    file('theBenchmark.p',fact_466_image__ident) ).

fof(fact_467_image__image,axiom,
    ! [X_b,X_a,X_c,F,G,A_1] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),G),A_1)) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G)),A_1),
    file('theBenchmark.p',fact_467_image__image) ).

fof(fact_468_image__iff,axiom,
    ! [X_a,X_b,Z_1,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
    <=> ? [X_1] :
          ( ti(X_a,Z_1) = hAPP(X_b,X_a,F,X_1)
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) ) ),
    file('theBenchmark.p',fact_468_image__iff) ).

fof(fact_469_imageI,axiom,
    ! [X_b,X_a,F,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) ),
    file('theBenchmark.p',fact_469_imageI) ).

fof(fact_470_rev__image__eqI,axiom,
    ! [X_b,X_a,Ba,F,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
     => ( ti(X_b,Ba) = hAPP(X_a,X_b,F,X_2)
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) ) ),
    file('theBenchmark.p',fact_470_rev__image__eqI) ).

fof(fact_471_atLeastLessThan__inj_I2_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Da))
             => ti(X_a,Ba) = ti(X_a,Da) ) ) ) ),
    file('theBenchmark.p',fact_471_atLeastLessThan__inj_I2_J) ).

fof(fact_472_atLeastLessThan__inj_I1_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Da))
             => ti(X_a,Aa) = ti(X_a,Ca) ) ) ) ),
    file('theBenchmark.p',fact_472_atLeastLessThan__inj_I1_J) ).

fof(fact_473_atLeastLessThan__eq__iff,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [Ca,Da,Aa,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Da))
           => ( hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)
            <=> ( ti(X_a,Ba) = ti(X_a,Da)
                & ti(X_a,Aa) = ti(X_a,Ca) ) ) ) ) ),
    file('theBenchmark.p',fact_473_atLeastLessThan__eq__iff) ).

fof(fact_474_f__inv__into__f,axiom,
    ! [X_a,X_b,Y_1,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
     => hAPP(X_b,X_a,F,hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F),Y_1)) = ti(X_a,Y_1) ),
    file('theBenchmark.p',fact_474_f__inv__into__f) ).

fof(fact_475_inv__into__into,axiom,
    ! [X_a,X_b,X_2,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F),X_2)),A_1)) ),
    file('theBenchmark.p',fact_475_inv__into__into) ).

fof(fact_476_inv__into__injective,axiom,
    ! [X_b,X_a,A_1,F,X_2,Y_1] :
      ( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),X_2) = hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),Y_1)
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
         => ti(X_b,X_2) = ti(X_b,Y_1) ) ) ),
    file('theBenchmark.p',fact_476_inv__into__injective) ).

fof(fact_477_range__composition,axiom,
    ! [X_b,X_a,X_c,F,G] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,X_c),fun(X_b,X_a),hAPP(fun(X_c,X_a),fun(fun(X_b,X_c),fun(X_b,X_a)),combb(X_c,X_a,X_b),F),G)),top_top(fun(X_b,bool))) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),F),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),top_top(fun(X_b,bool)))),
    file('theBenchmark.p',fact_477_range__composition) ).

fof(fact_478_finite__surj,axiom,
    ! [X_b,X_a,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
       => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B)) ) ),
    file('theBenchmark.p',fact_478_finite__surj) ).

fof(fact_479_finite__imageD,axiom,
    ! [X_a,X_b,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),F),A_1))
       => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) ) ),
    file('theBenchmark.p',fact_479_finite__imageD) ).

fof(fact_480_range__ex1__eq,axiom,
    ! [X_a,X_b,Ba,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),top_top(fun(X_a,bool)))))
      <=> ? [X_1] :
            ( ! [Y_2] :
                ( ti(X_b,Ba) = hAPP(X_a,X_b,F,Y_2)
               => ti(X_a,Y_2) = ti(X_a,X_1) )
            & ti(X_b,Ba) = hAPP(X_a,X_b,F,X_1) ) ) ),
    file('theBenchmark.p',fact_480_range__ex1__eq) ).

fof(fact_481_inj__image__mem__iff,axiom,
    ! [X_a,X_b,Aa,A_1,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,Aa)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      <=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),A_1)) ) ),
    file('theBenchmark.p',fact_481_inj__image__mem__iff) ).

fof(fact_482_inj__image__eq__iff,axiom,
    ! [X_a,X_b,A_1,B,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => ( hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)
      <=> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) ) ),
    file('theBenchmark.p',fact_482_inj__image__eq__iff) ).

fof(fact_483_card__image,axiom,
    ! [X_a,X_b,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) ),
    file('theBenchmark.p',fact_483_card__image) ).

fof(fact_484_image__inv__into__cancel,axiom,
    ! [X_b,X_a,B_2,F,A_1,A_3] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) = ti(fun(X_a,bool),A_3)
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3))
       => hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F)),B_2)) = ti(fun(X_a,bool),B_2) ) ),
    file('theBenchmark.p',fact_484_image__inv__into__cancel) ).

fof(fact_485_image__surj__f__inv__f,axiom,
    ! [X_b,X_a,A_1,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
     => hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F)),A_1)) = ti(fun(X_a,bool),A_1) ),
    file('theBenchmark.p',fact_485_image__surj__f__inv__f) ).

fof(fact_486_surj__f__inv__f,axiom,
    ! [X_b,X_a,Y_1,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
     => hAPP(X_b,X_a,F,hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F),Y_1)) = ti(X_a,Y_1) ),
    file('theBenchmark.p',fact_486_surj__f__inv__f) ).

fof(fact_487_surj__iff__all,axiom,
    ! [X_b,X_a,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
    <=> ! [X_1] : hAPP(X_b,X_a,F,hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F),X_1)) = ti(X_a,X_1) ),
    file('theBenchmark.p',fact_487_surj__iff__all) ).

fof(fact_488_inj__on__strict__subset,axiom,
    ! [X_a,X_b,A_1,F,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B))) ) ),
    file('theBenchmark.p',fact_488_inj__on__strict__subset) ).

fof(fact_489_subset__card__intvl__is__intvl,axiom,
    ! [A_1,K] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_1)))))
     => A_1 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_1))) ),
    file('theBenchmark.p',fact_489_subset__card__intvl__is__intvl) ).

fof(fact_490_finite__range__imageI,axiom,
    ! [X_c,X_a,X_b,F,G] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),top_top(fun(X_b,bool)))))
     => hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),combb(X_a,X_c,X_b),F),G)),top_top(fun(X_b,bool))))) ),
    file('theBenchmark.p',fact_490_finite__range__imageI) ).

fof(fact_491_atLeastLessThan__subset__iff,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)))
         => ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_491_atLeastLessThan__subset__iff) ).

fof(fact_492_funcset__image,axiom,
    ! [X_a,X_b,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B)) ),
    file('theBenchmark.p',fact_492_funcset__image) ).

fof(fact_493_finite__surj__inj,axiom,
    ! [X_a,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1)))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1)) ) ),
    file('theBenchmark.p',fact_493_finite__surj__inj) ).

fof(fact_494_endo__inj__surj,axiom,
    ! [X_a,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1)),A_1))
       => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1))
         => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1) = ti(fun(X_a,bool),A_1) ) ) ),
    file('theBenchmark.p',fact_494_endo__inj__surj) ).

fof(fact_495_finite__UNIV__inj__surj,axiom,
    ! [X_a,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),top_top(fun(X_a,bool))))
       => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),top_top(fun(X_a,bool))) = top_top(fun(X_a,bool)) ) ),
    file('theBenchmark.p',fact_495_finite__UNIV__inj__surj) ).

fof(fact_496_finite__UNIV__surj__inj,axiom,
    ! [X_a,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
     => ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),top_top(fun(X_a,bool))) = top_top(fun(X_a,bool))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),top_top(fun(X_a,bool)))) ) ),
    file('theBenchmark.p',fact_496_finite__UNIV__surj__inj) ).

fof(fact_497_inj__image__subset__iff,axiom,
    ! [X_a,X_b,A_1,B,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)))
      <=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ),
    file('theBenchmark.p',fact_497_inj__image__subset__iff) ).

fof(fact_498_card__image__le,axiom,
    ! [X_b,X_a,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1))) ),
    file('theBenchmark.p',fact_498_card__image__le) ).

fof(fact_499_eq__card__imp__inj__on,axiom,
    ! [X_b,X_a,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ) ),
    file('theBenchmark.p',fact_499_eq__card__imp__inj__on) ).

fof(fact_500_inj__on__iff__eq__card,axiom,
    ! [X_b,X_a,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
      <=> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) ) ),
    file('theBenchmark.p',fact_500_inj__on__iff__eq__card) ).

fof(fact_501_pigeonhole,axiom,
    ! [X_a,X_b,F,A_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)))
     => ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),F),A_1)) ),
    file('theBenchmark.p',fact_501_pigeonhole) ).

fof(fact_502_inv__into__image__cancel,axiom,
    ! [X_a,X_b,S,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),A_1))
       => hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),S)) = ti(fun(X_a,bool),S) ) ),
    file('theBenchmark.p',fact_502_inv__into__image__cancel) ).

fof(fact_503_inj__on__inv__into,axiom,
    ! [X_a,X_b,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F)),B)) ),
    file('theBenchmark.p',fact_503_inj__on__inv__into) ).

fof(fact_504_surj__imp__inj__inv,axiom,
    ! [X_b,X_a,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F)),top_top(fun(X_a,bool)))) ),
    file('theBenchmark.p',fact_504_surj__imp__inj__inv) ).

fof(fact_505_inv__image__comp,axiom,
    ! [X_a,X_b,X_4,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),X_4)) = ti(fun(X_a,bool),X_4) ),
    file('theBenchmark.p',fact_505_inv__image__comp) ).

fof(fact_506_image__inv__f__f,axiom,
    ! [X_a,X_b,A_1,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = ti(fun(X_a,bool),A_1) ),
    file('theBenchmark.p',fact_506_image__inv__f__f) ).

fof(fact_507_inj__imp__surj__inv,axiom,
    ! [X_a,X_b,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F)),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool)) ),
    file('theBenchmark.p',fact_507_inj__imp__surj__inv) ).

fof(fact_508_card__bij__eq,axiom,
    ! [X_a,X_b,G,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),G),B))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),B)),A_1))
           => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
             => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
               => hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_b,bool),nat,finite_card(X_b),B) ) ) ) ) ) ),
    file('theBenchmark.p',fact_508_card__bij__eq) ).

fof(fact_509_card__inj__on__le,axiom,
    ! [X_a,X_b,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B))) ) ) ),
    file('theBenchmark.p',fact_509_card__inj__on__le) ).

fof(fact_510_inj__on__iff__card__le,axiom,
    ! [X_b,X_a,B,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
       => ( ? [F_2] :
              ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F_2),A_1)),B))
              & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F_2),A_1)) )
        <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B))) ) ) ),
    file('theBenchmark.p',fact_510_inj__on__iff__card__le) ).

fof(fact_511_inj__transfer,axiom,
    ! [X_a,X_b,X_2,Pa,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => ( ! [Y_2] :
            ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),top_top(fun(X_a,bool)))))
           => hBOOL(hAPP(X_a,bool,Pa,hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),Y_2))) )
       => hBOOL(hAPP(X_a,bool,Pa,X_2)) ) ),
    file('theBenchmark.p',fact_511_inj__transfer) ).

fof(fact_512_imageE,axiom,
    ! [X_a,X_b,Ba,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
     => ~ ! [X_1] :
            ( ti(X_a,Ba) = hAPP(X_b,X_a,F,X_1)
           => ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) ) ),
    file('theBenchmark.p',fact_512_imageE) ).

fof(fact_513_surj__imp__inv__eq,axiom,
    ! [X_b,X_a,G,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
     => ( ! [X_1] : hAPP(X_a,X_b,G,hAPP(X_b,X_a,F,X_1)) = ti(X_b,X_1)
       => hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F) = ti(fun(X_a,X_b),G) ) ),
    file('theBenchmark.p',fact_513_surj__imp__inv__eq) ).

fof(fact_514_finite__subset__image,axiom,
    ! [X_b,X_a,F,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
       => ? [C_2] :
            ( ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C_2)
            & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),C_2))
            & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_2),A_1)) ) ) ),
    file('theBenchmark.p',fact_514_finite__subset__image) ).

fof(fact_515_image__Suc__atLeastLessThan,axiom,
    ! [I,J] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J)),
    file('theBenchmark.p',fact_515_image__Suc__atLeastLessThan) ).

fof(fact_516_nat__seg__image__imp__finite,axiom,
    ! [X_a,A_1,F,Na] :
      ( ti(fun(X_a,bool),A_1) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na)))
     => hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    file('theBenchmark.p',fact_516_nat__seg__image__imp__finite) ).

fof(fact_517_image__add__atLeastLessThan,axiom,
    ! [K,I,J] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(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_517_image__add__atLeastLessThan) ).

fof(fact_518_all__nat__less__eq,axiom,
    ! [Pa,Na] :
      ( ! [M_1] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
         => hBOOL(hAPP(nat,bool,Pa,M_1)) )
    <=> ! [X_1] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na)))
         => hBOOL(hAPP(nat,bool,Pa,X_1)) ) ),
    file('theBenchmark.p',fact_518_all__nat__less__eq) ).

fof(fact_519_ex__nat__less__eq,axiom,
    ! [Pa,Na] :
      ( ? [M_1] :
          ( hBOOL(hAPP(nat,bool,Pa,M_1))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) )
    <=> ? [X_1] :
          ( hBOOL(hAPP(nat,bool,Pa,X_1))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))) ) ),
    file('theBenchmark.p',fact_519_ex__nat__less__eq) ).

fof(fact_520_rangeE,axiom,
    ! [X_a,X_b,Ba,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool)))))
     => ~ ! [X_1] : ti(X_a,Ba) != hAPP(X_b,X_a,F,X_1) ),
    file('theBenchmark.p',fact_520_rangeE) ).

fof(fact_521_pigeonhole__infinite,axiom,
    ! [X_b,X_a,F,A_1] :
      ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,bool))),combb(X_b,fun(X_b,bool),X_a),fequal(X_b)),F)),hAPP(X_a,X_b,F,X_1))))))
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_521_pigeonhole__infinite) ).

fof(fact_522_finite__conv__nat__seg__image,axiom,
    ! [X_a,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
    <=> ? [N_2,F_2] : ti(fun(X_a,bool),A_1) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2))) ),
    file('theBenchmark.p',fact_522_finite__conv__nat__seg__image) ).

fof(fact_523_finite__imp__nat__seg__image__inj__on,axiom,
    ! [X_a,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ? [N_2,F_2] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X_a),fun(fun(nat,bool),bool),inj_on(nat,X_a),F_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2))))
          & ti(fun(X_a,bool),A_1) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2))) ) ),
    file('theBenchmark.p',fact_523_finite__imp__nat__seg__image__inj__on) ).

fof(fact_524_finite__imp__inj__to__nat__seg,axiom,
    ! [X_a,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ? [F_2,N_2] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,nat),fun(fun(X_a,bool),bool),inj_on(X_a,nat),F_2),A_1))
          & hAPP(fun(X_a,bool),fun(nat,bool),hAPP(fun(X_a,nat),fun(fun(X_a,bool),fun(nat,bool)),image(X_a,nat),F_2),A_1) = hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2)) ) ),
    file('theBenchmark.p',fact_524_finite__imp__inj__to__nat__seg) ).

fof(fact_525_inj__on__image__iff,axiom,
    ! [X_b,X_a,G,F,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => ! [Xa] :
              ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1))
             => ( hAPP(X_a,X_b,G,hAPP(X_a,X_a,F,X_1)) = hAPP(X_a,X_b,G,hAPP(X_a,X_a,F,Xa))
              <=> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,G,Xa) ) ) )
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1))
       => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1)))
        <=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),A_1)) ) ) ),
    file('theBenchmark.p',fact_525_inj__on__image__iff) ).

fof(fact_526_surjE,axiom,
    ! [X_b,X_a,Y_1,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
     => ~ ! [X_1] : ti(X_a,Y_1) != hAPP(X_b,X_a,F,X_1) ),
    file('theBenchmark.p',fact_526_surjE) ).

fof(fact_527_surjD,axiom,
    ! [X_b,X_a,Y_1,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
     => ? [X_1] : ti(X_a,Y_1) = hAPP(X_b,X_a,F,X_1) ),
    file('theBenchmark.p',fact_527_surjD) ).

fof(fact_528_surjI,axiom,
    ! [X_b,X_a,G,F] :
      ( ! [X_1] : hAPP(X_b,X_a,G,hAPP(X_a,X_b,F,X_1)) = ti(X_a,X_1)
     => hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool)) ),
    file('theBenchmark.p',fact_528_surjI) ).

fof(fact_529_surj__def,axiom,
    ! [X_b,X_a,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
    <=> ! [Y_2] :
        ? [X_1] : ti(X_a,Y_2) = hAPP(X_b,X_a,F,X_1) ),
    file('theBenchmark.p',fact_529_surj__def) ).

fof(fact_530_image__subsetI,axiom,
    ! [X_b,X_a,F,B,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B)) )
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B)) ),
    file('theBenchmark.p',fact_530_image__subsetI) ).

fof(fact_531_greaterThan__0,axiom,
    hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))),
    file('theBenchmark.p',fact_531_greaterThan__0) ).

fof(fact_532_Ints__odd__less__0,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [Aa] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a)))
          <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_532_Ints__odd__less__0) ).

fof(fact_533_less__eq__nat_Osimps_I2_J,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),M)),Na)) ),
    file('theBenchmark.p',fact_533_less__eq__nat_Osimps_I2_J) ).

fof(fact_534_greaterThan__eq__iff,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X_2,Y_1] :
          ( hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),X_2) = hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),Y_1)
        <=> ti(X_a,X_2) = ti(X_a,Y_1) ) ),
    file('theBenchmark.p',fact_534_greaterThan__eq__iff) ).

fof(fact_535_Ints__0,axiom,
    ! [X_a] :
      ( ring_1(X_a)
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),ring_1_Ints(X_a))) ),
    file('theBenchmark.p',fact_535_Ints__0) ).

fof(fact_536_Ints__add,axiom,
    ! [X_a] :
      ( ring_1(X_a)
     => ! [Ba,Aa] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))
           => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)),ring_1_Ints(X_a))) ) ) ),
    file('theBenchmark.p',fact_536_Ints__add) ).

fof(fact_537_Ints__1,axiom,
    ! [X_a] :
      ( ring_1(X_a)
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),ring_1_Ints(X_a))) ),
    file('theBenchmark.p',fact_537_Ints__1) ).

fof(fact_538_greaterThan__iff,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [I,K] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),K)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),K),I)) ) ),
    file('theBenchmark.p',fact_538_greaterThan__iff) ).

fof(fact_539_nat__case__0,axiom,
    ! [X_a,F1,F2] : hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),zero_zero(nat)) = ti(X_a,F1),
    file('theBenchmark.p',fact_539_nat__case__0) ).

fof(fact_540_nat__case__Suc,axiom,
    ! [X_a,F1,F2,Nat_1] : hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),hAPP(nat,nat,suc,Nat_1)) = hAPP(nat,X_a,F2,Nat_1),
    file('theBenchmark.p',fact_540_nat__case__Suc) ).

fof(fact_541_Ints__double__eq__0__iff,axiom,
    ! [X_a] :
      ( ring_char_0(X_a)
     => ! [Aa] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))
         => ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a)
          <=> ti(X_a,Aa) = zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_541_Ints__double__eq__0__iff) ).

fof(fact_542_greaterThan__subset__iff,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X_2,Y_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),X_2)),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),Y_1)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2)) ) ),
    file('theBenchmark.p',fact_542_greaterThan__subset__iff) ).

fof(fact_543_Ints__odd__nonzero,axiom,
    ! [X_a] :
      ( ring_char_0(X_a)
     => ! [Aa] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))
         => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa) != zero_zero(X_a) ) ),
    file('theBenchmark.p',fact_543_Ints__odd__nonzero) ).

fof(fact_544_greaterThanAtMost__subseteq__atLeastLessThan__iff,axiom,
    ! [X_a] :
      ( dense_linorder(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)))
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) ) ) ) ),
    file('theBenchmark.p',fact_544_greaterThanAtMost__subseteq__atLeastLessThan__iff) ).

fof(fact_545_greaterThanLessThan__subseteq__atLeastLessThan__iff,axiom,
    ! [X_a] :
      ( dense_linorder(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)))
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) ) ) ) ),
    file('theBenchmark.p',fact_545_greaterThanLessThan__subseteq__atLeastLessThan__iff) ).

fof(fact_546_inv__into__funcset,axiom,
    ! [X_b,X_a,F,A_1,B] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) = ti(fun(X_a,bool),B)
     => hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F)),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),B),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),A_1)))) ),
    file('theBenchmark.p',fact_546_inv__into__funcset) ).

fof(fact_547_the__inv__into__into,axiom,
    ! [X_a,X_b,B,X_2,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
       => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
         => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),X_2)),B)) ) ) ),
    file('theBenchmark.p',fact_547_the__inv__into__into) ).

fof(fact_548_finite__greaterThanAtMost,axiom,
    ! [L,U] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),L),U))),
    file('theBenchmark.p',fact_548_finite__greaterThanAtMost) ).

fof(fact_549_finite__greaterThanLessThan,axiom,
    ! [L,U] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U))),
    file('theBenchmark.p',fact_549_finite__greaterThanLessThan) ).

fof(fact_550_image__restrict__eq,axiom,
    ! [X_b,X_a,F,A_1] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,bool),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_b,X_a)),restrict(X_b,X_a),F),A_1)),A_1) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1),
    file('theBenchmark.p',fact_550_image__restrict__eq) ).

fof(fact_551_inj__on__restrict__eq,axiom,
    ! [X_a,X_b,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1)),A_1))
    <=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    file('theBenchmark.p',fact_551_inj__on__restrict__eq) ).

fof(fact_552_the__inv__into__f__eq,axiom,
    ! [X_a,X_b,X_2,Y_1,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hAPP(X_a,X_b,F,X_2) = ti(X_b,Y_1)
       => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
         => hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),Y_1) = ti(X_a,X_2) ) ) ),
    file('theBenchmark.p',fact_552_the__inv__into__f__eq) ).

fof(fact_553_the__inv__into__f__f,axiom,
    ! [X_a,X_b,X_2,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
       => hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2) ) ),
    file('theBenchmark.p',fact_553_the__inv__into__f__f) ).

fof(fact_554_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [L,U] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,L)),U) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U),
    file('theBenchmark.p',fact_554_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_555_the__inv__f__f,axiom,
    ! [X_a,X_b,X_2,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2) ),
    file('theBenchmark.p',fact_555_the__inv__f__f) ).

fof(fact_556_inj__on__the__inv__into,axiom,
    ! [X_a,X_b,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) ),
    file('theBenchmark.p',fact_556_inj__on__the__inv__into) ).

fof(fact_557_the__inv__into__onto,axiom,
    ! [X_a,X_b,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = ti(fun(X_a,bool),A_1) ),
    file('theBenchmark.p',fact_557_the__inv__into__onto) ).

fof(fact_558_f__the__inv__into__f,axiom,
    ! [X_a,X_b,Y_1,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
       => hAPP(X_a,X_b,F,hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),Y_1)) = ti(X_b,Y_1) ) ),
    file('theBenchmark.p',fact_558_f__the__inv__into__f) ).

fof(fact_559_restrictI,axiom,
    ! [X_b,X_a,F,B,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1))) )
     => hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ),
    file('theBenchmark.p',fact_559_restrictI) ).

fof(fact_560_restrict__in__funcset,axiom,
    ! [X_b,X_a,F,B,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B)) )
     => hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
    file('theBenchmark.p',fact_560_restrict__in__funcset) ).

fof(fact_561_restrict__ext,axiom,
    ! [X_b,X_a,F,G,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
         => hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1) )
     => hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1) = hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),G),A_1) ),
    file('theBenchmark.p',fact_561_restrict__ext) ).

fof(fact_562_compose__id__inv__into,axiom,
    ! [X_b,X_a,F,A_1,B] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) = ti(fun(X_a,bool),B)
     => hAPP(fun(X_a,X_b),fun(X_a,X_a),hAPP(fun(X_b,X_a),fun(fun(X_a,X_b),fun(X_a,X_a)),hAPP(fun(X_a,bool),fun(fun(X_b,X_a),fun(fun(X_a,X_b),fun(X_a,X_a))),compose(X_a,X_b,X_a),B),F),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F)),B)) = hAPP(fun(X_a,bool),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,X_a)),restrict(X_a,X_a),combi(X_a)),B) ),
    file('theBenchmark.p',fact_562_compose__id__inv__into) ).

fof(fact_563_compose__eq,axiom,
    ! [X_b,X_c,X_a,G,F,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
     => hAPP(X_a,X_b,hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b))),compose(X_a,X_c,X_b),A_1),G),F),X_2) = hAPP(X_c,X_b,G,hAPP(X_a,X_c,F,X_2)) ),
    file('theBenchmark.p',fact_563_compose__eq) ).

fof(fact_564_surj__compose,axiom,
    ! [X_c,X_b,X_a,G,C,F,A_1,B] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) = ti(fun(X_a,bool),B)
     => ( hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),G),B) = ti(fun(X_c,bool),C)
       => hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),hAPP(fun(X_b,bool),fun(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c))),compose(X_b,X_a,X_c),A_1),G),F)),A_1) = ti(fun(X_c,bool),C) ) ),
    file('theBenchmark.p',fact_564_surj__compose) ).

fof(fact_565_compose__assoc,axiom,
    ! [X_d,X_c,X_a,X_b,Ha,D_1,G,C,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
     => ( hBOOL(hAPP(fun(fun(X_b,X_c),bool),bool,hAPP(fun(X_b,X_c),fun(fun(fun(X_b,X_c),bool),bool),member(fun(X_b,X_c)),G),hAPP(fun(X_b,fun(X_c,bool)),fun(fun(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_b,fun(X_c,bool)),fun(fun(X_b,X_c),bool)),pi(X_b,X_c),B),hAPP(fun(X_c,bool),fun(X_b,fun(X_c,bool)),combk(fun(X_c,bool),X_b),C))))
       => ( hBOOL(hAPP(fun(fun(X_c,X_d),bool),bool,hAPP(fun(X_c,X_d),fun(fun(fun(X_c,X_d),bool),bool),member(fun(X_c,X_d)),Ha),hAPP(fun(X_c,fun(X_d,bool)),fun(fun(X_c,X_d),bool),hAPP(fun(X_c,bool),fun(fun(X_c,fun(X_d,bool)),fun(fun(X_c,X_d),bool)),pi(X_c,X_d),C),hAPP(fun(X_d,bool),fun(X_c,fun(X_d,bool)),combk(fun(X_d,bool),X_c),D_1))))
         => hAPP(fun(X_a,X_c),fun(X_a,X_d),hAPP(fun(X_c,X_d),fun(fun(X_a,X_c),fun(X_a,X_d)),hAPP(fun(X_a,bool),fun(fun(X_c,X_d),fun(fun(X_a,X_c),fun(X_a,X_d))),compose(X_a,X_c,X_d),A_1),Ha),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),hAPP(fun(X_a,bool),fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),compose(X_a,X_b,X_c),A_1),G),F)) = hAPP(fun(X_a,X_b),fun(X_a,X_d),hAPP(fun(X_b,X_d),fun(fun(X_a,X_b),fun(X_a,X_d)),hAPP(fun(X_a,bool),fun(fun(X_b,X_d),fun(fun(X_a,X_b),fun(X_a,X_d))),compose(X_a,X_b,X_d),A_1),hAPP(fun(X_b,X_c),fun(X_b,X_d),hAPP(fun(X_c,X_d),fun(fun(X_b,X_c),fun(X_b,X_d)),hAPP(fun(X_b,bool),fun(fun(X_c,X_d),fun(fun(X_b,X_c),fun(X_b,X_d))),compose(X_b,X_c,X_d),B),Ha),G)),F) ) ) ),
    file('theBenchmark.p',fact_565_compose__assoc) ).

fof(fact_566_funcset__compose,axiom,
    ! [X_c,X_a,X_b,G,C,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
     => ( hBOOL(hAPP(fun(fun(X_b,X_c),bool),bool,hAPP(fun(X_b,X_c),fun(fun(fun(X_b,X_c),bool),bool),member(fun(X_b,X_c)),G),hAPP(fun(X_b,fun(X_c,bool)),fun(fun(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_b,fun(X_c,bool)),fun(fun(X_b,X_c),bool)),pi(X_b,X_c),B),hAPP(fun(X_c,bool),fun(X_b,fun(X_c,bool)),combk(fun(X_c,bool),X_b),C))))
       => hBOOL(hAPP(fun(fun(X_a,X_c),bool),bool,hAPP(fun(X_a,X_c),fun(fun(fun(X_a,X_c),bool),bool),member(fun(X_a,X_c)),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),hAPP(fun(X_a,bool),fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),compose(X_a,X_b,X_c),A_1),G),F)),hAPP(fun(X_a,fun(X_c,bool)),fun(fun(X_a,X_c),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_c,bool)),fun(fun(X_a,X_c),bool)),pi(X_a,X_c),A_1),hAPP(fun(X_c,bool),fun(X_a,fun(X_c,bool)),combk(fun(X_c,bool),X_a),C)))) ) ),
    file('theBenchmark.p',fact_566_funcset__compose) ).

fof(fact_567_compose__def,axiom,
    ! [X_a,X_c,X_b,A_1,G,F] : hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b))),compose(X_a,X_c,X_b),A_1),G),F) = hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),combb(X_c,X_b,X_a),G),F)),A_1),
    file('theBenchmark.p',fact_567_compose__def) ).

fof(fact_568_compose__Id,axiom,
    ! [X_a,X_b,G,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
     => ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1)))
       => hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b))),compose(X_a,X_a,X_b),A_1),G),hAPP(fun(X_a,bool),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,X_a)),restrict(X_a,X_a),combi(X_a)),A_1)) = ti(fun(X_a,X_b),G) ) ),
    file('theBenchmark.p',fact_568_compose__Id) ).

fof(fact_569_Id__compose,axiom,
    ! [X_a,X_b,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
     => ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1)))
       => hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b))),compose(X_a,X_b,X_b),A_1),hAPP(fun(X_b,bool),fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,X_b)),restrict(X_b,X_b),combi(X_b)),B)),F) = ti(fun(X_a,X_b),F) ) ),
    file('theBenchmark.p',fact_569_Id__compose) ).

fof(fact_570_convex__bound__lt,axiom,
    ! [X_a] :
      ( linord626643107strict(X_a)
     => ! [V_2,U_1,Y,X,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_2))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V_2))
               => ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V_2) = one_one(X_a)
                 => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V_2),Y))),A_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_570_convex__bound__lt) ).

fof(fact_571_Ints__mult,axiom,
    ! [X_a] :
      ( ring_1(X_a)
     => ! [Ba,Aa] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))
           => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),ring_1_Ints(X_a))) ) ) ),
    file('theBenchmark.p',fact_571_Ints__mult) ).

fof(fact_572_le__square,axiom,
    ! [M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),M_3))),
    file('theBenchmark.p',fact_572_le__square) ).

fof(fact_573_le__cube,axiom,
    ! [M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),M_3)))),
    file('theBenchmark.p',fact_573_le__cube) ).

fof(fact_574_mult__le__mono1,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),K_2))) ),
    file('theBenchmark.p',fact_574_mult__le__mono1) ).

fof(fact_575_mult__le__mono2,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),J_1))) ),
    file('theBenchmark.p',fact_575_mult__le__mono2) ).

fof(fact_576_mult__le__mono,axiom,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),L_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),L_1))) ) ),
    file('theBenchmark.p',fact_576_mult__le__mono) ).

fof(fact_577_crossproduct__eq,axiom,
    ! [X_a] :
      ( semiri456707255roduct(X_a)
     => ! [W,Y_1,X_2,Z_1] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y_1))
        <=> ( ti(X_a,Y_1) = ti(X_a,Z_1)
            | ti(X_a,W) = ti(X_a,X_2) ) ) ),
    file('theBenchmark.p',fact_577_crossproduct__eq) ).

fof(fact_578_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2,M_3,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),M_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),M_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),M_3) ),
    file('theBenchmark.p',fact_578_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_579_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)) ),
    file('theBenchmark.p',fact_579_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_580_crossproduct__noteq,axiom,
    ! [X_a] :
      ( semiri456707255roduct(X_a)
     => ! [Ca,Da,Aa,Ba] :
          ( ( ti(X_a,Ca) != ti(X_a,Da)
            & ti(X_a,Aa) != ti(X_a,Ba) )
        <=> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),Da)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Da)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),Ca)) ) ),
    file('theBenchmark.p',fact_580_crossproduct__noteq) ).

fof(fact_581_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z)) ),
    file('theBenchmark.p',fact_581_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_582_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),one_one(X_a)) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_582_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_583_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_2) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_583_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_584_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),A_2) ),
    file('theBenchmark.p',fact_584_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_585_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry)) ),
    file('theBenchmark.p',fact_585_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(fact_586_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry) ),
    file('theBenchmark.p',fact_586_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

fof(fact_587_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Ly,Rx] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx)) ),
    file('theBenchmark.p',fact_587_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(fact_588_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Ly,Rx] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly) ),
    file('theBenchmark.p',fact_588_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(fact_589_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))) ),
    file('theBenchmark.p',fact_589_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry)) ),
    file('theBenchmark.p',fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_591_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry)) ),
    file('theBenchmark.p',fact_591_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

fof(fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_2) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),zero_zero(X_a)) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_594_divisors__zero,axiom,
    ! [X_a] :
      ( no_zero_divisors(X_a)
     => ! [A_2,B_1] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1) = zero_zero(X_a)
         => ( ti(X_a,B_1) = zero_zero(X_a)
            | ti(X_a,A_2) = zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_594_divisors__zero) ).

fof(fact_595_no__zero__divisors,axiom,
    ! [X_a] :
      ( no_zero_divisors(X_a)
     => ! [B_1,A_2] :
          ( ti(X_a,A_2) != zero_zero(X_a)
         => ( ti(X_a,B_1) != zero_zero(X_a)
           => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1) != zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_595_no__zero__divisors) ).

fof(fact_596_mult__eq__0__iff,axiom,
    ! [X_a] :
      ( ring_n68954251visors(X_a)
     => ! [Aa,Ba] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba) = zero_zero(X_a)
        <=> ( ti(X_a,Ba) = zero_zero(X_a)
            | ti(X_a,Aa) = zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_596_mult__eq__0__iff) ).

fof(fact_597_mult__zero__right,axiom,
    ! [X_a] :
      ( mult_zero(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),zero_zero(X_a)) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_597_mult__zero__right) ).

fof(fact_598_mult__zero__left,axiom,
    ! [X_a] :
      ( mult_zero(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_2) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_598_mult__zero__left) ).

fof(fact_599_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [X_a] :
      ( ab_semigroup_mult(X_a)
     => ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)) ),
    file('theBenchmark.p',fact_599_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_600_nat__mult__eq__1__iff,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = one_one(nat)
    <=> ( Na = one_one(nat)
        & M = one_one(nat) ) ),
    file('theBenchmark.p',fact_600_nat__mult__eq__1__iff) ).

fof(fact_601_nat__mult__1__right,axiom,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat)) = N,
    file('theBenchmark.p',fact_601_nat__mult__1__right) ).

fof(fact_602_nat__1__eq__mult__iff,axiom,
    ! [M,Na] :
      ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)
    <=> ( Na = one_one(nat)
        & M = one_one(nat) ) ),
    file('theBenchmark.p',fact_602_nat__1__eq__mult__iff) ).

fof(fact_603_nat__mult__1,axiom,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N) = N,
    file('theBenchmark.p',fact_603_nat__mult__1) ).

fof(fact_604_add__mult__distrib,axiom,
    ! [M_3,N,K_2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_2)),
    file('theBenchmark.p',fact_604_add__mult__distrib) ).

fof(fact_605_add__mult__distrib2,axiom,
    ! [K_2,M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),M_3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),N)),
    file('theBenchmark.p',fact_605_add__mult__distrib2) ).

fof(fact_606_Suc__mult__cancel1,axiom,
    ! [K,M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)
    <=> M = Na ),
    file('theBenchmark.p',fact_606_Suc__mult__cancel1) ).

fof(fact_607_mult__cancel2,axiom,
    ! [M,K,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)
    <=> ( K = zero_zero(nat)
        | M = Na ) ),
    file('theBenchmark.p',fact_607_mult__cancel2) ).

fof(fact_608_mult__cancel1,axiom,
    ! [K,M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
    <=> ( K = zero_zero(nat)
        | M = Na ) ),
    file('theBenchmark.p',fact_608_mult__cancel1) ).

fof(fact_609_mult__is__0,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = zero_zero(nat)
    <=> ( Na = zero_zero(nat)
        | M = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_609_mult__is__0) ).

fof(fact_610_mult__0__right,axiom,
    ! [M_3] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),zero_zero(nat)) = zero_zero(nat),
    file('theBenchmark.p',fact_610_mult__0__right) ).

fof(fact_611_mult__0,axiom,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N) = zero_zero(nat),
    file('theBenchmark.p',fact_611_mult__0) ).

fof(fact_612_mult__1__left,axiom,
    ! [X_a] :
      ( monoid_mult(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_2) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_612_mult__1__left) ).

fof(fact_613_mult__1,axiom,
    ! [X_a] :
      ( comm_monoid_mult(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_2) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_613_mult__1) ).

fof(fact_614_mult__1__right,axiom,
    ! [X_a] :
      ( monoid_mult(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),one_one(X_a)) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_614_mult__1__right) ).

fof(fact_615_mult_Ocomm__neutral,axiom,
    ! [X_a] :
      ( comm_monoid_mult(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),one_one(X_a)) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_615_mult_Ocomm__neutral) ).

fof(fact_616_comm__semiring__class_Odistrib,axiom,
    ! [X_a] :
      ( comm_semiring(X_a)
     => ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)) ),
    file('theBenchmark.p',fact_616_comm__semiring__class_Odistrib) ).

fof(fact_617_combine__common__factor,axiom,
    ! [X_a] :
      ( semiring(X_a)
     => ! [A_2,E,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E)),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),E)),C_1) ),
    file('theBenchmark.p',fact_617_combine__common__factor) ).

fof(fact_618_extensional__subset,axiom,
    ! [X_a,X_b,B,F,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1)))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
       => hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),B))) ) ),
    file('theBenchmark.p',fact_618_extensional__subset) ).

fof(fact_619_zero__le__square,axiom,
    ! [X_a] :
      ( linordered_ring(X_a)
     => ! [A_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),A_2))) ),
    file('theBenchmark.p',fact_619_zero__le__square) ).

fof(fact_620_zero__le__mult__iff,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [Aa,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)))
        <=> ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) ) ) ) ),
    file('theBenchmark.p',fact_620_zero__le__mult__iff) ).

fof(fact_621_mult__le__0__iff,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [Aa,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),zero_zero(X_a)))
        <=> ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) ) ) ) ),
    file('theBenchmark.p',fact_621_mult__le__0__iff) ).

fof(fact_622_mult__nonneg__nonneg,axiom,
    ! [X_a] :
      ( ordere453448008miring(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))) ) ) ),
    file('theBenchmark.p',fact_622_mult__nonneg__nonneg) ).

fof(fact_623_mult__nonneg__nonpos,axiom,
    ! [X_a] :
      ( ordere453448008miring(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_623_mult__nonneg__nonpos) ).

fof(fact_624_mult__nonneg__nonpos2,axiom,
    ! [X_a] :
      ( ordere453448008miring(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),A_2)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_624_mult__nonneg__nonpos2) ).

fof(fact_625_mult__nonpos__nonneg,axiom,
    ! [X_a] :
      ( ordere453448008miring(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_625_mult__nonpos__nonneg) ).

fof(fact_626_mult__nonpos__nonpos,axiom,
    ! [X_a] :
      ( ordered_ring(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))) ) ) ),
    file('theBenchmark.p',fact_626_mult__nonpos__nonpos) ).

fof(fact_627_mult__right__mono,axiom,
    ! [X_a] :
      ( ordered_semiring(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))) ) ) ),
    file('theBenchmark.p',fact_627_mult__right__mono) ).

fof(fact_628_mult__left__mono,axiom,
    ! [X_a] :
      ( ordered_semiring(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) ) ) ),
    file('theBenchmark.p',fact_628_mult__left__mono) ).

fof(fact_629_comm__mult__left__mono,axiom,
    ! [X_a] :
      ( ordere1490568538miring(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) ) ) ),
    file('theBenchmark.p',fact_629_comm__mult__left__mono) ).

fof(fact_630_mult__right__mono__neg,axiom,
    ! [X_a] :
      ( ordered_ring(X_a)
     => ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))) ) ) ),
    file('theBenchmark.p',fact_630_mult__right__mono__neg) ).

fof(fact_631_mult__left__mono__neg,axiom,
    ! [X_a] :
      ( ordered_ring(X_a)
     => ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) ) ) ),
    file('theBenchmark.p',fact_631_mult__left__mono__neg) ).

fof(fact_632_mult__mono_H,axiom,
    ! [X_a] :
      ( ordered_semiring(X_a)
     => ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
               => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_632_mult__mono_H) ).

fof(fact_633_mult__mono,axiom,
    ! [X_a] :
      ( ordered_semiring(X_a)
     => ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
               => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_633_mult__mono) ).

fof(fact_634_split__mult__pos__le,axiom,
    ! [X_a] :
      ( ordered_ring(X_a)
     => ! [B_1,A_2] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) ) )
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))) ) ),
    file('theBenchmark.p',fact_634_split__mult__pos__le) ).

fof(fact_635_split__mult__neg__le,axiom,
    ! [X_a] :
      ( ordere453448008miring(X_a)
     => ! [B_1,A_2] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) ) )
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) ) ),
    file('theBenchmark.p',fact_635_split__mult__neg__le) ).

fof(fact_636_not__square__less__zero,axiom,
    ! [X_a] :
      ( linordered_ring(X_a)
     => ! [A_2] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),A_2)),zero_zero(X_a))) ),
    file('theBenchmark.p',fact_636_not__square__less__zero) ).

fof(fact_637_mult__less__cancel__right__disj,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [Aa,Ca,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),Ca)))
        <=> ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),zero_zero(X_a))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ca)) ) ) ) ),
    file('theBenchmark.p',fact_637_mult__less__cancel__right__disj) ).

fof(fact_638_mult__less__cancel__left__disj,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [Ca,Aa,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba)))
        <=> ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),zero_zero(X_a))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ca)) ) ) ) ),
    file('theBenchmark.p',fact_638_mult__less__cancel__left__disj) ).

fof(fact_639_mult__less__cancel__left__pos,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [Aa,Ba,Ca] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ca))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba)))
          <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_639_mult__less__cancel__left__pos) ).

fof(fact_640_mult__pos__pos,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))) ) ) ),
    file('theBenchmark.p',fact_640_mult__pos__pos) ).

fof(fact_641_mult__pos__neg,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_641_mult__pos__neg) ).

fof(fact_642_mult__pos__neg2,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),A_2)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_642_mult__pos__neg2) ).

fof(fact_643_zero__less__mult__pos,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1)) ) ) ),
    file('theBenchmark.p',fact_643_zero__less__mult__pos) ).

fof(fact_644_zero__less__mult__pos2,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),A_2)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1)) ) ) ),
    file('theBenchmark.p',fact_644_zero__less__mult__pos2) ).

fof(fact_645_mult__less__cancel__left__neg,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [Aa,Ba,Ca] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba)))
          <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_645_mult__less__cancel__left__neg) ).

fof(fact_646_mult__neg__pos,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_646_mult__neg__pos) ).

fof(fact_647_mult__neg__neg,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))) ) ) ),
    file('theBenchmark.p',fact_647_mult__neg__neg) ).

fof(fact_648_mult__strict__right__mono,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))) ) ) ),
    file('theBenchmark.p',fact_648_mult__strict__right__mono) ).

fof(fact_649_mult__strict__left__mono,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) ) ) ),
    file('theBenchmark.p',fact_649_mult__strict__left__mono) ).

fof(fact_650_comm__mult__strict__left__mono,axiom,
    ! [X_a] :
      ( linord893533164strict(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) ) ) ),
    file('theBenchmark.p',fact_650_comm__mult__strict__left__mono) ).

fof(fact_651_mult__strict__right__mono__neg,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))) ) ) ),
    file('theBenchmark.p',fact_651_mult__strict__right__mono__neg) ).

fof(fact_652_mult__strict__left__mono__neg,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) ) ) ),
    file('theBenchmark.p',fact_652_mult__strict__left__mono__neg) ).

fof(fact_653_sum__squares__eq__zero__iff,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [X_2,Y_1] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)) = zero_zero(X_a)
        <=> ( ti(X_a,Y_1) = zero_zero(X_a)
            & ti(X_a,X_2) = zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_653_sum__squares__eq__zero__iff) ).

fof(fact_654_add__scale__eq__noteq,axiom,
    ! [X_a] :
      ( semiri456707255roduct(X_a)
     => ! [C_1,D,A_2,B_1,R_3] :
          ( ti(X_a,R_3) != zero_zero(X_a)
         => ( ( ti(X_a,C_1) != ti(X_a,D)
              & ti(X_a,A_2) = ti(X_a,B_1) )
           => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_3),C_1)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_3),D)) ) ) ),
    file('theBenchmark.p',fact_654_add__scale__eq__noteq) ).

fof(fact_655_less__1__mult,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [N,M_3] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M_3))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M_3),N))) ) ) ),
    file('theBenchmark.p',fact_655_less__1__mult) ).

fof(fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [A_2,M_3] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),M_3)),M_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),one_one(X_a))),M_3) ),
    file('theBenchmark.p',fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [M_3,A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),M_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),one_one(X_a))),M_3) ),
    file('theBenchmark.p',fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [X_a] :
      ( comm_semiring_1(X_a)
     => ! [M_3] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_3),M_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M_3) ),
    file('theBenchmark.p',fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_659_mult__eq__1__iff,axiom,
    ! [M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = hAPP(nat,nat,suc,zero_zero(nat))
    <=> ( Na = hAPP(nat,nat,suc,zero_zero(nat))
        & M = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    file('theBenchmark.p',fact_659_mult__eq__1__iff) ).

fof(fact_660_mult__less__mono2,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),J_1))) ) ),
    file('theBenchmark.p',fact_660_mult__less__mono2) ).

fof(fact_661_mult__less__mono1,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),K_2))) ) ),
    file('theBenchmark.p',fact_661_mult__less__mono1) ).

fof(fact_662_mult__less__cancel2,axiom,
    ! [M,K,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ) ),
    file('theBenchmark.p',fact_662_mult__less__cancel2) ).

fof(fact_663_mult__less__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ) ),
    file('theBenchmark.p',fact_663_mult__less__cancel1) ).

fof(fact_664_nat__0__less__mult__iff,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) ) ),
    file('theBenchmark.p',fact_664_nat__0__less__mult__iff) ).

fof(fact_665_Suc__mult__less__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ),
    file('theBenchmark.p',fact_665_Suc__mult__less__cancel1) ).

fof(fact_666_mult__Suc__right,axiom,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N)),
    file('theBenchmark.p',fact_666_mult__Suc__right) ).

fof(fact_667_mult__Suc,axiom,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M_3)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N)),
    file('theBenchmark.p',fact_667_mult__Suc) ).

fof(fact_668_Suc__mult__le__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ),
    file('theBenchmark.p',fact_668_Suc__mult__le__cancel1) ).

fof(fact_669_mult__eq__self__implies__10,axiom,
    ! [M_3,N] :
      ( M_3 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N)
     => ( M_3 = zero_zero(nat)
        | N = one_one(nat) ) ),
    file('theBenchmark.p',fact_669_mult__eq__self__implies__10) ).

fof(fact_670_restrict__extensional,axiom,
    ! [X_a,X_b,F,A_1] : hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1))),
    file('theBenchmark.p',fact_670_restrict__extensional) ).

fof(fact_671_extensional__restrict,axiom,
    ! [X_a,X_b,F,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1)))
     => hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1) = ti(fun(X_a,X_b),F) ),
    file('theBenchmark.p',fact_671_extensional__restrict) ).

fof(fact_672_compose__extensional,axiom,
    ! [X_a,X_b,X_c,A_1,F,G] : hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b))),compose(X_a,X_c,X_b),A_1),F),G)),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1))),
    file('theBenchmark.p',fact_672_compose__extensional) ).

fof(fact_673_mult__le__cancel__left__pos,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [Aa,Ba,Ca] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ca))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba)))
          <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_673_mult__le__cancel__left__pos) ).

fof(fact_674_mult__le__cancel__left__neg,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [Aa,Ba,Ca] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba)))
          <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_674_mult__le__cancel__left__neg) ).

fof(fact_675_mult__strict__mono,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
               => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_675_mult__strict__mono) ).

fof(fact_676_mult__strict__mono_H,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
               => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_676_mult__strict__mono_H) ).

fof(fact_677_mult__less__le__imp__less,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
               => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_677_mult__less__le__imp__less) ).

fof(fact_678_mult__le__less__imp__less,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
               => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D))) ) ) ) ) ),
    file('theBenchmark.p',fact_678_mult__le__less__imp__less) ).

fof(fact_679_mult__right__less__imp__less,axiom,
    ! [X_a] :
      ( linordered_semiring(X_a)
     => ! [A_2,C_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ),
    file('theBenchmark.p',fact_679_mult__right__less__imp__less) ).

fof(fact_680_mult__less__imp__less__right,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [A_2,C_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ),
    file('theBenchmark.p',fact_680_mult__less__imp__less__right) ).

fof(fact_681_mult__left__less__imp__less,axiom,
    ! [X_a] :
      ( linordered_semiring(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ),
    file('theBenchmark.p',fact_681_mult__left__less__imp__less) ).

fof(fact_682_mult__less__imp__less__left,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ) ),
    file('theBenchmark.p',fact_682_mult__less__imp__less__left) ).

fof(fact_683_mult__right__le__imp__le,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [A_2,C_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) ) ) ),
    file('theBenchmark.p',fact_683_mult__right__le__imp__le) ).

fof(fact_684_mult__left__le__imp__le,axiom,
    ! [X_a] :
      ( linord20386208strict(X_a)
     => ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) ) ) ),
    file('theBenchmark.p',fact_684_mult__left__le__imp__le) ).

fof(fact_685_sum__squares__ge__zero,axiom,
    ! [X_a] :
      ( linordered_ring(X_a)
     => ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y)))) ),
    file('theBenchmark.p',fact_685_sum__squares__ge__zero) ).

fof(fact_686_sum__squares__le__zero__iff,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [X_2,Y_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a)))
        <=> ( ti(X_a,Y_1) = zero_zero(X_a)
            & ti(X_a,X_2) = zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_686_sum__squares__le__zero__iff) ).

fof(fact_687_sum__squares__gt__zero__iff,axiom,
    ! [X_a] :
      ( linord581940658strict(X_a)
     => ! [X_2,Y_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))))
        <=> ( ti(X_a,Y_1) != zero_zero(X_a)
            | ti(X_a,X_2) != zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_687_sum__squares__gt__zero__iff) ).

fof(fact_688_not__sum__squares__lt__zero,axiom,
    ! [X_a] :
      ( linordered_ring(X_a)
     => ! [X,Y] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))),zero_zero(X_a))) ),
    file('theBenchmark.p',fact_688_not__sum__squares__lt__zero) ).

fof(fact_689_mult__left__le__one__le,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a)))
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)),X)) ) ) ) ),
    file('theBenchmark.p',fact_689_mult__left__le__one__le) ).

fof(fact_690_mult__right__le__one__le,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a)))
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),X)) ) ) ) ),
    file('theBenchmark.p',fact_690_mult__right__le__one__le) ).

fof(fact_691_n__less__m__mult__n,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_3))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N))) ) ),
    file('theBenchmark.p',fact_691_n__less__m__mult__n) ).

fof(fact_692_n__less__n__mult__m,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_3))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_3))) ) ),
    file('theBenchmark.p',fact_692_n__less__n__mult__m) ).

fof(fact_693_one__less__mult,axiom,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_3))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N))) ) ),
    file('theBenchmark.p',fact_693_one__less__mult) ).

fof(fact_694_one__le__mult__iff,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Na))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) ) ),
    file('theBenchmark.p',fact_694_one__le__mult__iff) ).

fof(fact_695_mult__le__cancel2,axiom,
    ! [M,K,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_695_mult__le__cancel2) ).

fof(fact_696_mult__le__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_696_mult__le__cancel1) ).

fof(fact_697_fold__image__distrib,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_mult(X_b)
     => ! [G,Ha,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Ha)),one_one(X_b)),A_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),one_one(X_b)),A_1)),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),Ha),one_one(X_b)),A_1)) ) ),
    file('theBenchmark.p',fact_697_fold__image__distrib) ).

fof(fact_698_convex__bound__le,axiom,
    ! [X_a] :
      ( linord1278240602ring_1(X_a)
     => ! [V_2,U_1,Y,X,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),A_2))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V_2))
               => ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V_2) = one_one(X_a)
                 => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V_2),Y))),A_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_698_convex__bound__le) ).

fof(fact_699_field__le__mult__one__interval,axiom,
    ! [X_a] :
      ( linord1117847801e_zero(X_a)
     => ! [X,Y] :
          ( ! [Z_2] :
              ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_2))
             => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),one_one(X_a)))
               => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_2),X)),Y)) ) )
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_699_field__le__mult__one__interval) ).

fof(fact_700_fold__image__1,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_mult(X_b)
     => ! [F,S] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S))
         => ( ! [X_1] :
                ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),S))
               => hAPP(X_a,X_b,F,X_1) = one_one(X_b) )
           => hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),F),one_one(X_b)),S) = one_one(X_b) ) ) ),
    file('theBenchmark.p',fact_700_fold__image__1) ).

fof(fact_701_fold__image__cong,axiom,
    ! [X_a,X_b] :
      ( ab_semigroup_mult(X_b)
     => ! [Z_1,G,Ha,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => ( ! [X_1] :
                ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
               => hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,Ha,X_1) )
           => hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),Z_1),A_1) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),Ha),Z_1),A_1) ) ) ),
    file('theBenchmark.p',fact_701_fold__image__cong) ).

fof(fact_702_nat__mult__commute,axiom,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_3),
    file('theBenchmark.p',fact_702_nat__mult__commute) ).

fof(fact_703_nat__mult__assoc,axiom,
    ! [M_3,N,K_2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_2)),
    file('theBenchmark.p',fact_703_nat__mult__assoc) ).

fof(fact_704_nat__mult__le__cancel1,axiom,
    ! [M,Na,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_704_nat__mult__le__cancel1) ).

fof(fact_705_nat__mult__less__cancel1,axiom,
    ! [M,Na,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    file('theBenchmark.p',fact_705_nat__mult__less__cancel1) ).

fof(fact_706_nat__mult__eq__cancel1,axiom,
    ! [M,Na,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
      <=> M = Na ) ),
    file('theBenchmark.p',fact_706_nat__mult__eq__cancel1) ).

fof(fact_707_nat__mult__eq__cancel__disj,axiom,
    ! [K,M,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
    <=> ( M = Na
        | K = zero_zero(nat) ) ),
    file('theBenchmark.p',fact_707_nat__mult__eq__cancel__disj) ).

fof(fact_708_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,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(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,hAPP(nat,fun(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_708_left__add__mult__distrib) ).

fof(fact_709_fold__image__related,axiom,
    ! [X_b,X_a] :
      ( comm_monoid_mult(X_a)
     => ! [Ha,G,S,R_2,Ea] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,Ea),Ea))
         => ( ! [X1,Y1,X2,Y2] :
                ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,Y1),Y2))
                  & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,X1),X2)) )
               => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X2),Y2))) )
           => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S))
             => ( ! [X_1] :
                    ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),S))
                   => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(X_b,X_a,Ha,X_1)),hAPP(X_b,X_a,G,X_1))) )
               => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold_image(X_a,X_b),times_times(X_a)),Ha),Ea),S)),hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold_image(X_a,X_b),times_times(X_a)),G),Ea),S))) ) ) ) ) ),
    file('theBenchmark.p',fact_709_fold__image__related) ).

fof(fact_710_fold__image__eq__general__inverses,axiom,
    ! [X_b,X_a,X_c] :
      ( comm_monoid_mult(X_c)
     => ! [Ea,G,F,Ha,K,T_3,S] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S))
         => ( ! [Y_2] :
                ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),T_3))
               => ( hAPP(X_a,X_b,Ha,hAPP(X_b,X_a,K,Y_2)) = ti(X_b,Y_2)
                  & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_b,X_a,K,Y_2)),S)) ) )
           => ( ! [X_1] :
                  ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),S))
                 => ( hAPP(X_b,X_c,G,hAPP(X_a,X_b,Ha,X_1)) = hAPP(X_a,X_c,F,X_1)
                    & hAPP(X_b,X_a,K,hAPP(X_a,X_b,Ha,X_1)) = ti(X_a,X_1)
                    & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,Ha,X_1)),T_3)) ) )
             => hAPP(fun(X_a,bool),X_c,hAPP(X_c,fun(fun(X_a,bool),X_c),hAPP(fun(X_a,X_c),fun(X_c,fun(fun(X_a,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_a,X_c),fun(X_c,fun(fun(X_a,bool),X_c))),finite_fold_image(X_c,X_a),times_times(X_c)),F),Ea),S) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Ea),T_3) ) ) ) ),
    file('theBenchmark.p',fact_710_fold__image__eq__general__inverses) ).

fof(fact_711_extensionalityI,axiom,
    ! [X_a,X_b,G,F,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1)))
     => ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1)))
       => ( ! [X_1] :
              ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
             => hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1) )
         => ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G) ) ) ),
    file('theBenchmark.p',fact_711_extensionalityI) ).

fof(fact_712_ex__has__least__nat,axiom,
    ! [X_a,M,Pa,K] :
      ( hBOOL(hAPP(X_a,bool,Pa,K))
     => ? [X_1] :
          ( ! [Y_2] :
              ( hBOOL(hAPP(X_a,bool,Pa,Y_2))
             => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X_a,nat,M,X_1)),hAPP(X_a,nat,M,Y_2))) )
          & hBOOL(hAPP(X_a,bool,Pa,X_1)) ) ),
    file('theBenchmark.p',fact_712_ex__has__least__nat) ).

fof(fact_713_image__cong,axiom,
    ! [X_b,X_a,F,G,M_2,N_1] :
      ( ti(fun(X_a,bool),M_2) = ti(fun(X_a,bool),N_1)
     => ( ! [X_1] :
            ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),N_1))
           => hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1) )
       => hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),M_2) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),G),N_1) ) ),
    file('theBenchmark.p',fact_713_image__cong) ).

fof(fact_714_UNIV__witness,axiom,
    ! [X_a] :
    ? [X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool)))),
    file('theBenchmark.p',fact_714_UNIV__witness) ).

fof(fact_715_UNIV__eq__I,axiom,
    ! [X_a,A_1] :
      ( ! [X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
     => top_top(fun(X_a,bool)) = ti(fun(X_a,bool),A_1) ),
    file('theBenchmark.p',fact_715_UNIV__eq__I) ).

fof(fact_716_Collect__mono,axiom,
    ! [X_a,Q_1,Pa] :
      ( ! [X_1] :
          ( hBOOL(hAPP(X_a,bool,Pa,X_1))
         => hBOOL(hAPP(X_a,bool,Q_1,X_1)) )
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) ),
    file('theBenchmark.p',fact_716_Collect__mono) ).

fof(fact_717_predicate1I,axiom,
    ! [X_a,Q_1,Pa] :
      ( ! [X_1] :
          ( hBOOL(hAPP(X_a,bool,Pa,X_1))
         => hBOOL(hAPP(X_a,bool,Q_1,X_1)) )
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1)) ),
    file('theBenchmark.p',fact_717_predicate1I) ).

fof(fact_718_fold__image__reindex,axiom,
    ! [X_b,X_a,X_c] :
      ( ab_semigroup_mult(X_c)
     => ! [G,Z_1,Ha,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),Ha),A_1))
           => hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),Ha),A_1)) = hAPP(fun(X_a,bool),X_c,hAPP(X_c,fun(fun(X_a,bool),X_c),hAPP(fun(X_a,X_c),fun(X_c,fun(fun(X_a,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_a,X_c),fun(X_c,fun(fun(X_a,bool),X_c))),finite_fold_image(X_c,X_a),times_times(X_c)),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),G),Ha)),Z_1),A_1) ) ) ),
    file('theBenchmark.p',fact_718_fold__image__reindex) ).

fof(fact_719_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_719_nat_Osize_I2_J) ).

fof(fact_720_comp__surj,axiom,
    ! [X_c,X_b,X_a,G,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
     => ( hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),G),top_top(fun(X_a,bool))) = top_top(fun(X_c,bool))
       => hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),comp(X_a,X_c,X_b),G),F)),top_top(fun(X_b,bool))) = top_top(fun(X_c,bool)) ) ),
    file('theBenchmark.p',fact_720_comp__surj) ).

fof(fact_721_inj__comp,axiom,
    ! [X_c,X_a,X_b,G,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),bool),inj_on(X_c,X_a),G),top_top(fun(X_c,bool))))
       => hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),bool),inj_on(X_c,X_b),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),comp(X_a,X_b,X_c),F),G)),top_top(fun(X_c,bool)))) ) ),
    file('theBenchmark.p',fact_721_inj__comp) ).

fof(fact_722_inj__on__imageI,axiom,
    ! [X_a,X_b,X_c,G,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),G),F)),A_1))
     => hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),bool),inj_on(X_c,X_b),G),hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),F),A_1))) ),
    file('theBenchmark.p',fact_722_inj__on__imageI) ).

fof(fact_723_comp__inj__on,axiom,
    ! [X_c,X_a,X_b,G,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),bool),inj_on(X_b,X_c),G),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),bool),inj_on(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),G),F)),A_1)) ) ),
    file('theBenchmark.p',fact_723_comp__inj__on) ).

fof(fact_724_comp__inj__on__iff,axiom,
    ! [X_c,X_a,X_b,F_1,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),bool),inj_on(X_b,X_c),F_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      <=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),bool),inj_on(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),F_1),F)),A_1)) ) ),
    file('theBenchmark.p',fact_724_comp__inj__on__iff) ).

fof(fact_725_image__compose,axiom,
    ! [X_b,X_a,X_c,F,G,R_1] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,X_c),fun(X_b,X_a),hAPP(fun(X_c,X_a),fun(fun(X_b,X_c),fun(X_b,X_a)),comp(X_c,X_a,X_b),F),G)),R_1) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),F),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),R_1)),
    file('theBenchmark.p',fact_725_image__compose) ).

fof(fact_726_inj__on__imageI2,axiom,
    ! [X_a,X_b,X_c,F_1,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),F_1),F)),A_1))
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),bool),inj_on(X_a,X_c),F),A_1)) ),
    file('theBenchmark.p',fact_726_inj__on__imageI2) ).

fof(fact_727_nat_Osize_I1_J,axiom,
    hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
    file('theBenchmark.p',fact_727_nat_Osize_I1_J) ).

fof(fact_728_o__def,axiom,
    ! [X_a,X_b,X_c,F,G,X_1] : hAPP(X_a,X_b,hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),F),G),X_1) = hAPP(X_c,X_b,F,hAPP(X_a,X_c,G,X_1)),
    file('theBenchmark.p',fact_728_o__def) ).

fof(fact_729_o__assoc,axiom,
    ! [X_a,X_c,X_b,X_d,F,G,Ha] : hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),F),hAPP(fun(X_a,X_d),fun(X_a,X_c),hAPP(fun(X_d,X_c),fun(fun(X_a,X_d),fun(X_a,X_c)),comp(X_d,X_c,X_a),G),Ha)) = hAPP(fun(X_a,X_d),fun(X_a,X_b),hAPP(fun(X_d,X_b),fun(fun(X_a,X_d),fun(X_a,X_b)),comp(X_d,X_b,X_a),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),comp(X_c,X_b,X_d),F),G)),Ha),
    file('theBenchmark.p',fact_729_o__assoc) ).

fof(fact_730_o__apply,axiom,
    ! [X_c,X_a,X_b,F,G,X_2] : hAPP(X_c,X_a,hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),comp(X_b,X_a,X_c),F),G),X_2) = hAPP(X_b,X_a,F,hAPP(X_c,X_b,G,X_2)),
    file('theBenchmark.p',fact_730_o__apply) ).

fof(fact_731_o__eq__dest,axiom,
    ! [X_a,X_c,X_b,X_d,V,Aa,Ba,Ca,Da] :
      ( hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),Aa),Ba) = hAPP(fun(X_a,X_d),fun(X_a,X_b),hAPP(fun(X_d,X_b),fun(fun(X_a,X_d),fun(X_a,X_b)),comp(X_d,X_b,X_a),Ca),Da)
     => hAPP(X_c,X_b,Aa,hAPP(X_a,X_c,Ba,V)) = hAPP(X_d,X_b,Ca,hAPP(X_a,X_d,Da,V)) ),
    file('theBenchmark.p',fact_731_o__eq__dest) ).

fof(fact_732_o__eq__elim,axiom,
    ! [X_a,X_c,X_b,X_d,Aa,Ba,Ca,Da] :
      ( hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),Aa),Ba) = hAPP(fun(X_a,X_d),fun(X_a,X_b),hAPP(fun(X_d,X_b),fun(fun(X_a,X_d),fun(X_a,X_b)),comp(X_d,X_b,X_a),Ca),Da)
     => ! [V_1] : hAPP(X_c,X_b,Aa,hAPP(X_a,X_c,Ba,V_1)) = hAPP(X_d,X_b,Ca,hAPP(X_a,X_d,Da,V_1)) ),
    file('theBenchmark.p',fact_732_o__eq__elim) ).

fof(fact_733_K__record__comp,axiom,
    ! [X_a,X_b,X_c,Ca,F,X_1] : hAPP(X_a,X_b,hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),hAPP(X_b,fun(X_c,X_b),combk(X_b,X_c),Ca)),F),X_1) = ti(X_b,Ca),
    file('theBenchmark.p',fact_733_K__record__comp) ).

fof(fact_734_o__eq__dest__lhs,axiom,
    ! [X_a,X_c,X_b,V,Aa,Ba,Ca] :
      ( hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),Aa),Ba) = ti(fun(X_a,X_b),Ca)
     => hAPP(X_c,X_b,Aa,hAPP(X_a,X_c,Ba,V)) = hAPP(X_a,X_b,Ca,V) ),
    file('theBenchmark.p',fact_734_o__eq__dest__lhs) ).

fof(fact_735_comp__cong,axiom,
    ! [X_b,X_a,X_c,X_d,X_e,F,G,X_2,F_1,G_2,X_3] :
      ( hAPP(X_b,X_a,F,hAPP(X_c,X_b,G,X_2)) = hAPP(X_d,X_a,F_1,hAPP(X_e,X_d,G_2,X_3))
     => hAPP(X_c,X_a,hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),comp(X_b,X_a,X_c),F),G),X_2) = hAPP(X_e,X_a,hAPP(fun(X_e,X_d),fun(X_e,X_a),hAPP(fun(X_d,X_a),fun(fun(X_e,X_d),fun(X_e,X_a)),comp(X_d,X_a,X_e),F_1),G_2),X_3) ),
    file('theBenchmark.p',fact_735_comp__cong) ).

fof(fact_736_o__inv__o__cancel,axiom,
    ! [X_c,X_a,X_b,G,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),comp(X_a,X_c,X_b),G),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F))),F) = ti(fun(X_a,X_c),G) ),
    file('theBenchmark.p',fact_736_o__inv__o__cancel) ).

fof(fact_737_inv__into__comp,axiom,
    ! [X_a,X_b,X_c,X_2,F,G,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1)))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),bool),inj_on(X_c,X_a),G),A_1))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1))))
         => hAPP(X_b,X_c,hAPP(fun(X_c,X_b),fun(X_b,X_c),hAPP(fun(X_c,bool),fun(fun(X_c,X_b),fun(X_b,X_c)),hilbert_inv_into(X_c,X_b),A_1),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),comp(X_a,X_b,X_c),F),G)),X_2) = hAPP(X_b,X_c,hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),comp(X_a,X_c,X_b),hAPP(fun(X_c,X_a),fun(X_a,X_c),hAPP(fun(X_c,bool),fun(fun(X_c,X_a),fun(X_a,X_c)),hilbert_inv_into(X_c,X_a),A_1),G)),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1)),F)),X_2) ) ) ),
    file('theBenchmark.p',fact_737_inv__into__comp) ).

fof(fact_738_the__inv__into__comp,axiom,
    ! [X_a,X_b,X_c,X_2,F,G,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1)))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),bool),inj_on(X_c,X_a),G),A_1))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1))))
         => hAPP(X_b,X_c,hAPP(fun(X_c,X_b),fun(X_b,X_c),hAPP(fun(X_c,bool),fun(fun(X_c,X_b),fun(X_b,X_c)),the_inv_into(X_c,X_b),A_1),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),comp(X_a,X_b,X_c),F),G)),X_2) = hAPP(X_b,X_c,hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),comp(X_a,X_c,X_b),hAPP(fun(X_c,X_a),fun(X_a,X_c),hAPP(fun(X_c,bool),fun(fun(X_c,X_a),fun(X_a,X_c)),the_inv_into(X_c,X_a),A_1),G)),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1)),F)),X_2) ) ) ),
    file('theBenchmark.p',fact_738_the__inv__into__comp) ).

fof(fact_739_folding__image_Oreindex,axiom,
    ! [X_b,X_a,G,Ha,A_1,F,Z_1,Fa] :
      ( hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_b),fun(fun(X_b,bool),bool),inj_on(X_b,X_b),Ha),A_1))
         => hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),Ha),A_1)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,hAPP(fun(X_b,X_b),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_b),fun(X_b,X_a)),comp(X_b,X_a,X_b),G),Ha)),A_1) ) ) ),
    file('theBenchmark.p',fact_739_folding__image_Oreindex) ).

fof(fact_740_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_740_nat_Osize_I4_J) ).

fof(fact_741_nat__size,axiom,
    ! [N] : hAPP(nat,nat,size_size(nat),N) = N,
    file('theBenchmark.p',fact_741_nat__size) ).

fof(fact_742_folding__image_Odistrib,axiom,
    ! [X_b,X_a,G,Ha,A_1,F,Z_1,Fa] :
      ( hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
       => hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),F),G)),Ha)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),A_1)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,Ha),A_1)) ) ),
    file('theBenchmark.p',fact_742_folding__image_Odistrib) ).

fof(fact_743_nat_Osize_I3_J,axiom,
    hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
    file('theBenchmark.p',fact_743_nat_Osize_I3_J) ).

fof(fact_744_folding__image_Oeq__fold,axiom,
    ! [X_b,X_a,G,A_1,F,Z_1,Fa] :
      ( hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
       => hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),A_1) = hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold_image(X_a,X_b),F),G),Z_1),A_1) ) ),
    file('theBenchmark.p',fact_744_folding__image_Oeq__fold) ).

fof(fact_745_folding__image_Ocong,axiom,
    ! [X_b,X_a,G,Ha,A_1,F,Z_1,Fa] :
      ( hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
       => ( ! [X_1] :
              ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))
             => hAPP(X_b,X_a,G,X_1) = hAPP(X_b,X_a,Ha,X_1) )
         => hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),A_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,Ha),A_1) ) ) ),
    file('theBenchmark.p',fact_745_folding__image_Ocong) ).

fof(fact_746_in__finite__psubset,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_a,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool))),product_Pair(fun(X_a,bool),fun(X_a,bool)),A_1),B)),finite_psubset(X_a)))
    <=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
        & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) ) ),
    file('theBenchmark.p',fact_746_in__finite__psubset) ).

fof(fact_747_folding__idem_Osubset__comp__idem,axiom,
    ! [X_a,X_b,B,A_1,F,Fa] :
      ( hBOOL(hAPP(fun(fun(X_a,bool),fun(X_b,X_b)),bool,hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool),finite_folding_idem(X_a,X_b),F),Fa))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
       => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
         => hAPP(fun(X_b,X_b),fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(fun(X_b,X_b),fun(X_b,X_b)),comp(X_b,X_b,X_b),hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,A_1)),hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,B)) = hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,A_1) ) ) ),
    file('theBenchmark.p',fact_747_folding__idem_Osubset__comp__idem) ).

fof(fact_748_in__measure,axiom,
    ! [X_a,X_2,Y_1,F] :
      ( hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),hAPP(fun(X_a,nat),fun(product_prod(X_a,X_a),bool),measure(X_a),F)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_2)),hAPP(X_a,nat,F,Y_1))) ),
    file('theBenchmark.p',fact_748_in__measure) ).

fof(fact_749_folding__idem_Oidem__left__comp,axiom,
    ! [X_c,X_a,X_b,X_2,G,F,Fa] :
      ( hBOOL(hAPP(fun(fun(X_a,bool),fun(X_b,X_b)),bool,hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool),finite_folding_idem(X_a,X_b),F),Fa))
     => hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),comp(X_b,X_b,X_c),hAPP(X_a,fun(X_b,X_b),F,X_2)),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),comp(X_b,X_b,X_c),hAPP(X_a,fun(X_b,X_b),F,X_2)),G)) = hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),comp(X_b,X_b,X_c),hAPP(X_a,fun(X_b,X_b),F,X_2)),G) ),
    file('theBenchmark.p',fact_749_folding__idem_Oidem__left__comp) ).

fof(fact_750_folding__idem_Oidem__comp,axiom,
    ! [X_a,X_b,X_2,F,Fa] :
      ( hBOOL(hAPP(fun(fun(X_a,bool),fun(X_b,X_b)),bool,hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool),finite_folding_idem(X_a,X_b),F),Fa))
     => hAPP(fun(X_b,X_b),fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(fun(X_b,X_b),fun(X_b,X_b)),comp(X_b,X_b,X_b),hAPP(X_a,fun(X_b,X_b),F,X_2)),hAPP(X_a,fun(X_b,X_b),F,X_2)) = hAPP(X_a,fun(X_b,X_b),F,X_2) ),
    file('theBenchmark.p',fact_750_folding__idem_Oidem__comp) ).

fof(fact_751_folding__idem_Oin__comp__idem,axiom,
    ! [X_a,X_b,X_2,A_1,F,Fa] :
      ( hBOOL(hAPP(fun(fun(X_a,bool),fun(X_b,X_b)),bool,hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool),finite_folding_idem(X_a,X_b),F),Fa))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
       => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
         => hAPP(fun(X_b,X_b),fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(fun(X_b,X_b),fun(X_b,X_b)),comp(X_b,X_b,X_b),hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,A_1)),hAPP(X_a,fun(X_b,X_b),F,X_2)) = hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,A_1) ) ) ),
    file('theBenchmark.p',fact_751_folding__idem_Oin__comp__idem) ).

fof(fact_752_weak__decr__stable,axiom,
    ! [F] :
      ( ! [I_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_752_weak__decr__stable) ).

fof(fact_753_mlex__leq,axiom,
    ! [X_a,R_2,F,X_2,Y_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X_a,nat,F,X_2)),hAPP(X_a,nat,F,Y_1)))
     => ( hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),R_2))
       => hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_2))) ) ),
    file('theBenchmark.p',fact_753_mlex__leq) ).

fof(fact_754_mlex__less,axiom,
    ! [X_a,R_2,F,X_2,Y_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_2)),hAPP(X_a,nat,F,Y_1)))
     => hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_2))) ),
    file('theBenchmark.p',fact_754_mlex__less) ).

fof(fact_755_bool_Osize_I1_J,axiom,
    hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
    file('theBenchmark.p',fact_755_bool_Osize_I1_J) ).

fof(fact_756_bool_Osize_I2_J,axiom,
    hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
    file('theBenchmark.p',fact_756_bool_Osize_I2_J) ).

fof(fact_757_folding__image_Oeq__general__inverses,axiom,
    ! [X_b,X_a,G,J,Ha,K,T_3,S,F,Z_1,Fa] :
      ( hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S))
       => ( ! [Y_2] :
              ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),T_3))
             => ( hAPP(X_b,X_b,Ha,hAPP(X_b,X_b,K,Y_2)) = ti(X_b,Y_2)
                & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,K,Y_2)),S)) ) )
         => ( ! [X_1] :
                ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),S))
               => ( hAPP(X_b,X_a,G,hAPP(X_b,X_b,Ha,X_1)) = hAPP(X_b,X_a,J,X_1)
                  & hAPP(X_b,X_b,K,hAPP(X_b,X_b,Ha,X_1)) = ti(X_b,X_1)
                  & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,Ha,X_1)),T_3)) ) )
           => hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,J),S) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),T_3) ) ) ) ),
    file('theBenchmark.p',fact_757_folding__image_Oeq__general__inverses) ).

fof(fact_758_folding__image_Orelated,axiom,
    ! [X_b,X_a,Ha,G,S,R_2,F,Z_1,Fa] :
      ( hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa))
     => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,Z_1),Z_1))
       => ( ! [X1,Y1,X2,Y2] :
              ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,Y1),Y2))
                & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,X1),X2)) )
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X2),Y2))) )
         => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S))
           => ( ! [X_1] :
                  ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),S))
                 => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(X_b,X_a,Ha,X_1)),hAPP(X_b,X_a,G,X_1))) )
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,Ha),S)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),S))) ) ) ) ) ),
    file('theBenchmark.p',fact_758_folding__image_Orelated) ).

fof(fact_759_greaterThanLessThan__subseteq__atLeastAtMost__iff,axiom,
    ! [X_a] :
      ( dense_linorder(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da)))
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) ) ) ) ),
    file('theBenchmark.p',fact_759_greaterThanLessThan__subseteq__atLeastAtMost__iff) ).

fof(fact_760_greaterThanAtMost__subseteq__atLeastAtMost__iff,axiom,
    ! [X_a] :
      ( dense_linorder(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da)))
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) ) ) ) ),
    file('theBenchmark.p',fact_760_greaterThanAtMost__subseteq__atLeastAtMost__iff) ).

fof(fact_761_finite__atLeastAtMost,axiom,
    ! [L,U] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U))),
    file('theBenchmark.p',fact_761_finite__atLeastAtMost) ).

fof(fact_762_atLeastatMost__subset__iff,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da)))
        <=> ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_762_atLeastatMost__subset__iff) ).

fof(fact_763_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [L,U] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),hAPP(nat,nat,suc,U)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U),
    file('theBenchmark.p',fact_763_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_764_ex__nat__less,axiom,
    ! [Pa,Na] :
      ( ? [M_1] :
          ( hBOOL(hAPP(nat,bool,Pa,M_1))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) )
    <=> ? [X_1] :
          ( hBOOL(hAPP(nat,bool,Pa,X_1))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),Na))) ) ),
    file('theBenchmark.p',fact_764_ex__nat__less) ).

fof(fact_765_all__nat__less,axiom,
    ! [Pa,Na] :
      ( ! [M_1] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
         => hBOOL(hAPP(nat,bool,Pa,M_1)) )
    <=> ! [X_1] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),Na)))
         => hBOOL(hAPP(nat,bool,Pa,X_1)) ) ),
    file('theBenchmark.p',fact_765_all__nat__less) ).

fof(fact_766_image__Suc__atLeastAtMost,axiom,
    ! [I,J] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J)),
    file('theBenchmark.p',fact_766_image__Suc__atLeastAtMost) ).

fof(fact_767_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [L,U] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,L)),U) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),L),U),
    file('theBenchmark.p',fact_767_atLeastSucAtMost__greaterThanAtMost) ).

fof(fact_768_image__add__atLeastAtMost,axiom,
    ! [K,I,J] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(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_768_image__add__atLeastAtMost) ).

fof(fact_769_atLeastatMost__psubset__iff,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da)))
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Da))
            & ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Da))
                  | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Aa)) )
                & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
                & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) ) ) ),
    file('theBenchmark.p',fact_769_atLeastatMost__psubset__iff) ).

fof(fact_770_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
    ! [X_a] :
      ( dense_linorder(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)))
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) ) ) ) ),
    file('theBenchmark.p',fact_770_atLeastAtMost__subseteq__atLeastLessThan__iff) ).

fof(fact_771_atLeastLessThan__subseteq__atLeastAtMost__iff,axiom,
    ! [X_a] :
      ( dense_linorder(X_a)
     => ! [Aa,Ba,Ca,Da] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da)))
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
           => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) ) ) ) ),
    file('theBenchmark.p',fact_771_atLeastLessThan__subseteq__atLeastAtMost__iff) ).

fof(fact_772_ivl__disj__un_I19_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [U,L,M] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),L),M))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
           => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),L),U) ) ) ),
    file('theBenchmark.p',fact_772_ivl__disj__un_I19_J) ).

fof(fact_773_ivl__disj__un_I18_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [U,L,M] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),M),U))
           => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),L),U) ) ) ),
    file('theBenchmark.p',fact_773_ivl__disj__un_I18_J) ).

fof(fact_774_UnE,axiom,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)))
     => ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B)) ) ),
    file('theBenchmark.p',fact_774_UnE) ).

fof(fact_775_sup1E,axiom,
    ! [X_a,A_1,B,X_2] :
      ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2))
     => ( ~ hBOOL(hAPP(X_a,bool,A_1,X_2))
       => hBOOL(hAPP(X_a,bool,B,X_2)) ) ),
    file('theBenchmark.p',fact_775_sup1E) ).

fof(fact_776_sup1CI,axiom,
    ! [X_a,A_1,B,X_2] :
      ( ( ~ hBOOL(hAPP(X_a,bool,B,X_2))
       => hBOOL(hAPP(X_a,bool,A_1,X_2)) )
     => hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2)) ),
    file('theBenchmark.p',fact_776_sup1CI) ).

fof(fact_777_UnCI,axiom,
    ! [X_a,A_1,Ca,B] :
      ( ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) )
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) ),
    file('theBenchmark.p',fact_777_UnCI) ).

fof(fact_778_ivl__disj__un_I20_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [U,L,M] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
           => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),L),U) ) ) ),
    file('theBenchmark.p',fact_778_ivl__disj__un_I20_J) ).

fof(fact_779_ivl__disj__un_I17_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [U,L,M] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
           => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),L),U) ) ) ),
    file('theBenchmark.p',fact_779_ivl__disj__un_I17_J) ).

fof(fact_780_inj__on__Un__image__eq__iff,axiom,
    ! [X_a,X_b,F,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)))
     => ( hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)
      <=> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) ) ),
    file('theBenchmark.p',fact_780_inj__on__Un__image__eq__iff) ).

fof(fact_781_image__Un,axiom,
    ! [X_b,X_a,F,A_1,B] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B)),
    file('theBenchmark.p',fact_781_image__Un) ).

fof(fact_782_Un__upper1,axiom,
    ! [X_a,A_1,B] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),
    file('theBenchmark.p',fact_782_Un__upper1) ).

fof(fact_783_Un__upper2,axiom,
    ! [X_a,B,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),
    file('theBenchmark.p',fact_783_Un__upper2) ).

fof(fact_784_subset__Un__eq,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
    <=> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),B) ),
    file('theBenchmark.p',fact_784_subset__Un__eq) ).

fof(fact_785_Un__absorb1,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
     => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),B) ),
    file('theBenchmark.p',fact_785_Un__absorb1) ).

fof(fact_786_Un__absorb2,axiom,
    ! [X_a,B,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
     => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),A_1) ),
    file('theBenchmark.p',fact_786_Un__absorb2) ).

fof(fact_787_Un__least,axiom,
    ! [X_a,B,A_1,C] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),C)) ) ),
    file('theBenchmark.p',fact_787_Un__least) ).

fof(fact_788_Un__mono,axiom,
    ! [X_a,B,D_1,A_1,C] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),D_1))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C),D_1))) ) ),
    file('theBenchmark.p',fact_788_Un__mono) ).

fof(fact_789_finite__UnI,axiom,
    ! [X_a,G_1,Fa] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),G_1))
       => hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),Fa),G_1))) ) ),
    file('theBenchmark.p',fact_789_finite__UnI) ).

fof(fact_790_finite__Un,axiom,
    ! [X_a,Fa,G_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),Fa),G_1)))
    <=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),G_1))
        & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa)) ) ),
    file('theBenchmark.p',fact_790_finite__Un) ).

fof(fact_791_Un__absorb,axiom,
    ! [X_a,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),A_1) = ti(fun(X_a,bool),A_1),
    file('theBenchmark.p',fact_791_Un__absorb) ).

fof(fact_792_Un__def,axiom,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))),
    file('theBenchmark.p',fact_792_Un__def) ).

fof(fact_793_Un__commute,axiom,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),A_1),
    file('theBenchmark.p',fact_793_Un__commute) ).

fof(fact_794_Un__left__absorb,axiom,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),
    file('theBenchmark.p',fact_794_Un__left__absorb) ).

fof(fact_795_Un__left__commute,axiom,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),C)),
    file('theBenchmark.p',fact_795_Un__left__commute) ).

fof(fact_796_Un__iff,axiom,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)))
    <=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
        | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) ) ),
    file('theBenchmark.p',fact_796_Un__iff) ).

fof(fact_797_Un__assoc,axiom,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)),
    file('theBenchmark.p',fact_797_Un__assoc) ).

fof(fact_798_bex__Un,axiom,
    ! [X_a,Pa,A_1,B] :
      ( ? [X_1] :
          ( hBOOL(hAPP(X_a,bool,Pa,X_1))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) )
    <=> ( ? [X_1] :
            ( hBOOL(hAPP(X_a,bool,Pa,X_1))
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) )
        | ? [X_1] :
            ( hBOOL(hAPP(X_a,bool,Pa,X_1))
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_798_bex__Un) ).

fof(fact_799_ball__Un,axiom,
    ! [X_a,Pa,A_1,B] :
      ( ! [X_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)))
         => hBOOL(hAPP(X_a,bool,Pa,X_1)) )
    <=> ( ! [X_1] :
            ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))
           => hBOOL(hAPP(X_a,bool,Pa,X_1)) )
        & ! [X_1] :
            ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
           => hBOOL(hAPP(X_a,bool,Pa,X_1)) ) ) ),
    file('theBenchmark.p',fact_799_ball__Un) ).

fof(fact_800_sup1I1,axiom,
    ! [X_a,B,A_1,X_2] :
      ( hBOOL(hAPP(X_a,bool,A_1,X_2))
     => hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2)) ),
    file('theBenchmark.p',fact_800_sup1I1) ).

fof(fact_801_sup1I2,axiom,
    ! [X_a,A_1,B,X_2] :
      ( hBOOL(hAPP(X_a,bool,B,X_2))
     => hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2)) ),
    file('theBenchmark.p',fact_801_sup1I2) ).

fof(fact_802_UnI1,axiom,
    ! [X_a,B,Ca,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) ),
    file('theBenchmark.p',fact_802_UnI1) ).

fof(fact_803_UnI2,axiom,
    ! [X_a,A_1,Ca,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) ),
    file('theBenchmark.p',fact_803_UnI2) ).

fof(fact_804_sup__Un__eq,axiom,
    ! [X_a,R_2,S,X_1] :
      ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)),X_1))
    <=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),R_2),S))) ),
    file('theBenchmark.p',fact_804_sup__Un__eq) ).

fof(fact_805_Collect__disj__eq,axiom,
    ! [X_a,Pa,Q_1] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),Pa)),Q_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)),
    file('theBenchmark.p',fact_805_Collect__disj__eq) ).

fof(fact_806_Un__UNIV__left,axiom,
    ! [X_a,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),top_top(fun(X_a,bool))),B) = top_top(fun(X_a,bool)),
    file('theBenchmark.p',fact_806_Un__UNIV__left) ).

fof(fact_807_Un__UNIV__right,axiom,
    ! [X_a,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),top_top(fun(X_a,bool))) = top_top(fun(X_a,bool)),
    file('theBenchmark.p',fact_807_Un__UNIV__right) ).

fof(fact_808_folding__image__simple__idem_Ounion__idem,axiom,
    ! [X_b,X_a,B,A_1,F,Z_1,G,Fa] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),Fa))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
         => hAPP(fun(X_b,bool),X_a,Fa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,A_1)),hAPP(fun(X_b,bool),X_a,Fa,B)) ) ) ),
    file('theBenchmark.p',fact_808_folding__image__simple__idem_Ounion__idem) ).

fof(fact_809_ivl__disj__un_I21_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [U,L,M] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
           => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),L),U) ) ) ),
    file('theBenchmark.p',fact_809_ivl__disj__un_I21_J) ).

fof(fact_810_atLeastLessThan__add__Un,axiom,
    ! [K,I,J] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J))
     => hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),J),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))) ),
    file('theBenchmark.p',fact_810_atLeastLessThan__add__Un) ).

fof(fact_811_ivl__disj__un_I22_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [U,L,M] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
           => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),L),U) ) ) ),
    file('theBenchmark.p',fact_811_ivl__disj__un_I22_J) ).

fof(fact_812_ivl__disj__un_I11_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [L,U] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),U))
         => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),L),U)),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),U)) = hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),L) ) ),
    file('theBenchmark.p',fact_812_ivl__disj__un_I11_J) ).

fof(fact_813_folding__idem_Ounion__idem,axiom,
    ! [X_a,X_b,B,A_1,F,Fa] :
      ( hBOOL(hAPP(fun(fun(X_a,bool),fun(X_b,X_b)),bool,hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool),finite_folding_idem(X_a,X_b),F),Fa))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
       => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
         => hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_b,X_b),fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(fun(X_b,X_b),fun(X_b,X_b)),comp(X_b,X_b,X_b),hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,A_1)),hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,B)) ) ) ),
    file('theBenchmark.p',fact_813_folding__idem_Ounion__idem) ).

fof(fact_814_ivl__disj__un_I15_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [U,L,M] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),L),M))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
           => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),L),U) ) ) ),
    file('theBenchmark.p',fact_814_ivl__disj__un_I15_J) ).

fof(fact_815_ivl__disj__un_I16_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [U,L,M] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),M),U))
           => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),L),U) ) ) ),
    file('theBenchmark.p',fact_815_ivl__disj__un_I16_J) ).

fof(fact_816_sup__apply,axiom,
    ! [X_b,X_a] :
      ( lattice(X_a)
     => ! [F,G,X_2] : hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),semilattice_sup_sup(fun(X_b,X_a)),F),G),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,G,X_2)) ),
    file('theBenchmark.p',fact_816_sup__apply) ).

fof(fact_817_sup__fun__def,axiom,
    ! [X_a,X_b] :
      ( lattice(X_b)
     => ! [F,G,X_1] : hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),semilattice_sup_sup(fun(X_a,X_b)),F),G),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)) ),
    file('theBenchmark.p',fact_817_sup__fun__def) ).

fof(fact_818_sup__Un__eq2,axiom,
    ! [X_b,X_a,R_2,S,X_1,Xa] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_2)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S)),X_1),Xa))
    <=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool)),semilattice_sup_sup(fun(product_prod(X_a,X_b),bool)),R_2),S))) ),
    file('theBenchmark.p',fact_818_sup__Un__eq2) ).

fof(fact_819_times_Oidem,axiom,
    ! [X_a] :
      ( ab_sem1668676832m_mult(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),A_2) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_819_times_Oidem) ).

fof(fact_820_mult__idem,axiom,
    ! [X_a] :
      ( ab_sem1668676832m_mult(X_a)
     => ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X) = ti(X_a,X) ),
    file('theBenchmark.p',fact_820_mult__idem) ).

fof(fact_821_mult__left__idem,axiom,
    ! [X_a] :
      ( ab_sem1668676832m_mult(X_a)
     => ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1) ),
    file('theBenchmark.p',fact_821_mult__left__idem) ).

fof(fact_822_sup_Oidem,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),A_2) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_822_sup_Oidem) ).

fof(fact_823_sup__idem,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),X) = ti(X_a,X) ),
    file('theBenchmark.p',fact_823_sup__idem) ).

fof(fact_824_sup_Ocommute,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),A_2) ),
    file('theBenchmark.p',fact_824_sup_Ocommute) ).

fof(fact_825_inf__sup__aci_I5_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X) ),
    file('theBenchmark.p',fact_825_inf__sup__aci_I5_J) ).

fof(fact_826_sup__commute,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X) ),
    file('theBenchmark.p',fact_826_sup__commute) ).

fof(fact_827_sup_Oleft__idem,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1) ),
    file('theBenchmark.p',fact_827_sup_Oleft__idem) ).

fof(fact_828_inf__sup__aci_I8_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) ),
    file('theBenchmark.p',fact_828_inf__sup__aci_I8_J) ).

fof(fact_829_sup__left__idem,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) ),
    file('theBenchmark.p',fact_829_sup__left__idem) ).

fof(fact_830_sup_Oleft__commute,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [B_1,A_2,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),C_1)) ),
    file('theBenchmark.p',fact_830_sup_Oleft__commute) ).

fof(fact_831_inf__sup__aci_I7_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z)) ),
    file('theBenchmark.p',fact_831_inf__sup__aci_I7_J) ).

fof(fact_832_sup__left__commute,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z)) ),
    file('theBenchmark.p',fact_832_sup__left__commute) ).

fof(fact_833_sup_Oassoc,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),C_1)) ),
    file('theBenchmark.p',fact_833_sup_Oassoc) ).

fof(fact_834_inf__sup__aci_I6_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) ),
    file('theBenchmark.p',fact_834_inf__sup__aci_I6_J) ).

fof(fact_835_sup__assoc,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) ),
    file('theBenchmark.p',fact_835_sup__assoc) ).

fof(fact_836_inf__sup__ord_I3_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y))) ),
    file('theBenchmark.p',fact_836_inf__sup__ord_I3_J) ).

fof(fact_837_sup__ge1,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y))) ),
    file('theBenchmark.p',fact_837_sup__ge1) ).

fof(fact_838_inf__sup__ord_I4_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [Y,X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y))) ),
    file('theBenchmark.p',fact_838_inf__sup__ord_I4_J) ).

fof(fact_839_sup__ge2,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [Y,X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y))) ),
    file('theBenchmark.p',fact_839_sup__ge2) ).

fof(fact_840_le__iff__sup,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [X_2,Y_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
        <=> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_1) = ti(X_a,Y_1) ) ),
    file('theBenchmark.p',fact_840_le__iff__sup) ).

fof(fact_841_le__sup__iff,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [X_2,Y_1,Z_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_1)),Z_1))
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z_1))
            & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)) ) ) ),
    file('theBenchmark.p',fact_841_le__sup__iff) ).

fof(fact_842_le__supI1,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [B_1,X,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1))) ) ),
    file('theBenchmark.p',fact_842_le__supI1) ).

fof(fact_843_le__supI2,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [A_2,X,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_1))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1))) ) ),
    file('theBenchmark.p',fact_843_le__supI2) ).

fof(fact_844_sup__absorb2,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = ti(X_a,Y) ) ),
    file('theBenchmark.p',fact_844_sup__absorb2) ).

fof(fact_845_sup__absorb1,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = ti(X_a,X) ) ),
    file('theBenchmark.p',fact_845_sup__absorb1) ).

fof(fact_846_le__supI,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [B_1,A_2,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),X))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)),X)) ) ) ),
    file('theBenchmark.p',fact_846_le__supI) ).

fof(fact_847_sup__least,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X)) ) ) ),
    file('theBenchmark.p',fact_847_sup__least) ).

fof(fact_848_sup__mono,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [B_1,D,A_2,C_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),C_1),D))) ) ) ),
    file('theBenchmark.p',fact_848_sup__mono) ).

fof(fact_849_le__supE,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [A_2,B_1,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)),X))
         => ~ ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X))
             => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),X)) ) ) ),
    file('theBenchmark.p',fact_849_le__supE) ).

fof(fact_850_less__supI2,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [A_2,X,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B_1))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1))) ) ),
    file('theBenchmark.p',fact_850_less__supI2) ).

fof(fact_851_less__supI1,axiom,
    ! [X_a] :
      ( semilattice_sup(X_a)
     => ! [B_1,X,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_2))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1))) ) ),
    file('theBenchmark.p',fact_851_less__supI1) ).

fof(fact_852_sup__top__left,axiom,
    ! [X_a] :
      ( bounded_lattice_top(X_a)
     => ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),top_top(X_a)),X) = top_top(X_a) ),
    file('theBenchmark.p',fact_852_sup__top__left) ).

fof(fact_853_sup__top__right,axiom,
    ! [X_a] :
      ( bounded_lattice_top(X_a)
     => ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),top_top(X_a)) = top_top(X_a) ),
    file('theBenchmark.p',fact_853_sup__top__right) ).

fof(fact_854_ivl__disj__un_I12_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [L,U] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),L),U))
         => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),L),U)),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),U)) = hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),L) ) ),
    file('theBenchmark.p',fact_854_ivl__disj__un_I12_J) ).

fof(fact_855_ivl__disj__un_I13_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [L,U] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),U))
         => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),L),U)),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),U)) = hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),L) ) ),
    file('theBenchmark.p',fact_855_ivl__disj__un_I13_J) ).

fof(fact_856_sup2E,axiom,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1))
     => ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1))
       => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1)) ) ),
    file('theBenchmark.p',fact_856_sup2E) ).

fof(fact_857_sup2CI,axiom,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1))
       => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1)) )
     => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1)) ),
    file('theBenchmark.p',fact_857_sup2CI) ).

fof(fact_858_sup2I1,axiom,
    ! [X_b,X_a,B,A_1,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1))
     => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1)) ),
    file('theBenchmark.p',fact_858_sup2I1) ).

fof(fact_859_sup2I2,axiom,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1))
     => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1)) ),
    file('theBenchmark.p',fact_859_sup2I2) ).

fof(fact_860_atLeast__iff,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [I,K] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),K)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),K),I)) ) ),
    file('theBenchmark.p',fact_860_atLeast__iff) ).

fof(fact_861_atLeast__eq__iff,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X_2,Y_1] :
          ( hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),X_2) = hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),Y_1)
        <=> ti(X_a,X_2) = ti(X_a,Y_1) ) ),
    file('theBenchmark.p',fact_861_atLeast__eq__iff) ).

fof(fact_862_atLeast__subset__iff,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X_2,Y_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),X_2)),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),Y_1)))
        <=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2)) ) ),
    file('theBenchmark.p',fact_862_atLeast__subset__iff) ).

fof(fact_863_atLeast__0,axiom,
    hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
    file('theBenchmark.p',fact_863_atLeast__0) ).

fof(fact_864_atLeast__Suc__greaterThan,axiom,
    ! [K] : hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,K)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),K),
    file('theBenchmark.p',fact_864_atLeast__Suc__greaterThan) ).

fof(fact_865_ivl__disj__un_I14_J,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [L,U] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),U))
         => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),L),U)),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),U)) = hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),L) ) ),
    file('theBenchmark.p',fact_865_ivl__disj__un_I14_J) ).

fof(fact_866_fold__image__Un__Int,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_mult(X_b)
     => ! [G,B,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
           => hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),one_one(X_b)),A_1)),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),one_one(X_b)),B)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),one_one(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),one_one(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) ) ) ),
    file('theBenchmark.p',fact_866_fold__image__Un__Int) ).

fof(fact_867_setsum__ub__add__nat,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,P_1,M,Na] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),one_one(nat))))
         => hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),P_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),P_1)))) ) ),
    file('theBenchmark.p',fact_867_setsum__ub__add__nat) ).

fof(fact_868_inf1E,axiom,
    ! [X_a,A_1,B,X_2] :
      ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2))
     => ~ ( hBOOL(hAPP(X_a,bool,A_1,X_2))
         => ~ hBOOL(hAPP(X_a,bool,B,X_2)) ) ),
    file('theBenchmark.p',fact_868_inf1E) ).

fof(fact_869_IntE,axiom,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
     => ~ ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
         => ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B)) ) ),
    file('theBenchmark.p',fact_869_IntE) ).

fof(fact_870_IntI,axiom,
    ! [X_a,B,Ca,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) ) ),
    file('theBenchmark.p',fact_870_IntI) ).

fof(fact_871_inf1I,axiom,
    ! [X_a,B,A_1,X_2] :
      ( hBOOL(hAPP(X_a,bool,A_1,X_2))
     => ( hBOOL(hAPP(X_a,bool,B,X_2))
       => hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2)) ) ),
    file('theBenchmark.p',fact_871_inf1I) ).

fof(fact_872_finite__Int,axiom,
    ! [X_a,G_1,Fa] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),G_1))
        | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa)) )
     => hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),Fa),G_1))) ),
    file('theBenchmark.p',fact_872_finite__Int) ).

fof(fact_873_distrib__inf__le,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y,Z] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)))) ),
    file('theBenchmark.p',fact_873_distrib__inf__le) ).

fof(fact_874_distrib__sup__le,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y,Z] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z)))) ),
    file('theBenchmark.p',fact_874_distrib__sup__le) ).

fof(fact_875_Un__Int__assoc__eq,axiom,
    ! [X_a,A_1,B,C] :
      ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C))
    <=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C),A_1)) ),
    file('theBenchmark.p',fact_875_Un__Int__assoc__eq) ).

fof(fact_876_sup__inf__distrib2,axiom,
    ! [X_a] :
      ( distrib_lattice(X_a)
     => ! [Y,Z,X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Z),X)) ),
    file('theBenchmark.p',fact_876_sup__inf__distrib2) ).

fof(fact_877_inf__sup__distrib2,axiom,
    ! [X_a] :
      ( distrib_lattice(X_a)
     => ! [Y,Z,X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Z),X)) ),
    file('theBenchmark.p',fact_877_inf__sup__distrib2) ).

fof(fact_878_sup__inf__distrib1,axiom,
    ! [X_a] :
      ( distrib_lattice(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z)) ),
    file('theBenchmark.p',fact_878_sup__inf__distrib1) ).

fof(fact_879_inf__sup__distrib1,axiom,
    ! [X_a] :
      ( distrib_lattice(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z)) ),
    file('theBenchmark.p',fact_879_inf__sup__distrib1) ).

fof(fact_880_sup__inf__absorb,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)) = ti(X_a,X) ),
    file('theBenchmark.p',fact_880_sup__inf__absorb) ).

fof(fact_881_inf__sup__absorb,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)) = ti(X_a,X) ),
    file('theBenchmark.p',fact_881_inf__sup__absorb) ).

fof(fact_882_Int__Un__distrib,axiom,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C)),
    file('theBenchmark.p',fact_882_Int__Un__distrib) ).

fof(fact_883_Un__Int__distrib,axiom,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),C)),
    file('theBenchmark.p',fact_883_Un__Int__distrib) ).

fof(fact_884_Int__Un__distrib2,axiom,
    ! [X_a,B,C,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),A_1)),
    file('theBenchmark.p',fact_884_Int__Un__distrib2) ).

fof(fact_885_Un__Int__distrib2,axiom,
    ! [X_a,B,C,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C),A_1)),
    file('theBenchmark.p',fact_885_Un__Int__distrib2) ).

fof(fact_886_Un__Int__crazy,axiom,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C),A_1)),
    file('theBenchmark.p',fact_886_Un__Int__crazy) ).

fof(fact_887_if__image__distrib,axiom,
    ! [X_b,X_a,Pa,F,G,S] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_b,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combs(X_b,X_a,fun(X_a,X_a)),hAPP(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),X_b),if(X_a)),Pa)),F)),G)),S) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),S),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),S),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),Pa))))),
    file('theBenchmark.p',fact_887_if__image__distrib) ).

fof(fact_888_setsum__shift__bounds__cl__nat__ivl,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,M,K,Na] : hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na)) ),
    file('theBenchmark.p',fact_888_setsum__shift__bounds__cl__nat__ivl) ).

fof(fact_889_setsum__shift__bounds__cl__Suc__ivl,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,M,Na] : hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na)) ),
    file('theBenchmark.p',fact_889_setsum__shift__bounds__cl__Suc__ivl) ).

fof(fact_890_setsum__shift__bounds__nat__ivl,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,M,K,Na] : hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Na)) ),
    file('theBenchmark.p',fact_890_setsum__shift__bounds__nat__ivl) ).

fof(fact_891_setsum__image__gen,axiom,
    ! [X_c,X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [G,F,S] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S))
         => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),S) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,X_b),hAPP(fun(fun(X_a,bool),X_b),fun(fun(X_c,fun(X_a,bool)),fun(X_c,X_b)),combb(fun(X_a,bool),X_b,X_c),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),collect(X_a)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_c,bool)),fun(X_c,fun(X_a,bool)),combc(X_a,X_c,bool),hAPP(fun(X_a,X_c),fun(X_a,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_a,X_c),fun(X_a,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_a),fequal(X_c)),F)))))),hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),F),S)) ) ),
    file('theBenchmark.p',fact_891_setsum__image__gen) ).

fof(fact_892_setsum__setsum__restrict,axiom,
    ! [X_b,X_a,X_c] :
      ( comm_monoid_add(X_c)
     => ! [F,R_2,T_3,S] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S))
         => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_3))
           => hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,X_c),hAPP(fun(X_a,fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,X_c)),combs(X_a,fun(X_b,bool),X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c)),hAPP(fun(fun(X_b,X_c),fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c))),combb(fun(X_b,X_c),fun(fun(X_b,bool),X_c),X_a),big_co1399186613setsum(X_b,X_c)),F)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),T_3)))),R_2)))),S) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,X_c)),combs(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),collect(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_2))))),T_3) ) ) ),
    file('theBenchmark.p',fact_892_setsum__setsum__restrict) ).

fof(fact_893_Int__UNIV__right,axiom,
    ! [X_a,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),top_top(fun(X_a,bool))) = ti(fun(X_a,bool),A_1),
    file('theBenchmark.p',fact_893_Int__UNIV__right) ).

fof(fact_894_Int__UNIV__left,axiom,
    ! [X_a,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),top_top(fun(X_a,bool))),B) = ti(fun(X_a,bool),B),
    file('theBenchmark.p',fact_894_Int__UNIV__left) ).

fof(fact_895_Collect__conj__eq,axiom,
    ! [X_a,Pa,Q_1] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),Pa)),Q_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)),
    file('theBenchmark.p',fact_895_Collect__conj__eq) ).

fof(fact_896_Int__Collect,axiom,
    ! [X_a,X_2,A_1,Pa] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa))))
    <=> ( hBOOL(hAPP(X_a,bool,Pa,X_2))
        & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ) ),
    file('theBenchmark.p',fact_896_Int__Collect) ).

fof(fact_897_inf__Int__eq,axiom,
    ! [X_a,R_2,S,X_1] :
      ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)),X_1))
    <=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),R_2),S))) ),
    file('theBenchmark.p',fact_897_inf__Int__eq) ).

fof(fact_898_inf1D2,axiom,
    ! [X_a,A_1,B,X_2] :
      ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2))
     => hBOOL(hAPP(X_a,bool,B,X_2)) ),
    file('theBenchmark.p',fact_898_inf1D2) ).

fof(fact_899_inf1D1,axiom,
    ! [X_a,A_1,B,X_2] :
      ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2))
     => hBOOL(hAPP(X_a,bool,A_1,X_2)) ),
    file('theBenchmark.p',fact_899_inf1D1) ).

fof(fact_900_IntD2,axiom,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B)) ),
    file('theBenchmark.p',fact_900_IntD2) ).

fof(fact_901_IntD1,axiom,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
     => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) ),
    file('theBenchmark.p',fact_901_IntD1) ).

fof(fact_902_Int__assoc,axiom,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)),
    file('theBenchmark.p',fact_902_Int__assoc) ).

fof(fact_903_Int__iff,axiom,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
    <=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
        & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) ) ),
    file('theBenchmark.p',fact_903_Int__iff) ).

fof(fact_904_Int__left__commute,axiom,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C)),
    file('theBenchmark.p',fact_904_Int__left__commute) ).

fof(fact_905_Int__left__absorb,axiom,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),
    file('theBenchmark.p',fact_905_Int__left__absorb) ).

fof(fact_906_Int__commute,axiom,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),A_1),
    file('theBenchmark.p',fact_906_Int__commute) ).

fof(fact_907_Int__def,axiom,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))),
    file('theBenchmark.p',fact_907_Int__def) ).

fof(fact_908_Int__absorb,axiom,
    ! [X_a,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),A_1) = ti(fun(X_a,bool),A_1),
    file('theBenchmark.p',fact_908_Int__absorb) ).

fof(fact_909_Int__mono,axiom,
    ! [X_a,B,D_1,A_1,C] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),D_1))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),D_1))) ) ),
    file('theBenchmark.p',fact_909_Int__mono) ).

fof(fact_910_Int__greatest,axiom,
    ! [X_a,B,C,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C),B))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) ) ),
    file('theBenchmark.p',fact_910_Int__greatest) ).

fof(fact_911_Int__absorb1,axiom,
    ! [X_a,B,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
     => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),B) ),
    file('theBenchmark.p',fact_911_Int__absorb1) ).

fof(fact_912_Int__absorb2,axiom,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
     => hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),A_1) ),
    file('theBenchmark.p',fact_912_Int__absorb2) ).

fof(fact_913_Int__lower2,axiom,
    ! [X_a,A_1,B] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),B)),
    file('theBenchmark.p',fact_913_Int__lower2) ).

fof(fact_914_Int__lower1,axiom,
    ! [X_a,A_1,B] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),A_1)),
    file('theBenchmark.p',fact_914_Int__lower1) ).

fof(fact_915_inj__on__Int,axiom,
    ! [X_a,X_b,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B))
       => hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) ) ),
    file('theBenchmark.p',fact_915_inj__on__Int) ).

fof(fact_916_setsum__restrict__set_H_H,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [F,Pa,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),Pa))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),Pa)),F)),zero_zero(X_b))),A_1) ) ),
    file('theBenchmark.p',fact_916_setsum__restrict__set_H_H) ).

fof(fact_917_setsum__restrict__set_H,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [F,B,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B)))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))),F)),zero_zero(X_b))),A_1) ) ),
    file('theBenchmark.p',fact_917_setsum__restrict__set_H) ).

fof(fact_918_image__Int__subset,axiom,
    ! [X_a,X_b,F,A_1,B] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B)))),
    file('theBenchmark.p',fact_918_image__Int__subset) ).

fof(fact_919_setsum__shift__bounds__Suc__ivl,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,M,Na] : hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Na)) ),
    file('theBenchmark.p',fact_919_setsum__shift__bounds__Suc__ivl) ).

fof(fact_920_le__infE,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)))
         => ~ ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2))
             => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_1)) ) ) ),
    file('theBenchmark.p',fact_920_le__infE) ).

fof(fact_921_inf__mono,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [B_1,D,A_2,C_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),C_1),D))) ) ) ),
    file('theBenchmark.p',fact_921_inf__mono) ).

fof(fact_922_inf__greatest,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))) ) ) ),
    file('theBenchmark.p',fact_922_inf__greatest) ).

fof(fact_923_le__infI,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [B_1,X,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1))) ) ) ),
    file('theBenchmark.p',fact_923_le__infI) ).

fof(fact_924_inf__absorb2,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = ti(X_a,Y) ) ),
    file('theBenchmark.p',fact_924_inf__absorb2) ).

fof(fact_925_inf__absorb1,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = ti(X_a,X) ) ),
    file('theBenchmark.p',fact_925_inf__absorb1) ).

fof(fact_926_le__infI2,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [A_2,B_1,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),X))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),X)) ) ),
    file('theBenchmark.p',fact_926_le__infI2) ).

fof(fact_927_le__infI1,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [B_1,A_2,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),X)) ) ),
    file('theBenchmark.p',fact_927_le__infI1) ).

fof(fact_928_le__inf__iff,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X_2,Y_1,Z_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y_1),Z_1)))
        <=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1))
            & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) ) ) ),
    file('theBenchmark.p',fact_928_le__inf__iff) ).

fof(fact_929_le__iff__inf,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X_2,Y_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
        <=> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),Y_1) = ti(X_a,X_2) ) ),
    file('theBenchmark.p',fact_929_le__iff__inf) ).

fof(fact_930_inf__le2,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Y)) ),
    file('theBenchmark.p',fact_930_inf__le2) ).

fof(fact_931_inf__sup__ord_I2_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Y)) ),
    file('theBenchmark.p',fact_931_inf__sup__ord_I2_J) ).

fof(fact_932_inf__le1,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),X)) ),
    file('theBenchmark.p',fact_932_inf__le1) ).

fof(fact_933_inf__sup__ord_I1_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),X)) ),
    file('theBenchmark.p',fact_933_inf__sup__ord_I1_J) ).

fof(fact_934_inf__eq__top__iff,axiom,
    ! [X_a] :
      ( bounded_lattice_top(X_a)
     => ! [X_2,Y_1] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),Y_1) = top_top(X_a)
        <=> ( ti(X_a,Y_1) = top_top(X_a)
            & ti(X_a,X_2) = top_top(X_a) ) ) ),
    file('theBenchmark.p',fact_934_inf__eq__top__iff) ).

fof(fact_935_inf__top__right,axiom,
    ! [X_a] :
      ( bounded_lattice_top(X_a)
     => ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),top_top(X_a)) = ti(X_a,X) ),
    file('theBenchmark.p',fact_935_inf__top__right) ).

fof(fact_936_inf__top__left,axiom,
    ! [X_a] :
      ( bounded_lattice_top(X_a)
     => ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),top_top(X_a)),X) = ti(X_a,X) ),
    file('theBenchmark.p',fact_936_inf__top__left) ).

fof(fact_937_inf__apply,axiom,
    ! [X_b,X_a] :
      ( lattice(X_a)
     => ! [F,G,X_2] : hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),semilattice_inf_inf(fun(X_b,X_a)),F),G),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,G,X_2)) ),
    file('theBenchmark.p',fact_937_inf__apply) ).

fof(fact_938_inf__assoc,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) ),
    file('theBenchmark.p',fact_938_inf__assoc) ).

fof(fact_939_inf__sup__aci_I2_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) ),
    file('theBenchmark.p',fact_939_inf__sup__aci_I2_J) ).

fof(fact_940_inf_Oassoc,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),C_1)) ),
    file('theBenchmark.p',fact_940_inf_Oassoc) ).

fof(fact_941_inf__left__commute,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z)) ),
    file('theBenchmark.p',fact_941_inf__left__commute) ).

fof(fact_942_inf__sup__aci_I3_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z)) ),
    file('theBenchmark.p',fact_942_inf__sup__aci_I3_J) ).

fof(fact_943_inf_Oleft__commute,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [B_1,A_2,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),C_1)) ),
    file('theBenchmark.p',fact_943_inf_Oleft__commute) ).

fof(fact_944_inf__left__idem,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) ),
    file('theBenchmark.p',fact_944_inf__left__idem) ).

fof(fact_945_inf__sup__aci_I4_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) ),
    file('theBenchmark.p',fact_945_inf__sup__aci_I4_J) ).

fof(fact_946_inf_Oleft__idem,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1) ),
    file('theBenchmark.p',fact_946_inf_Oleft__idem) ).

fof(fact_947_inf__commute,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X) ),
    file('theBenchmark.p',fact_947_inf__commute) ).

fof(fact_948_inf__sup__aci_I1_J,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X) ),
    file('theBenchmark.p',fact_948_inf__sup__aci_I1_J) ).

fof(fact_949_inf_Ocommute,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),A_2) ),
    file('theBenchmark.p',fact_949_inf_Ocommute) ).

fof(fact_950_inf__fun__def,axiom,
    ! [X_a,X_b] :
      ( lattice(X_b)
     => ! [F,G,X_1] : hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),semilattice_inf_inf(fun(X_a,X_b)),F),G),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)) ),
    file('theBenchmark.p',fact_950_inf__fun__def) ).

fof(fact_951_inf__idem,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),X) = ti(X_a,X) ),
    file('theBenchmark.p',fact_951_inf__idem) ).

fof(fact_952_inf_Oidem,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),A_2) = ti(X_a,A_2) ),
    file('theBenchmark.p',fact_952_inf_Oidem) ).

fof(fact_953_less__infI1,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [B_1,A_2,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),X))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),X)) ) ),
    file('theBenchmark.p',fact_953_less__infI1) ).

fof(fact_954_less__infI2,axiom,
    ! [X_a] :
      ( semilattice_inf(X_a)
     => ! [A_2,B_1,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),X))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),X)) ) ),
    file('theBenchmark.p',fact_954_less__infI2) ).

fof(fact_955_setsum__add__nat__ivl,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,P_1,M,Na] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),P_1))
           => hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Na))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Na),P_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),P_1)) ) ) ),
    file('theBenchmark.p',fact_955_setsum__add__nat__ivl) ).

fof(fact_956_setsum__shift__lb__Suc0__0,axiom,
    ! [K,F] :
      ( hAPP(nat,nat,F,zero_zero(nat)) = zero_zero(nat)
     => hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),K)) ),
    file('theBenchmark.p',fact_956_setsum__shift__lb__Suc0__0) ).

fof(fact_957_inj__on__image__Int,axiom,
    ! [X_a,X_b,B,A_1,F,C] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),C))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C))
       => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C))
         => hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)) ) ) ),
    file('theBenchmark.p',fact_957_inj__on__image__Int) ).

fof(fact_958_image__Int,axiom,
    ! [X_a,X_b,A_1,B,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
     => hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)) ),
    file('theBenchmark.p',fact_958_image__Int) ).

fof(fact_959_setsum__shift__lb__Suc0__0__upt,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [K,F] :
          ( hAPP(nat,X_a,F,zero_zero(nat)) = zero_zero(X_a)
         => hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)) ) ),
    file('theBenchmark.p',fact_959_setsum__shift__lb__Suc0__0__upt) ).

fof(fact_960_setsum__head__upt__Suc,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,M,Na] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
         => hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Na)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,M)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,M)),Na))) ) ),
    file('theBenchmark.p',fact_960_setsum__head__upt__Suc) ).

fof(fact_961_setsum__head__Suc,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,M,Na] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
         => hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,M)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,M)),Na))) ) ),
    file('theBenchmark.p',fact_961_setsum__head__Suc) ).

fof(fact_962_card__Un__Int,axiom,
    ! [X_a,B,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) ) ),
    file('theBenchmark.p',fact_962_card__Un__Int) ).

fof(fact_963_card_Ounion__inter,axiom,
    ! [X_a,B,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)) ) ),
    file('theBenchmark.p',fact_963_card_Ounion__inter) ).

fof(fact_964_setsum__op__ivl__Suc,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,Na,M] :
          ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
           => hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),hAPP(nat,nat,suc,Na))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Na))),hAPP(nat,X_a,F,Na)) )
          & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
           => hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),hAPP(nat,nat,suc,Na))) = zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_964_setsum__op__ivl__Suc) ).

fof(fact_965_setsum__cl__ivl__Suc,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,Na,M] :
          ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Na)),M))
           => hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,suc,Na))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,Na))) )
          & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Na)),M))
           => hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,suc,Na))) = zero_zero(X_a) ) ) ),
    file('theBenchmark.p',fact_965_setsum__cl__ivl__Suc) ).

fof(fact_966_setsum__head,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [Pa,M,Na] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
         => hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),Pa),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,Pa,M)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),Pa),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),M),Na))) ) ),
    file('theBenchmark.p',fact_966_setsum__head) ).

fof(fact_967_card_Ounion__inter__neutral,axiom,
    ! [X_a,B,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
       => ( ( ? [X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
           => one_one(nat) = zero_zero(nat) )
         => hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)) ) ) ),
    file('theBenchmark.p',fact_967_card_Ounion__inter__neutral) ).

fof(fact_968_fold__image__Un__one,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_mult(X_b)
     => ! [F,T_3,S] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3))
           => ( ! [X_1] :
                  ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),S),T_3)))
                 => hAPP(X_a,X_b,F,X_1) = one_one(X_b) )
             => hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),F),one_one(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),S),T_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),F),one_one(X_b)),S)),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),F),one_one(X_b)),T_3)) ) ) ) ),
    file('theBenchmark.p',fact_968_fold__image__Un__one) ).

fof(fact_969_inf__Int__eq2,axiom,
    ! [X_b,X_a,R_2,S,X_1,Xa] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_2)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S)),X_1),Xa))
    <=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool)),semilattice_inf_inf(fun(product_prod(X_a,X_b),bool)),R_2),S))) ),
    file('theBenchmark.p',fact_969_inf__Int__eq2) ).

fof(fact_970_setsum_OF__eq,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [G,A_1] :
          ( ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
           => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1) = zero_zero(X_b) )
          & ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
           => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),plus_plus(X_b)),G),zero_zero(X_b)),A_1) ) ) ),
    file('theBenchmark.p',fact_970_setsum_OF__eq) ).

fof(fact_971_setsum_Oeq__fold,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [G,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),plus_plus(X_b)),G),zero_zero(X_b)),A_1) ) ),
    file('theBenchmark.p',fact_971_setsum_Oeq__fold) ).

fof(fact_972_inf2E,axiom,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1))
     => ~ ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1))
         => ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1)) ) ),
    file('theBenchmark.p',fact_972_inf2E) ).

fof(fact_973_inf2I,axiom,
    ! [X_b,X_a,B,A_1,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1))
     => ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1))
       => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1)) ) ),
    file('theBenchmark.p',fact_973_inf2I) ).

fof(fact_974_inf2D2,axiom,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1))
     => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1)) ),
    file('theBenchmark.p',fact_974_inf2D2) ).

fof(fact_975_inf2D1,axiom,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1))
     => hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1)) ),
    file('theBenchmark.p',fact_975_inf2D1) ).

fof(fact_976_Sup__fin_Oidem,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),X) = ti(X_a,X) ),
    file('theBenchmark.p',fact_976_Sup__fin_Oidem) ).

fof(fact_977_Inf__fin_Oidem,axiom,
    ! [X_a] :
      ( lattice(X_a)
     => ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),X) = ti(X_a,X) ),
    file('theBenchmark.p',fact_977_Inf__fin_Oidem) ).

fof(fact_978_setsum__commute,axiom,
    ! [X_b,X_c,X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,B,A_1] : hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),F)),B)),A_1) = hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),hAPP(fun(X_b,bool),fun(X_c,X_a),hAPP(fun(X_c,fun(fun(X_b,bool),X_a)),fun(fun(X_b,bool),fun(X_c,X_a)),combc(X_c,fun(X_b,bool),X_a),hAPP(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a)),hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),fun(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a))),combb(fun(X_b,X_a),fun(fun(X_b,bool),X_a),X_c),big_co1399186613setsum(X_b,X_a)),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_c,fun(X_b,X_a)),combc(X_b,X_c,X_a),F))),A_1)),B) ),
    file('theBenchmark.p',fact_978_setsum__commute) ).

fof(fact_979_setsum__0,axiom,
    ! [X_b,X_a] :
      ( comm_monoid_add(X_a)
     => ! [A_1] : hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),zero_zero(X_a))),A_1) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_979_setsum__0) ).

fof(fact_980_setsum__addf,axiom,
    ! [X_b,X_a] :
      ( comm_monoid_add(X_a)
     => ! [F,G,A_1] : hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),plus_plus(X_a)),F)),G)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_1)) ),
    file('theBenchmark.p',fact_980_setsum__addf) ).

fof(fact_981_setsum__right__distrib,axiom,
    ! [X_b,X_a] :
      ( semiring_0(X_a)
     => ! [R_1,F,A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_1)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1)),F)),A_1) ),
    file('theBenchmark.p',fact_981_setsum__right__distrib) ).

fof(fact_982_setsum__left__distrib,axiom,
    ! [X_b,X_a] :
      ( semiring_0(X_a)
     => ! [F,A_1,R_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_1)),R_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F)),R_1)),A_1) ),
    file('theBenchmark.p',fact_982_setsum__left__distrib) ).

fof(fact_983_setsum__product,axiom,
    ! [X_b,X_c,X_a] :
      ( semiring_0(X_a)
     => ! [F,A_1,G,B] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_1)),hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),G),B)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),hAPP(fun(X_c,X_a),fun(X_b,fun(X_c,X_a)),hAPP(fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_c,X_a),fun(X_b,fun(X_c,X_a))),combc(X_b,fun(X_c,X_a),fun(X_c,X_a)),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),hAPP(fun(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a)))),combb(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a)),X_b),combb(X_a,X_a,X_c)),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F))),G))),B)),A_1) ),
    file('theBenchmark.p',fact_983_setsum__product) ).

fof(fact_984_setsum__infinite,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [F,A_1] :
          ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_1) = zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_984_setsum__infinite) ).

fof(fact_985_setsum_Oinfinite,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [G,A_1] :
          ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1) = zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_985_setsum_Oinfinite) ).

fof(fact_986_setsum__eq__0__iff,axiom,
    ! [X_a,F,Fa] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa))
     => ( hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),Fa) = zero_zero(nat)
      <=> ! [X_1] :
            ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),Fa))
           => hAPP(X_a,nat,F,X_1) = zero_zero(nat) ) ) ),
    file('theBenchmark.p',fact_986_setsum__eq__0__iff) ).

fof(fact_987_setsum__delta_H,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [Ba,Aa,S] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S))
         => ( ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S))
             => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),Aa))),Ba)),zero_zero(X_b))),S) = zero_zero(X_b) )
            & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S))
             => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),Aa))),Ba)),zero_zero(X_b))),S) = hAPP(X_a,X_b,Ba,Aa) ) ) ) ),
    file('theBenchmark.p',fact_987_setsum__delta_H) ).

fof(fact_988_setsum__delta,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [Ba,Aa,S] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S))
         => ( ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S))
             => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Aa))),Ba)),zero_zero(X_b))),S) = zero_zero(X_b) )
            & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S))
             => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Aa))),Ba)),zero_zero(X_b))),S) = hAPP(X_a,X_b,Ba,Aa) ) ) ) ),
    file('theBenchmark.p',fact_988_setsum__delta) ).

fof(fact_989_setsum_Odistrib,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [G,Ha,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),G)),Ha)),A_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),Ha),A_1)) ) ),
    file('theBenchmark.p',fact_989_setsum_Odistrib) ).

fof(fact_990_card__eq__setsum,axiom,
    ! [X_a,A_1] : hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),A_1),
    file('theBenchmark.p',fact_990_card__eq__setsum) ).

fof(fact_991_setsum__reindex,axiom,
    ! [X_a,X_b,X_c] :
      ( comm_monoid_add(X_c)
     => ! [Ha,F,B] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B))
         => hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),Ha),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)) = hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),Ha),F)),B) ) ),
    file('theBenchmark.p',fact_991_setsum__reindex) ).

fof(fact_992_setsum__eq__Suc0__iff,axiom,
    ! [X_a,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_1) = hAPP(nat,nat,suc,zero_zero(nat))
      <=> ? [X_1] :
            ( ! [Xa] :
                ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1))
               => ( ti(X_a,X_1) != ti(X_a,Xa)
                 => hAPP(X_a,nat,F,Xa) = zero_zero(nat) ) )
            & hAPP(X_a,nat,F,X_1) = hAPP(nat,nat,suc,zero_zero(nat))
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_992_setsum__eq__Suc0__iff) ).

fof(fact_993_setsum__eq__1__iff,axiom,
    ! [X_a,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
     => ( hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_1) = one_one(nat)
      <=> ? [X_1] :
            ( ! [Xa] :
                ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1))
               => ( ti(X_a,X_1) != ti(X_a,Xa)
                 => hAPP(X_a,nat,F,Xa) = zero_zero(nat) ) )
            & hAPP(X_a,nat,F,X_1) = one_one(nat)
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_993_setsum__eq__1__iff) ).

fof(fact_994_setsum__restrict__set,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [F,B,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))),F)),zero_zero(X_b))),A_1) ) ),
    file('theBenchmark.p',fact_994_setsum__restrict__set) ).

fof(fact_995_setsum__Un__Int,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [G,B,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
           => hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),B)) ) ) ),
    file('theBenchmark.p',fact_995_setsum__Un__Int) ).

fof(fact_996_setsum_Oreindex,axiom,
    ! [X_a,X_b] :
      ( comm_monoid_add(X_b)
     => ! [G,Ha,A_1] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
         => ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),Ha),A_1))
           => hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),Ha),A_1)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),comp(X_a,X_b,X_a),G),Ha)),A_1) ) ) ),
    file('theBenchmark.p',fact_996_setsum_Oreindex) ).

fof(arity_HOL_Obool___Lattices_Obounded__lattice,axiom,
    bounded_lattice(bool),
    file('theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice) ).

fof(arity_fun___Lattices_Obounded__lattice,axiom,
    ! [T_2,T_1] :
      ( bounded_lattice(T_1)
     => bounded_lattice(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Lattices_Obounded__lattice) ).

fof(arity_fun___Lattices_Obounded__lattice__top,axiom,
    ! [T_2,T_1] :
      ( bounded_lattice(T_1)
     => bounded_lattice_top(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Lattices_Obounded__lattice__top) ).

fof(arity_fun___Lattices_Osemilattice__sup,axiom,
    ! [T_2,T_1] :
      ( lattice(T_1)
     => semilattice_sup(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Lattices_Osemilattice__sup) ).

fof(arity_fun___Lattices_Osemilattice__inf,axiom,
    ! [T_2,T_1] :
      ( lattice(T_1)
     => semilattice_inf(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Lattices_Osemilattice__inf) ).

fof(arity_fun___Lattices_Odistrib__lattice,axiom,
    ! [T_2,T_1] :
      ( distrib_lattice(T_1)
     => distrib_lattice(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Lattices_Odistrib__lattice) ).

fof(arity_fun___Orderings_Opreorder,axiom,
    ! [T_2,T_1] :
      ( preorder(T_1)
     => preorder(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Orderings_Opreorder) ).

fof(arity_fun___Finite__Set_Ofinite,axiom,
    ! [T_2,T_1] :
      ( ( finite_finite(T_2)
        & finite_finite(T_1) )
     => finite_finite(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).

fof(arity_fun___Lattices_Olattice,axiom,
    ! [T_2,T_1] :
      ( lattice(T_1)
     => lattice(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Lattices_Olattice) ).

fof(arity_fun___Orderings_Oorder,axiom,
    ! [T_2,T_1] :
      ( order(T_1)
     => order(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Orderings_Oorder) ).

fof(arity_fun___Orderings_Otop,axiom,
    ! [T_2,T_1] :
      ( top(T_1)
     => top(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Orderings_Otop) ).

fof(arity_fun___Orderings_Oord,axiom,
    ! [T_2,T_1] :
      ( ord(T_1)
     => ord(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Orderings_Oord) ).

fof(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc,axiom,
    semiri456707255roduct(nat),
    file('theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).

fof(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
    ordere223160158up_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    ordere236663937imp_le(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict,axiom,
    linord893533164strict(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Nat_Onat___Rings_Olinordered__semiring__strict,axiom,
    linord20386208strict(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring__strict) ).

fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
    ordere779506340up_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).

fof(arity_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
    ordere216010020id_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).

fof(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
    cancel146912293up_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Nat_Onat___Rings_Oordered__cancel__semiring,axiom,
    ordere453448008miring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Oordered__cancel__semiring) ).

fof(arity_Nat_Onat___Rings_Oordered__comm__semiring,axiom,
    ordere1490568538miring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Oordered__comm__semiring) ).

fof(arity_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
    cancel_semigroup_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).

fof(arity_Nat_Onat___Rings_Olinordered__semiring,axiom,
    linordered_semiring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring) ).

fof(arity_Nat_Onat___Rings_Olinordered__semidom,axiom,
    linordered_semidom(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).

fof(arity_Nat_Onat___Lattices_Osemilattice__sup,axiom,
    semilattice_sup(nat),
    file('theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__sup) ).

fof(arity_Nat_Onat___Lattices_Osemilattice__inf,axiom,
    semilattice_inf(nat),
    file('theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__inf) ).

fof(arity_Nat_Onat___Lattices_Odistrib__lattice,axiom,
    distrib_lattice(nat),
    file('theBenchmark.p',arity_Nat_Onat___Lattices_Odistrib__lattice) ).

fof(arity_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
    ab_semigroup_mult(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).

fof(arity_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
    comm_monoid_mult(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).

fof(arity_Nat_Onat___Groups_Oab__semigroup__add,axiom,
    ab_semigroup_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).

fof(arity_Nat_Onat___Rings_Oordered__semiring,axiom,
    ordered_semiring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Oordered__semiring) ).

fof(arity_Nat_Onat___Rings_Ono__zero__divisors,axiom,
    no_zero_divisors(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).

fof(arity_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
    comm_monoid_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).

fof(arity_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
    comm_semiring_1(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).

fof(arity_Nat_Onat___Rings_Ocomm__semiring,axiom,
    comm_semiring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring) ).

fof(arity_Nat_Onat___Rings_Ozero__neq__one,axiom,
    zero_neq_one(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).

fof(arity_Nat_Onat___Orderings_Opreorder,axiom,
    preorder(nat),
    file('theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).

fof(arity_Nat_Onat___Orderings_Olinorder,axiom,
    linorder(nat),
    file('theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).

fof(arity_Nat_Onat___Groups_Omonoid__mult,axiom,
    monoid_mult(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).

fof(arity_Nat_Onat___Groups_Omonoid__add,axiom,
    monoid_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).

fof(arity_Nat_Onat___Rings_Osemiring__0,axiom,
    semiring_0(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).

fof(arity_Nat_Onat___Lattices_Olattice,axiom,
    lattice(nat),
    file('theBenchmark.p',arity_Nat_Onat___Lattices_Olattice) ).

fof(arity_Nat_Onat___Rings_Omult__zero,axiom,
    mult_zero(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).

fof(arity_Nat_Onat___Orderings_Oorder,axiom,
    order(nat),
    file('theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).

fof(arity_Nat_Onat___Rings_Osemiring,axiom,
    semiring(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).

fof(arity_Nat_Onat___Orderings_Oord,axiom,
    ord(nat),
    file('theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).

fof(arity_Nat_Onat___Groups_Ozero,axiom,
    zero(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

fof(arity_Nat_Onat___Groups_Oone,axiom,
    one(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).

fof(arity_HOL_Obool___Lattices_Obounded__lattice__top,axiom,
    bounded_lattice_top(bool),
    file('theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice__top) ).

fof(arity_HOL_Obool___Lattices_Osemilattice__sup,axiom,
    semilattice_sup(bool),
    file('theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__sup) ).

fof(arity_HOL_Obool___Lattices_Osemilattice__inf,axiom,
    semilattice_inf(bool),
    file('theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__inf) ).

fof(arity_HOL_Obool___Lattices_Odistrib__lattice,axiom,
    distrib_lattice(bool),
    file('theBenchmark.p',arity_HOL_Obool___Lattices_Odistrib__lattice) ).

fof(arity_HOL_Obool___Orderings_Opreorder,axiom,
    preorder(bool),
    file('theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).

fof(arity_HOL_Obool___Finite__Set_Ofinite,axiom,
    finite_finite(bool),
    file('theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).

fof(arity_HOL_Obool___Lattices_Olattice,axiom,
    lattice(bool),
    file('theBenchmark.p',arity_HOL_Obool___Lattices_Olattice) ).

fof(arity_HOL_Obool___Orderings_Oorder,axiom,
    order(bool),
    file('theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).

fof(arity_HOL_Obool___Orderings_Otop,axiom,
    top(bool),
    file('theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).

fof(arity_HOL_Obool___Orderings_Oord,axiom,
    ord(bool),
    file('theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).

fof(arity_sum___Finite__Set_Ofinite,axiom,
    ! [T_2,T_1] :
      ( ( finite_finite(T_2)
        & finite_finite(T_1) )
     => finite_finite(sum_sum(T_2,T_1)) ),
    file('theBenchmark.p',arity_sum___Finite__Set_Ofinite) ).

fof(arity_Option_Ooption___Finite__Set_Ofinite,axiom,
    ! [T_1] :
      ( finite_finite(T_1)
     => finite_finite(option(T_1)) ),
    file('theBenchmark.p',arity_Option_Ooption___Finite__Set_Ofinite) ).

fof(arity_prod___Finite__Set_Ofinite,axiom,
    ! [T_2,T_1] :
      ( ( finite_finite(T_2)
        & finite_finite(T_1) )
     => finite_finite(product_prod(T_2,T_1)) ),
    file('theBenchmark.p',arity_prod___Finite__Set_Ofinite) ).

fof(arity_Product__Type_Ounit___Finite__Set_Ofinite,axiom,
    finite_finite(product_unit),
    file('theBenchmark.p',arity_Product__Type_Ounit___Finite__Set_Ofinite) ).

fof(help_ti_idem,axiom,
    ! [T,A] : ti(T,ti(T,A)) = ti(T,A),
    file('theBenchmark.p',help_ti_idem) ).

fof(help_If_1_1_T,axiom,
    ! [X_a,X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X),
    file('theBenchmark.p',help_If_1_1_T) ).

fof(help_If_2_1_T,axiom,
    ! [X_a,X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y),
    file('theBenchmark.p',help_If_2_1_T) ).

fof(help_If_3_1_T,axiom,
    ! [P] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    file('theBenchmark.p',help_If_3_1_T) ).

fof(help_fNot_1_1_U,axiom,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,fNot,P)) ),
    file('theBenchmark.p',help_fNot_1_1_U) ).

fof(help_fNot_2_1_U,axiom,
    ! [P] :
      ( hBOOL(hAPP(bool,bool,fNot,P))
      | hBOOL(P) ),
    file('theBenchmark.p',help_fNot_2_1_U) ).

fof(help_COMBB_1_1_U,axiom,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_U) ).

fof(help_COMBC_1_1_U,axiom,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_U) ).

fof(help_COMBI_1_1_U,axiom,
    ! [X_a,P] : hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P),
    file('theBenchmark.p',help_COMBI_1_1_U) ).

fof(help_COMBK_1_1_U,axiom,
    ! [X_b,X_a,P,Q] : hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P),
    file('theBenchmark.p',help_COMBK_1_1_U) ).

fof(help_COMBS_1_1_U,axiom,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_U) ).

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] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    file('theBenchmark.p',help_fTrue_1_1_T) ).

fof(help_fconj_1_1_U,axiom,
    ! [Q,P] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,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(bool,fun(bool,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(bool,fun(bool,bool),fconj,P),Q)) ),
    file('theBenchmark.p',help_fconj_3_1_U) ).

fof(help_fdisj_1_1_U,axiom,
    ! [Q,P] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
      | ~ hBOOL(P) ),
    file('theBenchmark.p',help_fdisj_1_1_U) ).

fof(help_fdisj_2_1_U,axiom,
    ! [P,Q] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
      | ~ hBOOL(Q) ),
    file('theBenchmark.p',help_fdisj_2_1_U) ).

fof(help_fdisj_3_1_U,axiom,
    ! [P,Q] :
      ( hBOOL(Q)
      | hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) ),
    file('theBenchmark.p',help_fdisj_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] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    file('theBenchmark.p',help_fFalse_1_1_T) ).

fof(help_fequal_1_1_T,axiom,
    ! [X_a,X,Y] :
      ( ti(X_a,X) = ti(X_a,Y)
      | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) ),
    file('theBenchmark.p',help_fequal_1_1_T) ).

fof(help_fequal_2_1_T,axiom,
    ! [X_a,X,Y] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y))
      | ti(X_a,X) != ti(X_a,Y) ),
    file('theBenchmark.p',help_fequal_2_1_T) ).

fof(conj_0,conjecture,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
    file('theBenchmark.p',conj_0) ).

fof(f_1_1,plain,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
    inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OIIA_res]) ).

cnf(f_1_2,plain,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
    inference(clausify,[status(thm)],[f_1_1]) ).

fof(f_2_1,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
    inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OLin_res]) ).

cnf(f_2_2,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
    inference(clausify,[status(thm)],[f_2_1]) ).

fof(f_3_1,plain,
    ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
    inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OProf_res]) ).

cnf(f_3_2,plain,
    ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
    inference(clausify,[status(thm)],[f_3_1]) ).

fof(f_4_1,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
    inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Oabove_res]) ).

cnf(f_4_2,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
    inference(clausify,[status(thm)],[f_4_1]) ).

fof(f_5_1,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
    inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Obelow_res]) ).

cnf(f_5_2,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
    inference(clausify,[status(thm)],[f_5_1]) ).

fof(f_6_1,plain,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
    inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Odictator_res]) ).

cnf(f_6_2,plain,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
    inference(clausify,[status(thm)],[f_6_1]) ).

fof(f_7_1,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
    inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omkbot_res]) ).

cnf(f_7_2,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
    inference(clausify,[status(thm)],[f_7_1]) ).

fof(f_8_1,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
    inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omktop_res]) ).

cnf(f_8_2,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
    inference(clausify,[status(thm)],[f_8_1]) ).

fof(f_9_1,plain,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
    inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Ounanimity_res]) ).

cnf(f_9_2,plain,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
    inference(clausify,[status(thm)],[f_9_1]) ).

fof(f_10_1,plain,
    ! [X_a,X_b] :
      ( ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co1399186613setsum(X_a,X_b)) = big_co1399186613setsum(X_a,X_b)
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res]) ).

fof(f_10_2,plain,
    ! [U_1,U_0] :
      ( ti(fun(fun(U_1,U_0),fun(fun(U_1,bool),U_0)),big_co1399186613setsum(U_1,U_0)) = big_co1399186613setsum(U_1,U_0)
      | ~ comm_monoid_add(U_0) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

cnf(f_10_3,plain,
    ( ti(fun(fun(U_1,U_0),fun(fun(U_1,bool),U_0)),big_co1399186613setsum(U_1,U_0)) = big_co1399186613setsum(U_1,U_0)
    | ~ comm_monoid_add(U_0) ),
    inference(clausify,[status(thm)],[f_10_2]) ).

fof(f_11_1,plain,
    ! [X_b,X_c,X_a] : ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_COMBB_res]) ).

fof(f_11_2,plain,
    ! [U_4,U_3,U_2] : ti(fun(fun(U_4,U_3),fun(fun(U_2,U_4),fun(U_2,U_3))),combb(U_4,U_3,U_2)) = combb(U_4,U_3,U_2),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

cnf(f_11_3,plain,
    ti(fun(fun(U_4,U_3),fun(fun(U_2,U_4),fun(U_2,U_3))),combb(U_4,U_3,U_2)) = combb(U_4,U_3,U_2),
    inference(clausify,[status(thm)],[f_11_2]) ).

fof(f_12_1,plain,
    ! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_COMBC_res]) ).

fof(f_12_2,plain,
    ! [U_7,U_6,U_5] : ti(fun(fun(U_7,fun(U_6,U_5)),fun(U_6,fun(U_7,U_5))),combc(U_7,U_6,U_5)) = combc(U_7,U_6,U_5),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

cnf(f_12_3,plain,
    ti(fun(fun(U_7,fun(U_6,U_5)),fun(U_6,fun(U_7,U_5))),combc(U_7,U_6,U_5)) = combc(U_7,U_6,U_5),
    inference(clausify,[status(thm)],[f_12_2]) ).

fof(f_13_1,plain,
    ! [X_a] : ti(fun(X_a,X_a),combi(X_a)) = combi(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_COMBI_res]) ).

fof(f_13_2,plain,
    ! [U_8] : ti(fun(U_8,U_8),combi(U_8)) = combi(U_8),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

cnf(f_13_3,plain,
    ti(fun(U_8,U_8),combi(U_8)) = combi(U_8),
    inference(clausify,[status(thm)],[f_13_2]) ).

fof(f_14_1,plain,
    ! [X_a,X_b] : ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_COMBK_res]) ).

fof(f_14_2,plain,
    ! [U_10,U_9] : ti(fun(U_10,fun(U_9,U_10)),combk(U_10,U_9)) = combk(U_10,U_9),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

cnf(f_14_3,plain,
    ti(fun(U_10,fun(U_9,U_10)),combk(U_10,U_9)) = combk(U_10,U_9),
    inference(clausify,[status(thm)],[f_14_2]) ).

fof(f_15_1,plain,
    ! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_COMBS_res]) ).

fof(f_15_2,plain,
    ! [U_13,U_12,U_11] : ti(fun(fun(U_13,fun(U_12,U_11)),fun(fun(U_13,U_12),fun(U_13,U_11))),combs(U_13,U_12,U_11)) = combs(U_13,U_12,U_11),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

cnf(f_15_3,plain,
    ti(fun(fun(U_13,fun(U_12,U_11)),fun(fun(U_13,U_12),fun(U_13,U_11))),combs(U_13,U_12,U_11)) = combs(U_13,U_12,U_11),
    inference(clausify,[status(thm)],[f_15_2]) ).

fof(f_16_1,plain,
    ! [X_a] : ti(fun(fun(X_a,bool),nat),finite_card(X_a)) = finite_card(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ocard_res]) ).

fof(f_16_2,plain,
    ! [U_14] : ti(fun(fun(U_14,bool),nat),finite_card(U_14)) = finite_card(U_14),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

cnf(f_16_3,plain,
    ti(fun(fun(U_14,bool),nat),finite_card(U_14)) = finite_card(U_14),
    inference(clausify,[status(thm)],[f_16_2]) ).

fof(f_17_1,plain,
    ! [X_b] : ti(fun(fun(X_b,bool),bool),finite_finite_1(X_b)) = finite_finite_1(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofinite_res]) ).

fof(f_17_2,plain,
    ! [U_15] : ti(fun(fun(U_15,bool),bool),finite_finite_1(U_15)) = finite_finite_1(U_15),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

cnf(f_17_3,plain,
    ti(fun(fun(U_15,bool),bool),finite_finite_1(U_15)) = finite_finite_1(U_15),
    inference(clausify,[status(thm)],[f_17_2]) ).

fof(f_18_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)))),finite_fold_image(X_a,X_b)) = finite_fold_image(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofold__image_res]) ).

fof(f_18_2,plain,
    ! [U_17,U_16] : ti(fun(fun(U_17,fun(U_17,U_17)),fun(fun(U_16,U_17),fun(U_17,fun(fun(U_16,bool),U_17)))),finite_fold_image(U_17,U_16)) = finite_fold_image(U_17,U_16),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

cnf(f_18_3,plain,
    ti(fun(fun(U_17,fun(U_17,U_17)),fun(fun(U_16,U_17),fun(U_17,fun(fun(U_16,bool),U_17)))),finite_fold_image(U_17,U_16)) = finite_fold_image(U_17,U_16),
    inference(clausify,[status(thm)],[f_18_2]) ).

fof(f_19_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool)),finite_folding_idem(X_a,X_b)) = finite_folding_idem(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofolding__idem_res]) ).

fof(f_19_2,plain,
    ! [U_19,U_18] : ti(fun(fun(U_19,fun(U_18,U_18)),fun(fun(fun(U_19,bool),fun(U_18,U_18)),bool)),finite_folding_idem(U_19,U_18)) = finite_folding_idem(U_19,U_18),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

cnf(f_19_3,plain,
    ti(fun(fun(U_19,fun(U_18,U_18)),fun(fun(fun(U_19,bool),fun(U_18,U_18)),bool)),finite_folding_idem(U_19,U_18)) = finite_folding_idem(U_19,U_18),
    inference(clausify,[status(thm)],[f_19_2]) ).

fof(f_20_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool))),finite_folding_image(X_a,X_b)) = finite_folding_image(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofolding__image_res]) ).

fof(f_20_2,plain,
    ! [U_21,U_20] : ti(fun(fun(U_21,fun(U_21,U_21)),fun(U_21,fun(fun(fun(U_20,U_21),fun(fun(U_20,bool),U_21)),bool))),finite_folding_image(U_21,U_20)) = finite_folding_image(U_21,U_20),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

cnf(f_20_3,plain,
    ti(fun(fun(U_21,fun(U_21,U_21)),fun(U_21,fun(fun(fun(U_20,U_21),fun(fun(U_20,bool),U_21)),bool))),finite_folding_image(U_21,U_20)) = finite_folding_image(U_21,U_20),
    inference(clausify,[status(thm)],[f_20_2]) ).

fof(f_21_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)))),finite908156982e_idem(X_a,X_b)) = finite908156982e_idem(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofolding__image__simple__idem_res]) ).

fof(f_21_2,plain,
    ! [U_23,U_22] : ti(fun(fun(U_23,fun(U_23,U_23)),fun(U_23,fun(fun(U_22,U_23),fun(fun(fun(U_22,bool),U_23),bool)))),finite908156982e_idem(U_23,U_22)) = finite908156982e_idem(U_23,U_22),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

cnf(f_21_3,plain,
    ti(fun(fun(U_23,fun(U_23,U_23)),fun(U_23,fun(fun(U_22,U_23),fun(fun(fun(U_22,bool),U_23),bool)))),finite908156982e_idem(U_23,U_22)) = finite908156982e_idem(U_23,U_22),
    inference(clausify,[status(thm)],[f_21_2]) ).

fof(f_22_1,plain,
    ! [X_a,X_b] : ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b)) = in_rel(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_FunDef_Oin__rel_res]) ).

fof(f_22_2,plain,
    ! [U_25,U_24] : ti(fun(fun(product_prod(U_25,U_24),bool),fun(U_25,fun(U_24,bool))),in_rel(U_25,U_24)) = in_rel(U_25,U_24),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

cnf(f_22_3,plain,
    ti(fun(fun(product_prod(U_25,U_24),bool),fun(U_25,fun(U_24,bool))),in_rel(U_25,U_24)) = in_rel(U_25,U_24),
    inference(clausify,[status(thm)],[f_22_2]) ).

fof(f_23_1,plain,
    ! [X_a,X_c,X_b] : ti(fun(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c))),comp(X_a,X_c,X_b)) = comp(X_a,X_c,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Fun_Ocomp_res]) ).

fof(f_23_2,plain,
    ! [U_28,U_27,U_26] : ti(fun(fun(U_28,U_27),fun(fun(U_26,U_28),fun(U_26,U_27))),comp(U_28,U_27,U_26)) = comp(U_28,U_27,U_26),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

cnf(f_23_3,plain,
    ti(fun(fun(U_28,U_27),fun(fun(U_26,U_28),fun(U_26,U_27))),comp(U_28,U_27,U_26)) = comp(U_28,U_27,U_26),
    inference(clausify,[status(thm)],[f_23_2]) ).

fof(f_24_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),inj_on(X_a,X_b)) = inj_on(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Fun_Oinj__on_res]) ).

fof(f_24_2,plain,
    ! [U_30,U_29] : ti(fun(fun(U_30,U_29),fun(fun(U_30,bool),bool)),inj_on(U_30,U_29)) = inj_on(U_30,U_29),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

cnf(f_24_3,plain,
    ti(fun(fun(U_30,U_29),fun(fun(U_30,bool),bool)),inj_on(U_30,U_29)) = inj_on(U_30,U_29),
    inference(clausify,[status(thm)],[f_24_2]) ).

fof(f_25_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a))),the_inv_into(X_a,X_b)) = the_inv_into(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Fun_Othe__inv__into_res]) ).

fof(f_25_2,plain,
    ! [U_32,U_31] : ti(fun(fun(U_32,bool),fun(fun(U_32,U_31),fun(U_31,U_32))),the_inv_into(U_32,U_31)) = the_inv_into(U_32,U_31),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

cnf(f_25_3,plain,
    ti(fun(fun(U_32,bool),fun(fun(U_32,U_31),fun(U_31,U_32))),the_inv_into(U_32,U_31)) = the_inv_into(U_32,U_31),
    inference(clausify,[status(thm)],[f_25_2]) ).

fof(f_26_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool))),pi(X_a,X_b)) = pi(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_FuncSet_OPi_res]) ).

fof(f_26_2,plain,
    ! [U_34,U_33] : ti(fun(fun(U_34,bool),fun(fun(U_34,fun(U_33,bool)),fun(fun(U_34,U_33),bool))),pi(U_34,U_33)) = pi(U_34,U_33),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

cnf(f_26_3,plain,
    ti(fun(fun(U_34,bool),fun(fun(U_34,fun(U_33,bool)),fun(fun(U_34,U_33),bool))),pi(U_34,U_33)) = pi(U_34,U_33),
    inference(clausify,[status(thm)],[f_26_2]) ).

fof(f_27_1,plain,
    ! [X_a,X_c,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)))),compose(X_a,X_c,X_b)) = compose(X_a,X_c,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_FuncSet_Ocompose_res]) ).

fof(f_27_2,plain,
    ! [U_37,U_36,U_35] : ti(fun(fun(U_37,bool),fun(fun(U_36,U_35),fun(fun(U_37,U_36),fun(U_37,U_35)))),compose(U_37,U_36,U_35)) = compose(U_37,U_36,U_35),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

cnf(f_27_3,plain,
    ti(fun(fun(U_37,bool),fun(fun(U_36,U_35),fun(fun(U_37,U_36),fun(U_37,U_35)))),compose(U_37,U_36,U_35)) = compose(U_37,U_36,U_35),
    inference(clausify,[status(thm)],[f_27_2]) ).

fof(f_28_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,X_b),bool)),extensional(X_a,X_b)) = extensional(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_FuncSet_Oextensional_res]) ).

fof(f_28_2,plain,
    ! [U_39,U_38] : ti(fun(fun(U_39,bool),fun(fun(U_39,U_38),bool)),extensional(U_39,U_38)) = extensional(U_39,U_38),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

cnf(f_28_3,plain,
    ti(fun(fun(U_39,bool),fun(fun(U_39,U_38),bool)),extensional(U_39,U_38)) = extensional(U_39,U_38),
    inference(clausify,[status(thm)],[f_28_2]) ).

fof(f_29_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),restrict(X_a,X_b)) = restrict(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_FuncSet_Orestrict_res]) ).

fof(f_29_2,plain,
    ! [U_41,U_40] : ti(fun(fun(U_41,U_40),fun(fun(U_41,bool),fun(U_41,U_40))),restrict(U_41,U_40)) = restrict(U_41,U_40),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

cnf(f_29_3,plain,
    ti(fun(fun(U_41,U_40),fun(fun(U_41,bool),fun(U_41,U_40))),restrict(U_41,U_40)) = restrict(U_41,U_40),
    inference(clausify,[status(thm)],[f_29_2]) ).

fof(f_30_1,plain,
    ! [X_a] :
      ( ti(X_a,one_one(X_a)) = one_one(X_a)
      | ~ one(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oone__class_Oone_res]) ).

fof(f_30_2,plain,
    ! [U_42] :
      ( ti(U_42,one_one(U_42)) = one_one(U_42)
      | ~ one(U_42) ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

cnf(f_30_3,plain,
    ( ti(U_42,one_one(U_42)) = one_one(U_42)
    | ~ one(U_42) ),
    inference(clausify,[status(thm)],[f_30_2]) ).

fof(f_31_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a)
      | ~ monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_0_res]) ).

fof(f_31_2,plain,
    ! [U_43] :
      ( ti(fun(U_43,fun(U_43,U_43)),plus_plus(U_43)) = plus_plus(U_43)
      | ~ monoid_add(U_43) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

cnf(f_31_3,plain,
    ( ti(fun(U_43,fun(U_43,U_43)),plus_plus(U_43)) = plus_plus(U_43)
    | ~ monoid_add(U_43) ),
    inference(clausify,[status(thm)],[f_31_2]) ).

fof(f_32_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a)
      | ~ ab_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_1_res]) ).

fof(f_32_2,plain,
    ! [U_44] :
      ( ti(fun(U_44,fun(U_44,U_44)),plus_plus(U_44)) = plus_plus(U_44)
      | ~ ab_semigroup_add(U_44) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

cnf(f_32_3,plain,
    ( ti(fun(U_44,fun(U_44,U_44)),plus_plus(U_44)) = plus_plus(U_44)
    | ~ ab_semigroup_add(U_44) ),
    inference(clausify,[status(thm)],[f_32_2]) ).

fof(f_33_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a)
      | ~ cancel_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_2_res]) ).

fof(f_33_2,plain,
    ! [U_45] :
      ( ti(fun(U_45,fun(U_45,U_45)),plus_plus(U_45)) = plus_plus(U_45)
      | ~ cancel_semigroup_add(U_45) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

cnf(f_33_3,plain,
    ( ti(fun(U_45,fun(U_45,U_45)),plus_plus(U_45)) = plus_plus(U_45)
    | ~ cancel_semigroup_add(U_45) ),
    inference(clausify,[status(thm)],[f_33_2]) ).

fof(f_34_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a)
      | ~ semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_0_res]) ).

fof(f_34_2,plain,
    ! [U_46] :
      ( ti(fun(U_46,fun(U_46,U_46)),times_times(U_46)) = times_times(U_46)
      | ~ semiring(U_46) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

cnf(f_34_3,plain,
    ( ti(fun(U_46,fun(U_46,U_46)),times_times(U_46)) = times_times(U_46)
    | ~ semiring(U_46) ),
    inference(clausify,[status(thm)],[f_34_2]) ).

fof(f_35_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a)
      | ~ monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_1_res]) ).

fof(f_35_2,plain,
    ! [U_47] :
      ( ti(fun(U_47,fun(U_47,U_47)),times_times(U_47)) = times_times(U_47)
      | ~ monoid_mult(U_47) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

cnf(f_35_3,plain,
    ( ti(fun(U_47,fun(U_47,U_47)),times_times(U_47)) = times_times(U_47)
    | ~ monoid_mult(U_47) ),
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a)
      | ~ ab_semigroup_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_2_res]) ).

fof(f_36_2,plain,
    ! [U_48] :
      ( ti(fun(U_48,fun(U_48,U_48)),times_times(U_48)) = times_times(U_48)
      | ~ ab_semigroup_mult(U_48) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

cnf(f_36_3,plain,
    ( ti(fun(U_48,fun(U_48,U_48)),times_times(U_48)) = times_times(U_48)
    | ~ ab_semigroup_mult(U_48) ),
    inference(clausify,[status(thm)],[f_36_2]) ).

fof(f_37_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a)
      | ~ mult_zero(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_3_res]) ).

fof(f_37_2,plain,
    ! [U_49] :
      ( ti(fun(U_49,fun(U_49,U_49)),times_times(U_49)) = times_times(U_49)
      | ~ mult_zero(U_49) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

cnf(f_37_3,plain,
    ( ti(fun(U_49,fun(U_49,U_49)),times_times(U_49)) = times_times(U_49)
    | ~ mult_zero(U_49) ),
    inference(clausify,[status(thm)],[f_37_2]) ).

fof(f_38_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a)
      | ~ no_zero_divisors(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_4_res]) ).

fof(f_38_2,plain,
    ! [U_50] :
      ( ti(fun(U_50,fun(U_50,U_50)),times_times(U_50)) = times_times(U_50)
      | ~ no_zero_divisors(U_50) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

cnf(f_38_3,plain,
    ( ti(fun(U_50,fun(U_50,U_50)),times_times(U_50)) = times_times(U_50)
    | ~ no_zero_divisors(U_50) ),
    inference(clausify,[status(thm)],[f_38_2]) ).

fof(f_39_1,plain,
    ! [X_a] :
      ( ti(X_a,zero_zero(X_a)) = zero_zero(X_a)
      | ~ zero(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Ozero__class_Ozero_res]) ).

fof(f_39_2,plain,
    ! [U_51] :
      ( ti(U_51,zero_zero(U_51)) = zero_zero(U_51)
      | ~ zero(U_51) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

cnf(f_39_3,plain,
    ( ti(U_51,zero_zero(U_51)) = zero_zero(U_51)
    | ~ zero(U_51) ),
    inference(clausify,[status(thm)],[f_39_2]) ).

fof(f_40_1,plain,
    ti(fun(bool,nat),bool_size) = bool_size,
    inference(fof_nnf,[status(thm)],[tsy_c_HOL_Obool_Obool__size_res]) ).

cnf(f_40_2,plain,
    ti(fun(bool,nat),bool_size) = bool_size,
    inference(clausify,[status(thm)],[f_40_1]) ).

fof(f_41_1,plain,
    ! [X_a] : ti(X_a,undefined(X_a)) = undefined(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_HOL_Oundefined_res]) ).

fof(f_41_2,plain,
    ! [U_52] : ti(U_52,undefined(U_52)) = undefined(U_52),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

cnf(f_41_3,plain,
    ti(U_52,undefined(U_52)) = undefined(U_52),
    inference(clausify,[status(thm)],[f_41_2]) ).

fof(f_42_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a))),hilbert_inv_into(X_a,X_b)) = hilbert_inv_into(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Hilbert__Choice_Oinv__into_res]) ).

fof(f_42_2,plain,
    ! [U_54,U_53] : ti(fun(fun(U_54,bool),fun(fun(U_54,U_53),fun(U_53,U_54))),hilbert_inv_into(U_54,U_53)) = hilbert_inv_into(U_54,U_53),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

cnf(f_42_3,plain,
    ti(fun(fun(U_54,bool),fun(fun(U_54,U_53),fun(U_53,U_54))),hilbert_inv_into(U_54,U_53)) = hilbert_inv_into(U_54,U_53),
    inference(clausify,[status(thm)],[f_42_2]) ).

fof(f_43_1,plain,
    ! [X_a] : ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_If_res]) ).

fof(f_43_2,plain,
    ! [U_55] : ti(fun(bool,fun(U_55,fun(U_55,U_55))),if(U_55)) = if(U_55),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

cnf(f_43_3,plain,
    ti(fun(bool,fun(U_55,fun(U_55,U_55))),if(U_55)) = if(U_55),
    inference(clausify,[status(thm)],[f_43_2]) ).

fof(f_44_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,bool),ring_1_Ints(X_a)) = ring_1_Ints(X_a)
      | ~ ring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Int_Oring__1__class_OInts_res]) ).

fof(f_44_2,plain,
    ! [U_56] :
      ( ti(fun(U_56,bool),ring_1_Ints(U_56)) = ring_1_Ints(U_56)
      | ~ ring_1(U_56) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

cnf(f_44_3,plain,
    ( ti(fun(U_56,bool),ring_1_Ints(U_56)) = ring_1_Ints(U_56)
    | ~ ring_1(U_56) ),
    inference(clausify,[status(thm)],[f_44_2]) ).

fof(f_45_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),semilattice_inf_inf(X_a)) = semilattice_inf_inf(X_a)
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Lattices_Osemilattice__inf__class_Oinf_res]) ).

fof(f_45_2,plain,
    ! [U_57] :
      ( ti(fun(U_57,fun(U_57,U_57)),semilattice_inf_inf(U_57)) = semilattice_inf_inf(U_57)
      | ~ semilattice_inf(U_57) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

cnf(f_45_3,plain,
    ( ti(fun(U_57,fun(U_57,U_57)),semilattice_inf_inf(U_57)) = semilattice_inf_inf(U_57)
    | ~ semilattice_inf(U_57) ),
    inference(clausify,[status(thm)],[f_45_2]) ).

fof(f_46_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),semilattice_sup_sup(X_a)) = semilattice_sup_sup(X_a)
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Lattices_Osemilattice__sup__class_Osup_res]) ).

fof(f_46_2,plain,
    ! [U_58] :
      ( ti(fun(U_58,fun(U_58,U_58)),semilattice_sup_sup(U_58)) = semilattice_sup_sup(U_58)
      | ~ semilattice_sup(U_58) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

cnf(f_46_3,plain,
    ( ti(fun(U_58,fun(U_58,U_58)),semilattice_sup_sup(U_58)) = semilattice_sup_sup(U_58)
    | ~ semilattice_sup(U_58) ),
    inference(clausify,[status(thm)],[f_46_2]) ).

fof(f_47_1,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(fof_nnf,[status(thm)],[tsy_c_Nat_OSuc_res]) ).

cnf(f_47_2,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(clausify,[status(thm)],[f_47_1]) ).

fof(f_48_1,plain,
    ! [X_a] : ti(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),nat_case(X_a)) = nat_case(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_Nat_Onat_Onat__case_res]) ).

fof(f_48_2,plain,
    ! [U_59] : ti(fun(U_59,fun(fun(nat,U_59),fun(nat,U_59))),nat_case(U_59)) = nat_case(U_59),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

cnf(f_48_3,plain,
    ti(fun(U_59,fun(fun(nat,U_59),fun(nat,U_59))),nat_case(U_59)) = nat_case(U_59),
    inference(clausify,[status(thm)],[f_48_2]) ).

fof(f_49_1,plain,
    ti(fun(nat,nat),nat_size) = nat_size,
    inference(fof_nnf,[status(thm)],[tsy_c_Nat_Onat_Onat__size_res]) ).

cnf(f_49_2,plain,
    ti(fun(nat,nat),nat_size) = nat_size,
    inference(clausify,[status(thm)],[f_49_1]) ).

fof(f_50_1,plain,
    ti(fun(nat,nat),size_size(nat)) = size_size(nat),
    inference(fof_nnf,[status(thm)],[tsy_c_Nat_Osize__class_Osize_res]) ).

cnf(f_50_2,plain,
    ti(fun(nat,nat),size_size(nat)) = size_size(nat),
    inference(clausify,[status(thm)],[f_50_1]) ).

fof(f_51_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a)
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless_res]) ).

fof(f_51_2,plain,
    ! [U_60] :
      ( ti(fun(U_60,fun(U_60,bool)),ord_less(U_60)) = ord_less(U_60)
      | ~ ord(U_60) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

cnf(f_51_3,plain,
    ( ti(fun(U_60,fun(U_60,bool)),ord_less(U_60)) = ord_less(U_60)
    | ~ ord(U_60) ),
    inference(clausify,[status(thm)],[f_51_2]) ).

fof(f_52_1,plain,
    ! [X_b] :
      ( ti(fun(X_b,fun(X_b,bool)),ord_less_eq(X_b)) = ord_less_eq(X_b)
      | ~ ord(X_b) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_res]) ).

fof(f_52_2,plain,
    ! [U_61] :
      ( ti(fun(U_61,fun(U_61,bool)),ord_less_eq(U_61)) = ord_less_eq(U_61)
      | ~ ord(U_61) ),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

cnf(f_52_3,plain,
    ( ti(fun(U_61,fun(U_61,bool)),ord_less_eq(U_61)) = ord_less_eq(U_61)
    | ~ ord(U_61) ),
    inference(clausify,[status(thm)],[f_52_2]) ).

fof(f_53_1,plain,
    ! [X_a] :
      ( ti(X_a,top_top(X_a)) = top_top(X_a)
      | ~ top(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Otop__class_Otop_res]) ).

fof(f_53_2,plain,
    ! [U_62] :
      ( ti(U_62,top_top(U_62)) = top_top(U_62)
      | ~ top(U_62) ),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

cnf(f_53_3,plain,
    ( ti(U_62,top_top(U_62)) = top_top(U_62)
    | ~ top(U_62) ),
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_1,plain,
    ! [X_a,X_b] : ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b)) = product_Pair(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Product__Type_OPair_res]) ).

fof(f_54_2,plain,
    ! [U_64,U_63] : ti(fun(U_64,fun(U_63,product_prod(U_64,U_63))),product_Pair(U_64,U_63)) = product_Pair(U_64,U_63),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

cnf(f_54_3,plain,
    ti(fun(U_64,fun(U_63,product_prod(U_64,U_63))),product_Pair(U_64,U_63)) = product_Pair(U_64,U_63),
    inference(clausify,[status(thm)],[f_54_2]) ).

fof(f_55_1,plain,
    ! [X_b,X_c,X_a] : ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a)) = product_prod_rec(X_b,X_c,X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_Product__Type_Oprod_Oprod__rec_res]) ).

fof(f_55_2,plain,
    ! [U_67,U_66,U_65] : ti(fun(fun(U_67,fun(U_66,U_65)),fun(product_prod(U_67,U_66),U_65)),product_prod_rec(U_67,U_66,U_65)) = product_prod_rec(U_67,U_66,U_65),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

cnf(f_55_3,plain,
    ti(fun(fun(U_67,fun(U_66,U_65)),fun(product_prod(U_67,U_66),U_65)),product_prod_rec(U_67,U_66,U_65)) = product_prod_rec(U_67,U_66,U_65),
    inference(clausify,[status(thm)],[f_55_2]) ).

fof(f_56_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,bool)),ord_atLeast(X_a)) = ord_atLeast(X_a)
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OatLeast_res]) ).

fof(f_56_2,plain,
    ! [U_68] :
      ( ti(fun(U_68,fun(U_68,bool)),ord_atLeast(U_68)) = ord_atLeast(U_68)
      | ~ ord(U_68) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

cnf(f_56_3,plain,
    ( ti(fun(U_68,fun(U_68,bool)),ord_atLeast(U_68)) = ord_atLeast(U_68)
    | ~ ord(U_68) ),
    inference(clausify,[status(thm)],[f_56_2]) ).

fof(f_57_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastAtMost(X_a)) = ord_atLeastAtMost(X_a)
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OatLeastAtMost_res]) ).

fof(f_57_2,plain,
    ! [U_69] :
      ( ti(fun(U_69,fun(U_69,fun(U_69,bool))),ord_atLeastAtMost(U_69)) = ord_atLeastAtMost(U_69)
      | ~ order(U_69) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

cnf(f_57_3,plain,
    ( ti(fun(U_69,fun(U_69,fun(U_69,bool))),ord_atLeastAtMost(U_69)) = ord_atLeastAtMost(U_69)
    | ~ order(U_69) ),
    inference(clausify,[status(thm)],[f_57_2]) ).

fof(f_58_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastLessThan(X_a)) = ord_atLeastLessThan(X_a)
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OatLeastLessThan_res]) ).

fof(f_58_2,plain,
    ! [U_70] :
      ( ti(fun(U_70,fun(U_70,fun(U_70,bool))),ord_atLeastLessThan(U_70)) = ord_atLeastLessThan(U_70)
      | ~ linorder(U_70) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

cnf(f_58_3,plain,
    ( ti(fun(U_70,fun(U_70,fun(U_70,bool))),ord_atLeastLessThan(U_70)) = ord_atLeastLessThan(U_70)
    | ~ linorder(U_70) ),
    inference(clausify,[status(thm)],[f_58_2]) ).

fof(f_59_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,bool)),ord_greaterThan(X_a)) = ord_greaterThan(X_a)
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OgreaterThan_res]) ).

fof(f_59_2,plain,
    ! [U_71] :
      ( ti(fun(U_71,fun(U_71,bool)),ord_greaterThan(U_71)) = ord_greaterThan(U_71)
      | ~ ord(U_71) ),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

cnf(f_59_3,plain,
    ( ti(fun(U_71,fun(U_71,bool)),ord_greaterThan(U_71)) = ord_greaterThan(U_71)
    | ~ ord(U_71) ),
    inference(clausify,[status(thm)],[f_59_2]) ).

fof(f_60_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr1471790799AtMost(X_a)) = ord_gr1471790799AtMost(X_a)
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OgreaterThanAtMost_res]) ).

fof(f_60_2,plain,
    ! [U_72] :
      ( ti(fun(U_72,fun(U_72,fun(U_72,bool))),ord_gr1471790799AtMost(U_72)) = ord_gr1471790799AtMost(U_72)
      | ~ linorder(U_72) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

cnf(f_60_3,plain,
    ( ti(fun(U_72,fun(U_72,fun(U_72,bool))),ord_gr1471790799AtMost(U_72)) = ord_gr1471790799AtMost(U_72)
    | ~ linorder(U_72) ),
    inference(clausify,[status(thm)],[f_60_2]) ).

fof(f_61_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)) = ord_gr676655987ssThan(X_a)
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_res]) ).

fof(f_61_2,plain,
    ! [U_73] :
      ( ti(fun(U_73,fun(U_73,fun(U_73,bool))),ord_gr676655987ssThan(U_73)) = ord_gr676655987ssThan(U_73)
      | ~ linorder(U_73) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

cnf(f_61_3,plain,
    ( ti(fun(U_73,fun(U_73,fun(U_73,bool))),ord_gr676655987ssThan(U_73)) = ord_gr676655987ssThan(U_73)
    | ~ linorder(U_73) ),
    inference(clausify,[status(thm)],[f_61_2]) ).

fof(f_62_1,plain,
    ! [X_a] : ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_Set_OCollect_res]) ).

fof(f_62_2,plain,
    ! [U_74] : ti(fun(fun(U_74,bool),fun(U_74,bool)),collect(U_74)) = collect(U_74),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

cnf(f_62_3,plain,
    ti(fun(fun(U_74,bool),fun(U_74,bool)),collect(U_74)) = collect(U_74),
    inference(clausify,[status(thm)],[f_62_2]) ).

fof(f_63_1,plain,
    ! [X_b,X_a] : ti(fun(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool))),image(X_b,X_a)) = image(X_b,X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_Set_Oimage_res]) ).

fof(f_63_2,plain,
    ! [U_76,U_75] : ti(fun(fun(U_76,U_75),fun(fun(U_76,bool),fun(U_75,bool))),image(U_76,U_75)) = image(U_76,U_75),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

cnf(f_63_3,plain,
    ti(fun(fun(U_76,U_75),fun(fun(U_76,bool),fun(U_75,bool))),image(U_76,U_75)) = image(U_76,U_75),
    inference(clausify,[status(thm)],[f_63_2]) ).

fof(f_64_1,plain,
    ! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool))),sum_Plus(X_a,X_b)) = sum_Plus(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Sum__Type_OPlus_res]) ).

fof(f_64_2,plain,
    ! [U_78,U_77] : ti(fun(fun(U_78,bool),fun(fun(U_77,bool),fun(sum_sum(U_78,U_77),bool))),sum_Plus(U_78,U_77)) = sum_Plus(U_78,U_77),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

cnf(f_64_3,plain,
    ti(fun(fun(U_78,bool),fun(fun(U_77,bool),fun(sum_sum(U_78,U_77),bool))),sum_Plus(U_78,U_77)) = sum_Plus(U_78,U_77),
    inference(clausify,[status(thm)],[f_64_2]) ).

fof(f_65_1,plain,
    ! [X_a] : ti(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),finite_psubset(X_a)) = finite_psubset(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_Wellfounded_Ofinite__psubset_res]) ).

fof(f_65_2,plain,
    ! [U_79] : ti(fun(product_prod(fun(U_79,bool),fun(U_79,bool)),bool),finite_psubset(U_79)) = finite_psubset(U_79),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

cnf(f_65_3,plain,
    ti(fun(product_prod(fun(U_79,bool),fun(U_79,bool)),bool),finite_psubset(U_79)) = finite_psubset(U_79),
    inference(clausify,[status(thm)],[f_65_2]) ).

fof(f_66_1,plain,
    ! [X_a] : ti(fun(fun(X_a,nat),fun(product_prod(X_a,X_a),bool)),measure(X_a)) = measure(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_Wellfounded_Omeasure_res]) ).

fof(f_66_2,plain,
    ! [U_80] : ti(fun(fun(U_80,nat),fun(product_prod(U_80,U_80),bool)),measure(U_80)) = measure(U_80),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

cnf(f_66_3,plain,
    ti(fun(fun(U_80,nat),fun(product_prod(U_80,U_80),bool)),measure(U_80)) = measure(U_80),
    inference(clausify,[status(thm)],[f_66_2]) ).

fof(f_67_1,plain,
    ! [X_a] : ti(fun(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool))),mlex_prod(X_a)) = mlex_prod(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_Wellfounded_Omlex__prod_res]) ).

fof(f_67_2,plain,
    ! [U_81] : ti(fun(fun(U_81,nat),fun(fun(product_prod(U_81,U_81),bool),fun(product_prod(U_81,U_81),bool))),mlex_prod(U_81)) = mlex_prod(U_81),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

cnf(f_67_3,plain,
    ti(fun(fun(U_81,nat),fun(fun(product_prod(U_81,U_81),bool),fun(product_prod(U_81,U_81),bool))),mlex_prod(U_81)) = mlex_prod(U_81),
    inference(clausify,[status(thm)],[f_67_2]) ).

fof(f_68_1,plain,
    ti(bool,fFalse) = fFalse,
    inference(fof_nnf,[status(thm)],[tsy_c_fFalse_res]) ).

cnf(f_68_2,plain,
    ti(bool,fFalse) = fFalse,
    inference(clausify,[status(thm)],[f_68_1]) ).

fof(f_69_1,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(fof_nnf,[status(thm)],[tsy_c_fNot_res]) ).

cnf(f_69_2,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(clausify,[status(thm)],[f_69_1]) ).

fof(f_70_1,plain,
    ti(bool,fTrue) = fTrue,
    inference(fof_nnf,[status(thm)],[tsy_c_fTrue_res]) ).

cnf(f_70_2,plain,
    ti(bool,fTrue) = fTrue,
    inference(clausify,[status(thm)],[f_70_1]) ).

fof(f_71_1,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(fof_nnf,[status(thm)],[tsy_c_fconj_res]) ).

cnf(f_71_2,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(clausify,[status(thm)],[f_71_1]) ).

fof(f_72_1,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(fof_nnf,[status(thm)],[tsy_c_fdisj_res]) ).

cnf(f_72_2,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(clausify,[status(thm)],[f_72_1]) ).

fof(f_73_1,plain,
    ! [X_a] : ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_fequal_res]) ).

fof(f_73_2,plain,
    ! [U_82] : ti(fun(U_82,fun(U_82,bool)),fequal(U_82)) = fequal(U_82),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

cnf(f_73_3,plain,
    ti(fun(U_82,fun(U_82,bool)),fequal(U_82)) = fequal(U_82),
    inference(clausify,[status(thm)],[f_73_2]) ).

fof(f_74_1,plain,
    ! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1),
    inference(fof_nnf,[status(thm)],[tsy_c_hAPP_arg1]) ).

fof(f_74_2,plain,
    ! [U_86,U_85,U_84,U_83] : hAPP(U_86,U_85,ti(fun(U_86,U_85),U_84),U_83) = hAPP(U_86,U_85,U_84,U_83),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

cnf(f_74_3,plain,
    hAPP(U_86,U_85,ti(fun(U_86,U_85),U_84),U_83) = hAPP(U_86,U_85,U_84,U_83),
    inference(clausify,[status(thm)],[f_74_2]) ).

fof(f_75_1,plain,
    ! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
    inference(fof_nnf,[status(thm)],[tsy_c_hAPP_arg2]) ).

fof(f_75_2,plain,
    ! [U_90,U_89,U_88,U_87] : hAPP(U_90,U_89,U_88,ti(U_90,U_87)) = hAPP(U_90,U_89,U_88,U_87),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

cnf(f_75_3,plain,
    hAPP(U_90,U_89,U_88,ti(U_90,U_87)) = hAPP(U_90,U_89,U_88,U_87),
    inference(clausify,[status(thm)],[f_75_2]) ).

fof(f_76_1,plain,
    ! [X_c,X_a,B_1_1,B_2_1] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
    inference(fof_nnf,[status(thm)],[tsy_c_hAPP_res]) ).

fof(f_76_2,plain,
    ! [U_94,U_93,U_92,U_91] : ti(U_94,hAPP(U_93,U_94,U_92,U_91)) = hAPP(U_93,U_94,U_92,U_91),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

cnf(f_76_3,plain,
    ti(U_94,hAPP(U_93,U_94,U_92,U_91)) = hAPP(U_93,U_94,U_92,U_91),
    inference(clausify,[status(thm)],[f_76_2]) ).

fof(f_77_1,plain,
    ! [B_1_1] :
      ( ( hBOOL(ti(bool,B_1_1))
        | ~ hBOOL(B_1_1) )
      & ( hBOOL(B_1_1)
        | ~ hBOOL(ti(bool,B_1_1)) ) ),
    inference(fof_nnf,[status(thm)],[tsy_c_hBOOL_arg1]) ).

fof(f_77_2,plain,
    ! [U_95] :
      ( ( hBOOL(ti(bool,U_95))
        | ~ hBOOL(U_95) )
      & ( hBOOL(U_95)
        | ~ hBOOL(ti(bool,U_95)) ) ),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ( ! [U_97] :
        ( hBOOL(ti(bool,U_97))
        | ~ hBOOL(U_97) )
    & ! [U_96] :
        ( hBOOL(U_96)
        | ~ hBOOL(ti(bool,U_96)) ) ),
    inference(miniscope,[status(thm)],[f_77_2]) ).

cnf(f_77_4,plain,
    ( hBOOL(U_96)
    | ~ hBOOL(ti(bool,U_96)) ),
    inference(clausify,[status(thm)],[f_77_3]) ).

cnf(f_77_5,plain,
    ( hBOOL(ti(bool,U_97))
    | ~ hBOOL(U_97) ),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_1,plain,
    ! [X_a] : ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_member_res]) ).

fof(f_78_2,plain,
    ! [U_98] : ti(fun(U_98,fun(fun(U_98,bool),bool)),member(U_98)) = member(U_98),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

cnf(f_78_3,plain,
    ti(fun(U_98,fun(fun(U_98,bool),bool)),member(U_98)) = member(U_98),
    inference(clausify,[status(thm)],[f_78_2]) ).

fof(f_79_1,plain,
    ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),f) = f,
    inference(fof_nnf,[status(thm)],[tsy_v_F_res]) ).

cnf(f_79_2,plain,
    ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),f) = f,
    inference(clausify,[status(thm)],[f_79_1]) ).

fof(f_80_1,plain,
    ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
    inference(fof_nnf,[status(thm)],[tsy_v_Lab_____res]) ).

cnf(f_80_2,plain,
    ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
    inference(clausify,[status(thm)],[f_80_1]) ).

fof(f_81_1,plain,
    ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
    inference(fof_nnf,[status(thm)],[tsy_v_Lba_____res]) ).

cnf(f_81_2,plain,
    ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
    inference(clausify,[status(thm)],[f_81_1]) ).

fof(f_82_1,plain,
    ti(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),p) = p,
    inference(fof_nnf,[status(thm)],[tsy_v_P_____res]) ).

cnf(f_82_2,plain,
    ti(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),p) = p,
    inference(clausify,[status(thm)],[f_82_1]) ).

fof(f_83_1,plain,
    ti(arrow_2142409994le_alt,a) = a,
    inference(fof_nnf,[status(thm)],[tsy_v_a_____res]) ).

cnf(f_83_2,plain,
    ti(arrow_2142409994le_alt,a) = a,
    inference(clausify,[status(thm)],[f_83_1]) ).

fof(f_84_1,plain,
    ti(arrow_2142409994le_alt,b) = b,
    inference(fof_nnf,[status(thm)],[tsy_v_b_____res]) ).

cnf(f_84_2,plain,
    ti(arrow_2142409994le_alt,b) = b,
    inference(clausify,[status(thm)],[f_84_1]) ).

fof(f_85_1,plain,
    ti(arrow_2142409994le_alt,c) = c,
    inference(fof_nnf,[status(thm)],[tsy_v_c_____res]) ).

cnf(f_85_2,plain,
    ti(arrow_2142409994le_alt,c) = c,
    inference(clausify,[status(thm)],[f_85_1]) ).

fof(f_86_1,plain,
    ti(arrow_2142409994le_alt,d) = d,
    inference(fof_nnf,[status(thm)],[tsy_v_d_____res]) ).

cnf(f_86_2,plain,
    ti(arrow_2142409994le_alt,d) = d,
    inference(clausify,[status(thm)],[f_86_1]) ).

fof(f_87_1,plain,
    ti(arrow_2142409994le_alt,e) = e,
    inference(fof_nnf,[status(thm)],[tsy_v_e_____res]) ).

cnf(f_87_2,plain,
    ti(arrow_2142409994le_alt,e) = e,
    inference(clausify,[status(thm)],[f_87_1]) ).

fof(f_88_1,plain,
    ti(fun(arrow_1998540521e_indi,nat),h) = h,
    inference(fof_nnf,[status(thm)],[tsy_v_h_____res]) ).

cnf(f_88_2,plain,
    ti(fun(arrow_1998540521e_indi,nat),h) = h,
    inference(clausify,[status(thm)],[f_88_1]) ).

fof(f_89_1,plain,
    ti(nat,n) = n,
    inference(fof_nnf,[status(thm)],[tsy_v_n_____res]) ).

cnf(f_89_2,plain,
    ti(nat,n) = n,
    inference(clausify,[status(thm)],[f_89_1]) ).

fof(f_90_1,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
    inference(fof_nnf,[status(thm)],[fact_0_assms_I3_J]) ).

cnf(f_90_2,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
    inference(clausify,[status(thm)],[f_90_1]) ).

fof(f_91_1,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,f)),
    inference(fof_nnf,[status(thm)],[fact_1_u]) ).

cnf(f_91_2,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,f)),
    inference(clausify,[status(thm)],[f_91_1]) ).

fof(f_92_1,plain,
    c != d,
    inference(fof_nnf,[status(thm)],[fact_2__096c_A_126_061_Ad_096]) ).

cnf(f_92_2,plain,
    c != d,
    inference(clausify,[status(thm)],[f_92_1]) ).

fof(f_93_1,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
    inference(fof_nnf,[status(thm)],[fact_3__096P_A_058_AProf_096]) ).

cnf(f_93_2,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
    inference(clausify,[status(thm)],[f_93_1]) ).

fof(f_94_1,plain,
    ! [X_2,Y_1,L_3,Z_1] :
      ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,L_3),Z_1)))
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3))
          & ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Z_1) )
        | ( ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Y_1)
          & ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Z_1) )
        | ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Z_1) )
      & ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3))
            | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Z_1) )
          & ( ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1)
            | ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Z_1) )
          & ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Z_1) )
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,L_3),Z_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_4_in__mkbot]) ).

fof(f_94_2,plain,
    ! [U_102,U_101,U_100,U_99] :
      ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_102),U_101)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_100),U_99)))
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_102),U_101)),U_100))
          & ti(arrow_2142409994le_alt,U_102) != ti(arrow_2142409994le_alt,U_99) )
        | ( ti(arrow_2142409994le_alt,U_102) = ti(arrow_2142409994le_alt,U_101)
          & ti(arrow_2142409994le_alt,U_102) = ti(arrow_2142409994le_alt,U_99) )
        | ti(arrow_2142409994le_alt,U_101) = ti(arrow_2142409994le_alt,U_99) )
      & ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_102),U_101)),U_100))
            | ti(arrow_2142409994le_alt,U_102) = ti(arrow_2142409994le_alt,U_99) )
          & ( ti(arrow_2142409994le_alt,U_102) != ti(arrow_2142409994le_alt,U_101)
            | ti(arrow_2142409994le_alt,U_102) != ti(arrow_2142409994le_alt,U_99) )
          & ti(arrow_2142409994le_alt,U_101) != ti(arrow_2142409994le_alt,U_99) )
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_102),U_101)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_100),U_99))) ) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ( ! [U_110,U_108,U_106,U_104] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_110),U_108)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_106),U_104)))
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_110),U_108)),U_106))
          & ti(arrow_2142409994le_alt,U_110) != ti(arrow_2142409994le_alt,U_104) )
        | ( ti(arrow_2142409994le_alt,U_110) = ti(arrow_2142409994le_alt,U_108)
          & ti(arrow_2142409994le_alt,U_110) = ti(arrow_2142409994le_alt,U_104) )
        | ti(arrow_2142409994le_alt,U_108) = ti(arrow_2142409994le_alt,U_104) )
    & ! [U_109,U_107,U_105,U_103] :
        ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_109),U_107)),U_105))
            | ti(arrow_2142409994le_alt,U_109) = ti(arrow_2142409994le_alt,U_103) )
          & ( ti(arrow_2142409994le_alt,U_109) != ti(arrow_2142409994le_alt,U_107)
            | ti(arrow_2142409994le_alt,U_109) != ti(arrow_2142409994le_alt,U_103) )
          & ti(arrow_2142409994le_alt,U_107) != ti(arrow_2142409994le_alt,U_103) )
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_109),U_107)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_105),U_103))) ) ),
    inference(miniscope,[status(thm)],[f_94_2]) ).

cnf(f_94_4,plain,
    ( ti(arrow_2142409994le_alt,U_107) != ti(arrow_2142409994le_alt,U_103)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_109),U_107)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_105),U_103))) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_5,plain,
    ( ti(arrow_2142409994le_alt,U_109) != ti(arrow_2142409994le_alt,U_107)
    | ti(arrow_2142409994le_alt,U_109) != ti(arrow_2142409994le_alt,U_103)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_109),U_107)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_105),U_103))) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_6,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_109),U_107)),U_105))
    | ti(arrow_2142409994le_alt,U_109) = ti(arrow_2142409994le_alt,U_103)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_109),U_107)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_105),U_103))) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_7,plain,
    ( ti(arrow_2142409994le_alt,U_110) != ti(arrow_2142409994le_alt,U_104)
    | ti(arrow_2142409994le_alt,U_110) = ti(arrow_2142409994le_alt,U_104)
    | ti(arrow_2142409994le_alt,U_108) = ti(arrow_2142409994le_alt,U_104)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_110),U_108)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_106),U_104))) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_8,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_110),U_108)),U_106))
    | ti(arrow_2142409994le_alt,U_110) = ti(arrow_2142409994le_alt,U_104)
    | ti(arrow_2142409994le_alt,U_108) = ti(arrow_2142409994le_alt,U_104)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_110),U_108)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_106),U_104))) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_9,plain,
    ( ti(arrow_2142409994le_alt,U_110) != ti(arrow_2142409994le_alt,U_104)
    | ti(arrow_2142409994le_alt,U_110) = ti(arrow_2142409994le_alt,U_108)
    | ti(arrow_2142409994le_alt,U_108) = ti(arrow_2142409994le_alt,U_104)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_110),U_108)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_106),U_104))) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_10,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_110),U_108)),U_106))
    | ti(arrow_2142409994le_alt,U_110) = ti(arrow_2142409994le_alt,U_108)
    | ti(arrow_2142409994le_alt,U_108) = ti(arrow_2142409994le_alt,U_104)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_110),U_108)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_106),U_104))) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

fof(f_95_1,plain,
    ! [X_2,Y_1,L_3,Z_1] :
      ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,L_3),Z_1)))
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3))
          & ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Z_1) )
        | ( ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Y_1)
          & ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Z_1) )
        | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Z_1) )
      & ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3))
            | ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Z_1) )
          & ( ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1)
            | ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Z_1) )
          & ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Z_1) )
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,L_3),Z_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_5_in__mktop]) ).

fof(f_95_2,plain,
    ! [U_114,U_113,U_112,U_111] :
      ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_114),U_113)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_112),U_111)))
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_114),U_113)),U_112))
          & ti(arrow_2142409994le_alt,U_113) != ti(arrow_2142409994le_alt,U_111) )
        | ( ti(arrow_2142409994le_alt,U_114) = ti(arrow_2142409994le_alt,U_113)
          & ti(arrow_2142409994le_alt,U_113) = ti(arrow_2142409994le_alt,U_111) )
        | ti(arrow_2142409994le_alt,U_114) = ti(arrow_2142409994le_alt,U_111) )
      & ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_114),U_113)),U_112))
            | ti(arrow_2142409994le_alt,U_113) = ti(arrow_2142409994le_alt,U_111) )
          & ( ti(arrow_2142409994le_alt,U_114) != ti(arrow_2142409994le_alt,U_113)
            | ti(arrow_2142409994le_alt,U_113) != ti(arrow_2142409994le_alt,U_111) )
          & ti(arrow_2142409994le_alt,U_114) != ti(arrow_2142409994le_alt,U_111) )
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_114),U_113)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_112),U_111))) ) ),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ( ! [U_122,U_120,U_118,U_116] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_122),U_120)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_118),U_116)))
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_122),U_120)),U_118))
          & ti(arrow_2142409994le_alt,U_120) != ti(arrow_2142409994le_alt,U_116) )
        | ( ti(arrow_2142409994le_alt,U_122) = ti(arrow_2142409994le_alt,U_120)
          & ti(arrow_2142409994le_alt,U_120) = ti(arrow_2142409994le_alt,U_116) )
        | ti(arrow_2142409994le_alt,U_122) = ti(arrow_2142409994le_alt,U_116) )
    & ! [U_121,U_119,U_117,U_115] :
        ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_121),U_119)),U_117))
            | ti(arrow_2142409994le_alt,U_119) = ti(arrow_2142409994le_alt,U_115) )
          & ( ti(arrow_2142409994le_alt,U_121) != ti(arrow_2142409994le_alt,U_119)
            | ti(arrow_2142409994le_alt,U_119) != ti(arrow_2142409994le_alt,U_115) )
          & ti(arrow_2142409994le_alt,U_121) != ti(arrow_2142409994le_alt,U_115) )
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_121),U_119)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_117),U_115))) ) ),
    inference(miniscope,[status(thm)],[f_95_2]) ).

cnf(f_95_4,plain,
    ( ti(arrow_2142409994le_alt,U_121) != ti(arrow_2142409994le_alt,U_115)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_121),U_119)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_117),U_115))) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

cnf(f_95_5,plain,
    ( ti(arrow_2142409994le_alt,U_121) != ti(arrow_2142409994le_alt,U_119)
    | ti(arrow_2142409994le_alt,U_119) != ti(arrow_2142409994le_alt,U_115)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_121),U_119)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_117),U_115))) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

cnf(f_95_6,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_121),U_119)),U_117))
    | ti(arrow_2142409994le_alt,U_119) = ti(arrow_2142409994le_alt,U_115)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_121),U_119)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_117),U_115))) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

cnf(f_95_7,plain,
    ( ti(arrow_2142409994le_alt,U_120) != ti(arrow_2142409994le_alt,U_116)
    | ti(arrow_2142409994le_alt,U_120) = ti(arrow_2142409994le_alt,U_116)
    | ti(arrow_2142409994le_alt,U_122) = ti(arrow_2142409994le_alt,U_116)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_122),U_120)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_118),U_116))) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

cnf(f_95_8,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_122),U_120)),U_118))
    | ti(arrow_2142409994le_alt,U_120) = ti(arrow_2142409994le_alt,U_116)
    | ti(arrow_2142409994le_alt,U_122) = ti(arrow_2142409994le_alt,U_116)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_122),U_120)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_118),U_116))) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

cnf(f_95_9,plain,
    ( ti(arrow_2142409994le_alt,U_120) != ti(arrow_2142409994le_alt,U_116)
    | ti(arrow_2142409994le_alt,U_122) = ti(arrow_2142409994le_alt,U_120)
    | ti(arrow_2142409994le_alt,U_122) = ti(arrow_2142409994le_alt,U_116)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_122),U_120)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_118),U_116))) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

cnf(f_95_10,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_122),U_120)),U_118))
    | ti(arrow_2142409994le_alt,U_122) = ti(arrow_2142409994le_alt,U_120)
    | ti(arrow_2142409994le_alt,U_122) = ti(arrow_2142409994le_alt,U_116)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_122),U_120)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_118),U_116))) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_1,plain,
    ! [P_2,Pa,A_5,B_4,Aa,Ba] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa))) ) )
      | ? [I_1] :
          ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1))) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1))) ) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_2),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,Ba) = ti(arrow_2142409994le_alt,A_5)
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,B_4)
      | ti(arrow_2142409994le_alt,A_5) = ti(arrow_2142409994le_alt,B_4)
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,Ba) ),
    inference(fof_nnf,[status(thm)],[fact_6__C2_C]) ).

fof(f_96_2,plain,
    ! [U_129,U_128,U_127,U_126,U_125,U_124] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128))) ) )
      | ? [U_123] :
          ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,U_123)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,U_123))) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,U_123)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,U_123))) ) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
      | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
      | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
      | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_129,U_128,U_127,U_126,U_125,U_124] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128))) ) )
      | ? [U_131] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,U_131)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,U_131))) )
      | ? [U_130] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,U_130)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,U_130))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
      | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
      | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
      | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(miniscope,[status(thm)],[f_96_2]) ).

fof(f_96_4,plain,
    ! [U_129,U_128,U_127,U_126,U_125,U_124] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128))) ) )
      | ? [U_131] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,U_131)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,U_131))) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK1(U_129,U_128,U_127,U_126,U_125,U_124))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK1(U_129,U_128,U_127,U_126,U_125,U_124)))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
      | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
      | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
      | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_130,sK1(U_129,U_128,U_127,U_126,U_125,U_124))],[f_96_3]) ).

fof(f_96_5,plain,
    ! [U_129,U_128,U_127,U_126,U_125,U_124] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128))) ) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK2(U_129,U_128,U_127,U_126,U_125,U_124))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK2(U_129,U_128,U_127,U_126,U_125,U_124)))) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK1(U_129,U_128,U_127,U_126,U_125,U_124))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK1(U_129,U_128,U_127,U_126,U_125,U_124)))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
      | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
      | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
      | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_131,sK2(U_129,U_128,U_127,U_126,U_125,U_124))],[f_96_4]) ).

cnf(f_96_6,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK2(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK1(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(clausify,[status(thm)],[f_96_5]) ).

cnf(f_96_7,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK2(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK1(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(clausify,[status(thm)],[f_96_5]) ).

cnf(f_96_8,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK2(U_129,U_128,U_127,U_126,U_125,U_124))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK1(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(clausify,[status(thm)],[f_96_5]) ).

cnf(f_96_9,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK2(U_129,U_128,U_127,U_126,U_125,U_124))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK1(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(clausify,[status(thm)],[f_96_5]) ).

cnf(f_96_10,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK2(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK1(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(clausify,[status(thm)],[f_96_5]) ).

cnf(f_96_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK2(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK1(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(clausify,[status(thm)],[f_96_5]) ).

cnf(f_96_12,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK2(U_129,U_128,U_127,U_126,U_125,U_124))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK1(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(clausify,[status(thm)],[f_96_5]) ).

cnf(f_96_13,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_128,sK2(U_129,U_128,U_127,U_126,U_125,U_124))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_129,sK1(U_129,U_128,U_127,U_126,U_125,U_124))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_125),U_124)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_128)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_127),U_126)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_129)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_129),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_128),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_124) = ti(arrow_2142409994le_alt,U_127)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_127) = ti(arrow_2142409994le_alt,U_126)
    | ti(arrow_2142409994le_alt,U_125) = ti(arrow_2142409994le_alt,U_124) ),
    inference(clausify,[status(thm)],[f_96_5]) ).

fof(f_97_1,plain,
    ! [P_2,Pa,A_5,B_4,Aa,Ba] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2)))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa)))
      | ? [I_1] :
          ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1))) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1))) ) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_2),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,Ba) = ti(arrow_2142409994le_alt,A_5)
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,B_4)
      | ti(arrow_2142409994le_alt,A_5) = ti(arrow_2142409994le_alt,B_4)
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,Ba) ),
    inference(fof_nnf,[status(thm)],[fact_7__C1_C]) ).

fof(f_97_2,plain,
    ! [U_138,U_137,U_136,U_135,U_134,U_133] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_138)))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_137)))
      | ? [U_132] :
          ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,U_132)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,U_132))) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,U_132)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,U_132))) ) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_138),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_137),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_133) = ti(arrow_2142409994le_alt,U_136)
      | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_135)
      | ti(arrow_2142409994le_alt,U_136) = ti(arrow_2142409994le_alt,U_135)
      | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_133) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

fof(f_97_3,plain,
    ! [U_138,U_137,U_136,U_135,U_134,U_133] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_138)))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_137)))
      | ? [U_140] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,U_140)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,U_140))) )
      | ? [U_139] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,U_139)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,U_139))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_138),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_137),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_133) = ti(arrow_2142409994le_alt,U_136)
      | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_135)
      | ti(arrow_2142409994le_alt,U_136) = ti(arrow_2142409994le_alt,U_135)
      | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_133) ),
    inference(miniscope,[status(thm)],[f_97_2]) ).

fof(f_97_4,plain,
    ! [U_138,U_137,U_136,U_135,U_134,U_133] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_138)))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_137)))
      | ? [U_140] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,U_140)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,U_140))) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,sK3(U_138,U_137,U_136,U_135,U_134,U_133))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,sK3(U_138,U_137,U_136,U_135,U_134,U_133)))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_138),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_137),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_133) = ti(arrow_2142409994le_alt,U_136)
      | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_135)
      | ti(arrow_2142409994le_alt,U_136) = ti(arrow_2142409994le_alt,U_135)
      | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_133) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_139,sK3(U_138,U_137,U_136,U_135,U_134,U_133))],[f_97_3]) ).

fof(f_97_5,plain,
    ! [U_138,U_137,U_136,U_135,U_134,U_133] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_138)))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_137)))
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,sK4(U_138,U_137,U_136,U_135,U_134,U_133))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,sK4(U_138,U_137,U_136,U_135,U_134,U_133)))) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,sK3(U_138,U_137,U_136,U_135,U_134,U_133))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,sK3(U_138,U_137,U_136,U_135,U_134,U_133)))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_138),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_137),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_133) = ti(arrow_2142409994le_alt,U_136)
      | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_135)
      | ti(arrow_2142409994le_alt,U_136) = ti(arrow_2142409994le_alt,U_135)
      | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_133) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_140,sK4(U_138,U_137,U_136,U_135,U_134,U_133))],[f_97_4]) ).

cnf(f_97_6,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,sK4(U_138,U_137,U_136,U_135,U_134,U_133))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,sK3(U_138,U_137,U_136,U_135,U_134,U_133))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_138)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_137)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_138),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_137),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_133) = ti(arrow_2142409994le_alt,U_136)
    | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_135)
    | ti(arrow_2142409994le_alt,U_136) = ti(arrow_2142409994le_alt,U_135)
    | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_133) ),
    inference(clausify,[status(thm)],[f_97_5]) ).

cnf(f_97_7,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,sK4(U_138,U_137,U_136,U_135,U_134,U_133))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,sK3(U_138,U_137,U_136,U_135,U_134,U_133))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_138)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_137)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_138),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_137),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_133) = ti(arrow_2142409994le_alt,U_136)
    | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_135)
    | ti(arrow_2142409994le_alt,U_136) = ti(arrow_2142409994le_alt,U_135)
    | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_133) ),
    inference(clausify,[status(thm)],[f_97_5]) ).

cnf(f_97_8,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,sK4(U_138,U_137,U_136,U_135,U_134,U_133))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,sK3(U_138,U_137,U_136,U_135,U_134,U_133))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_138)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_137)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_138),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_137),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_133) = ti(arrow_2142409994le_alt,U_136)
    | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_135)
    | ti(arrow_2142409994le_alt,U_136) = ti(arrow_2142409994le_alt,U_135)
    | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_133) ),
    inference(clausify,[status(thm)],[f_97_5]) ).

cnf(f_97_9,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_137,sK4(U_138,U_137,U_136,U_135,U_134,U_133))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_138,sK3(U_138,U_137,U_136,U_135,U_134,U_133))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_136),U_135)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_138)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_134),U_133)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_137)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_138),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_137),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_133) = ti(arrow_2142409994le_alt,U_136)
    | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_135)
    | ti(arrow_2142409994le_alt,U_136) = ti(arrow_2142409994le_alt,U_135)
    | ti(arrow_2142409994le_alt,U_134) = ti(arrow_2142409994le_alt,U_133) ),
    inference(clausify,[status(thm)],[f_97_5]) ).

fof(f_98_1,plain,
    ! [P_2,Pa,Ca,Aa,Ba] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Ca)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Ca)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa))) ) )
      | ? [I_1] :
          ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Ca)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1))) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Ca)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1))) ) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_2),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,Ca)
      | ti(arrow_2142409994le_alt,Ba) = ti(arrow_2142409994le_alt,Ca)
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,Ba) ),
    inference(fof_nnf,[status(thm)],[fact_8__C4_C]) ).

fof(f_98_2,plain,
    ! [U_146,U_145,U_144,U_143,U_142] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145))) ) )
      | ? [U_141] :
          ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,U_141)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,U_141))) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,U_141)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,U_141))) ) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
      | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
      | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

fof(f_98_3,plain,
    ! [U_146,U_145,U_144,U_143,U_142] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145))) ) )
      | ? [U_148] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,U_148)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,U_148))) )
      | ? [U_147] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,U_147)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,U_147))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
      | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
      | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(miniscope,[status(thm)],[f_98_2]) ).

fof(f_98_4,plain,
    ! [U_146,U_145,U_144,U_143,U_142] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145))) ) )
      | ? [U_148] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,U_148)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,U_148))) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK5(U_146,U_145,U_144,U_143,U_142))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK5(U_146,U_145,U_144,U_143,U_142)))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
      | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
      | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_147,sK5(U_146,U_145,U_144,U_143,U_142))],[f_98_3]) ).

fof(f_98_5,plain,
    ! [U_146,U_145,U_144,U_143,U_142] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145))) ) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK6(U_146,U_145,U_144,U_143,U_142))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK6(U_146,U_145,U_144,U_143,U_142)))) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK5(U_146,U_145,U_144,U_143,U_142))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK5(U_146,U_145,U_144,U_143,U_142)))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
      | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
      | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_148,sK6(U_146,U_145,U_144,U_143,U_142))],[f_98_4]) ).

cnf(f_98_6,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK6(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK5(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(clausify,[status(thm)],[f_98_5]) ).

cnf(f_98_7,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK6(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK5(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(clausify,[status(thm)],[f_98_5]) ).

cnf(f_98_8,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK6(U_146,U_145,U_144,U_143,U_142))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK5(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(clausify,[status(thm)],[f_98_5]) ).

cnf(f_98_9,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK6(U_146,U_145,U_144,U_143,U_142))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK5(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(clausify,[status(thm)],[f_98_5]) ).

cnf(f_98_10,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK6(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK5(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(clausify,[status(thm)],[f_98_5]) ).

cnf(f_98_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK6(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK5(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(clausify,[status(thm)],[f_98_5]) ).

cnf(f_98_12,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK6(U_146,U_145,U_144,U_143,U_142))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK5(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(clausify,[status(thm)],[f_98_5]) ).

cnf(f_98_13,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_145,sK6(U_146,U_145,U_144,U_143,U_142))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_146,sK5(U_146,U_145,U_144,U_143,U_142))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_143),U_142)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_145)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_142),U_144)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_146)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_146),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_145),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_142) = ti(arrow_2142409994le_alt,U_144)
    | ti(arrow_2142409994le_alt,U_143) = ti(arrow_2142409994le_alt,U_142) ),
    inference(clausify,[status(thm)],[f_98_5]) ).

fof(f_99_1,plain,
    ! [P_2,Pa,A_5,B_4,Aa,Ba] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa))) ) )
      | ? [I_1] :
          ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1))) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_5),B_4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1))) ) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_2),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,A_5) = ti(arrow_2142409994le_alt,B_4)
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,Ba) ),
    inference(fof_nnf,[status(thm)],[fact_9_pairwise__neutrality]) ).

fof(f_99_2,plain,
    ! [U_155,U_154,U_153,U_152,U_151,U_150] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154))) ) )
      | ? [U_149] :
          ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,U_149)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,U_149))) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,U_149)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,U_149))) ) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
      | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ! [U_155,U_154,U_153,U_152,U_151,U_150] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154))) ) )
      | ? [U_157] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,U_157)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,U_157))) )
      | ? [U_156] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,U_156)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,U_156))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
      | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(miniscope,[status(thm)],[f_99_2]) ).

fof(f_99_4,plain,
    ! [U_155,U_154,U_153,U_152,U_151,U_150] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154))) ) )
      | ? [U_157] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,U_157)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,U_157))) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK7(U_155,U_154,U_153,U_152,U_151,U_150))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK7(U_155,U_154,U_153,U_152,U_151,U_150)))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
      | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_156,sK7(U_155,U_154,U_153,U_152,U_151,U_150))],[f_99_3]) ).

fof(f_99_5,plain,
    ! [U_155,U_154,U_153,U_152,U_151,U_150] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154))) ) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK8(U_155,U_154,U_153,U_152,U_151,U_150))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK8(U_155,U_154,U_153,U_152,U_151,U_150)))) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK7(U_155,U_154,U_153,U_152,U_151,U_150))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK7(U_155,U_154,U_153,U_152,U_151,U_150)))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
      | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_157,sK8(U_155,U_154,U_153,U_152,U_151,U_150))],[f_99_4]) ).

cnf(f_99_6,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK8(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK7(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
    | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

cnf(f_99_7,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK8(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK7(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
    | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

cnf(f_99_8,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK8(U_155,U_154,U_153,U_152,U_151,U_150))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK7(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
    | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

cnf(f_99_9,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK8(U_155,U_154,U_153,U_152,U_151,U_150))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK7(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
    | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

cnf(f_99_10,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK8(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK7(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
    | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

cnf(f_99_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK8(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK7(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
    | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

cnf(f_99_12,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK8(U_155,U_154,U_153,U_152,U_151,U_150))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK7(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
    | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

cnf(f_99_13,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_154,sK8(U_155,U_154,U_153,U_152,U_151,U_150))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_155,sK7(U_155,U_154,U_153,U_152,U_151,U_150))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_151),U_150)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_154)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_153),U_152)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_155)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_155),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_154),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_153) = ti(arrow_2142409994le_alt,U_152)
    | ti(arrow_2142409994le_alt,U_151) = ti(arrow_2142409994le_alt,U_150) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

fof(f_100_1,plain,
    ! [P_2,Pa,Aa,Ba] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Aa)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Aa)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,P_2)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,Pa))) ) )
      | ? [I_1] :
          ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Aa)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1))) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Aa)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),P_2,I_1)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Pa,I_1))) ) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),P_2),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Pa),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,Ba) ),
    inference(fof_nnf,[status(thm)],[fact_10__C3_C]) ).

fof(f_100_2,plain,
    ! [U_162,U_161,U_160,U_159] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161))) ) )
      | ? [U_158] :
          ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,U_158)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,U_158))) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,U_158)))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,U_158))) ) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

fof(f_100_3,plain,
    ! [U_162,U_161,U_160,U_159] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161))) ) )
      | ? [U_164] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,U_164)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,U_164))) )
      | ? [U_163] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,U_163)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,U_163))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(miniscope,[status(thm)],[f_100_2]) ).

fof(f_100_4,plain,
    ! [U_162,U_161,U_160,U_159] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161))) ) )
      | ? [U_164] :
          ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,U_164)))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,U_164))) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK9(U_162,U_161,U_160,U_159))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK9(U_162,U_161,U_160,U_159)))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_163,sK9(U_162,U_161,U_160,U_159))],[f_100_3]) ).

fof(f_100_5,plain,
    ! [U_162,U_161,U_160,U_159] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162))) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161))) ) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK10(U_162,U_161,U_160,U_159))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK10(U_162,U_161,U_160,U_159)))) )
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK9(U_162,U_161,U_160,U_159))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK9(U_162,U_161,U_160,U_159)))) )
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
      | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_164,sK10(U_162,U_161,U_160,U_159))],[f_100_4]) ).

cnf(f_100_6,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK10(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK9(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

cnf(f_100_7,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK10(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK9(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

cnf(f_100_8,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK10(U_162,U_161,U_160,U_159))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK9(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

cnf(f_100_9,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK10(U_162,U_161,U_160,U_159))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK9(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

cnf(f_100_10,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK10(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK9(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

cnf(f_100_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK10(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK9(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

cnf(f_100_12,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK10(U_162,U_161,U_160,U_159))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK9(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

cnf(f_100_13,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_161,sK10(U_162,U_161,U_160,U_159))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_162,sK9(U_162,U_161,U_160,U_159))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_160),U_159)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_161)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_159),U_160)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,U_162)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_162),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_161),arrow_301600364e_Prof))
    | ti(arrow_2142409994le_alt,U_160) = ti(arrow_2142409994le_alt,U_159) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

fof(f_101_1,plain,
    ! [I_1] :
      ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)))
        | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,I_1) != n )
            | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),c),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,I_1) = n ) )
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) ) )
      & ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,I_1) = n )
              & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),c),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,I_1) != n ) )
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) ) )
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),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_101_2,plain,
    ! [U_165] :
      ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_165)))
        | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_165)),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_165) != n )
            | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_165)),c),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_165) = n ) )
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_165)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_165)),e)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_165)),n)) ) )
      & ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_165)),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_165) = n )
              & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_165)),c),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_165) != n ) )
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_165)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_165)),e)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_165)),n)) ) )
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_165))) ) ),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

fof(f_101_3,plain,
    ( ! [U_167] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)))
        | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_167) != n )
            | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),c),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_167) = n ) )
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_167)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_167)),n)) ) )
    & ! [U_166] :
        ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_166)),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_166) = n )
              & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_166)),c),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_166) != n ) )
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_166)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_166)),e)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_166)),n)) ) )
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_166))) ) ),
    inference(miniscope,[status(thm)],[f_101_2]) ).

cnf(f_101_4,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_166)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_166)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_166))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_5,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_166)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_166) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_166)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_166))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_6,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_166)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_166) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_166)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_166))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_167)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_167)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_8,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_167) != n
    | hAPP(arrow_1998540521e_indi,nat,h,U_167) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_167)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_9,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_167) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_167)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_10,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_167) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_167)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_167)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_12,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_167)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_13,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_167) != n
    | hAPP(arrow_1998540521e_indi,nat,h,U_167) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_14,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_167) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_15,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_167) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

cnf(f_101_16,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_167))) ),
    inference(clausify,[status(thm)],[f_101_3]) ).

fof(f_102_1,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_indi,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_102_2,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_indi,bool))),h),n)))),
    inference(clausify,[status(thm)],[f_102_1]) ).

fof(f_103_1,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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_103_2,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
    inference(clausify,[status(thm)],[f_103_1]) ).

fof(f_104_1,plain,
    ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_214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)
    & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ) ),
    inference(fof_nnf,[status(thm)],[fact_14_PW]) ).

cnf(f_104_2,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ),
    inference(clausify,[status(thm)],[f_104_1]) ).

cnf(f_104_3,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
    inference(clausify,[status(thm)],[f_104_1]) ).

fof(f_105_1,plain,
    ! [X_a,X_b,Pa] :
      ( ( ! [X1] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))
        | ? [A_4,B_3] : ~ hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3))) )
      & ( ! [A_4,B_3] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3)))
        | ? [X1] : ~ hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_15_split__paired__All]) ).

fof(f_105_2,plain,
    ! [U_176,U_175,U_174] :
      ( ( ! [U_173] : hBOOL(hAPP(product_prod(U_176,U_175),bool,U_174,U_173))
        | ? [U_172,U_171] : ~ hBOOL(hAPP(product_prod(U_176,U_175),bool,U_174,hAPP(U_175,product_prod(U_176,U_175),hAPP(U_176,fun(U_175,product_prod(U_176,U_175)),product_Pair(U_176,U_175),U_172),U_171))) )
      & ( ! [U_170,U_169] : hBOOL(hAPP(product_prod(U_176,U_175),bool,U_174,hAPP(U_175,product_prod(U_176,U_175),hAPP(U_176,fun(U_175,product_prod(U_176,U_175)),product_Pair(U_176,U_175),U_170),U_169)))
        | ? [U_168] : ~ hBOOL(hAPP(product_prod(U_176,U_175),bool,U_174,U_168)) ) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ( ! [U_182,U_180,U_178] :
        ( ! [U_173] : hBOOL(hAPP(product_prod(U_182,U_180),bool,U_178,U_173))
        | ? [U_172,U_171] : ~ hBOOL(hAPP(product_prod(U_182,U_180),bool,U_178,hAPP(U_180,product_prod(U_182,U_180),hAPP(U_182,fun(U_180,product_prod(U_182,U_180)),product_Pair(U_182,U_180),U_172),U_171))) )
    & ! [U_181,U_179,U_177] :
        ( ! [U_170,U_169] : hBOOL(hAPP(product_prod(U_181,U_179),bool,U_177,hAPP(U_179,product_prod(U_181,U_179),hAPP(U_181,fun(U_179,product_prod(U_181,U_179)),product_Pair(U_181,U_179),U_170),U_169)))
        | ? [U_168] : ~ hBOOL(hAPP(product_prod(U_181,U_179),bool,U_177,U_168)) ) ),
    inference(miniscope,[status(thm)],[f_105_2]) ).

fof(f_105_4,plain,
    ( ! [U_182,U_180,U_178] :
        ( ! [U_173] : hBOOL(hAPP(product_prod(U_182,U_180),bool,U_178,U_173))
        | ? [U_172,U_171] : ~ hBOOL(hAPP(product_prod(U_182,U_180),bool,U_178,hAPP(U_180,product_prod(U_182,U_180),hAPP(U_182,fun(U_180,product_prod(U_182,U_180)),product_Pair(U_182,U_180),U_172),U_171))) )
    & ! [U_181,U_179,U_177] :
        ( ! [U_170,U_169] : hBOOL(hAPP(product_prod(U_181,U_179),bool,U_177,hAPP(U_179,product_prod(U_181,U_179),hAPP(U_181,fun(U_179,product_prod(U_181,U_179)),product_Pair(U_181,U_179),U_170),U_169)))
        | ~ hBOOL(hAPP(product_prod(U_181,U_179),bool,U_177,sK11(U_181,U_179,U_177))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_168,sK11(U_181,U_179,U_177))],[f_105_3]) ).

fof(f_105_5,plain,
    ( ! [U_182,U_180,U_178] :
        ( ! [U_173] : hBOOL(hAPP(product_prod(U_182,U_180),bool,U_178,U_173))
        | ? [U_171] : ~ hBOOL(hAPP(product_prod(U_182,U_180),bool,U_178,hAPP(U_180,product_prod(U_182,U_180),hAPP(U_182,fun(U_180,product_prod(U_182,U_180)),product_Pair(U_182,U_180),sK12(U_182,U_180,U_178)),U_171))) )
    & ! [U_181,U_179,U_177] :
        ( ! [U_170,U_169] : hBOOL(hAPP(product_prod(U_181,U_179),bool,U_177,hAPP(U_179,product_prod(U_181,U_179),hAPP(U_181,fun(U_179,product_prod(U_181,U_179)),product_Pair(U_181,U_179),U_170),U_169)))
        | ~ hBOOL(hAPP(product_prod(U_181,U_179),bool,U_177,sK11(U_181,U_179,U_177))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_172,sK12(U_182,U_180,U_178))],[f_105_4]) ).

fof(f_105_6,plain,
    ( ! [U_182,U_180,U_178] :
        ( ! [U_173] : hBOOL(hAPP(product_prod(U_182,U_180),bool,U_178,U_173))
        | ~ hBOOL(hAPP(product_prod(U_182,U_180),bool,U_178,hAPP(U_180,product_prod(U_182,U_180),hAPP(U_182,fun(U_180,product_prod(U_182,U_180)),product_Pair(U_182,U_180),sK12(U_182,U_180,U_178)),sK13(U_182,U_180,U_178)))) )
    & ! [U_181,U_179,U_177] :
        ( ! [U_170,U_169] : hBOOL(hAPP(product_prod(U_181,U_179),bool,U_177,hAPP(U_179,product_prod(U_181,U_179),hAPP(U_181,fun(U_179,product_prod(U_181,U_179)),product_Pair(U_181,U_179),U_170),U_169)))
        | ~ hBOOL(hAPP(product_prod(U_181,U_179),bool,U_177,sK11(U_181,U_179,U_177))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_171,sK13(U_182,U_180,U_178))],[f_105_5]) ).

cnf(f_105_7,plain,
    ( hBOOL(hAPP(product_prod(U_181,U_179),bool,U_177,hAPP(U_179,product_prod(U_181,U_179),hAPP(U_181,fun(U_179,product_prod(U_181,U_179)),product_Pair(U_181,U_179),U_170),U_169)))
    | ~ hBOOL(hAPP(product_prod(U_181,U_179),bool,U_177,sK11(U_181,U_179,U_177))) ),
    inference(clausify,[status(thm)],[f_105_6]) ).

cnf(f_105_8,plain,
    ( hBOOL(hAPP(product_prod(U_182,U_180),bool,U_178,U_173))
    | ~ hBOOL(hAPP(product_prod(U_182,U_180),bool,U_178,hAPP(U_180,product_prod(U_182,U_180),hAPP(U_182,fun(U_180,product_prod(U_182,U_180)),product_Pair(U_182,U_180),sK12(U_182,U_180,U_178)),sK13(U_182,U_180,U_178)))) ),
    inference(clausify,[status(thm)],[f_105_6]) ).

fof(f_106_1,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_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_106_2,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_Prof)),
    inference(clausify,[status(thm)],[f_106_1]) ).

fof(f_107_1,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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_107_2,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
    inference(clausify,[status(thm)],[f_107_1]) ).

fof(f_108_1,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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_108_2,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
    inference(clausify,[status(thm)],[f_108_1]) ).

fof(f_109_1,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
    inference(fof_nnf,[status(thm)],[fact_19_n_I1_J]) ).

cnf(f_109_2,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
    inference(clausify,[status(thm)],[f_109_1]) ).

fof(f_110_1,plain,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(fof_nnf,[status(thm)],[fact_20_injh]) ).

cnf(f_110_2,plain,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(clausify,[status(thm)],[f_110_1]) ).

fof(f_111_1,plain,
    ! [X_b,X_a,A_2,B_1,A_6,B_5] :
      ( ( ti(X_b,B_1) = ti(X_b,B_5)
        & ti(X_a,A_2) = ti(X_a,A_6) )
      | hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_6),B_5) ),
    inference(fof_nnf,[status(thm)],[fact_21_Pair__inject]) ).

fof(f_111_2,plain,
    ! [U_188,U_187,U_186,U_185,U_184,U_183] :
      ( ( ti(U_188,U_185) = ti(U_188,U_183)
        & ti(U_187,U_186) = ti(U_187,U_184) )
      | hAPP(U_188,product_prod(U_187,U_188),hAPP(U_187,fun(U_188,product_prod(U_187,U_188)),product_Pair(U_187,U_188),U_186),U_185) != hAPP(U_188,product_prod(U_187,U_188),hAPP(U_187,fun(U_188,product_prod(U_187,U_188)),product_Pair(U_187,U_188),U_184),U_183) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

cnf(f_111_3,plain,
    ( ti(U_187,U_186) = ti(U_187,U_184)
    | hAPP(U_188,product_prod(U_187,U_188),hAPP(U_187,fun(U_188,product_prod(U_187,U_188)),product_Pair(U_187,U_188),U_186),U_185) != hAPP(U_188,product_prod(U_187,U_188),hAPP(U_187,fun(U_188,product_prod(U_187,U_188)),product_Pair(U_187,U_188),U_184),U_183) ),
    inference(clausify,[status(thm)],[f_111_2]) ).

cnf(f_111_4,plain,
    ( ti(U_188,U_185) = ti(U_188,U_183)
    | hAPP(U_188,product_prod(U_187,U_188),hAPP(U_187,fun(U_188,product_prod(U_187,U_188)),product_Pair(U_187,U_188),U_186),U_185) != hAPP(U_188,product_prod(U_187,U_188),hAPP(U_187,fun(U_188,product_prod(U_187,U_188)),product_Pair(U_187,U_188),U_184),U_183) ),
    inference(clausify,[status(thm)],[f_111_2]) ).

fof(f_112_1,plain,
    ! [X_b,X_a,Aa,Ba,A_5,B_4] :
      ( ( hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_4)
        | ti(X_b,Ba) != ti(X_b,B_4)
        | ti(X_a,Aa) != ti(X_a,A_5) )
      & ( ( ti(X_b,Ba) = ti(X_b,B_4)
          & ti(X_a,Aa) = ti(X_a,A_5) )
        | hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_4) ) ),
    inference(fof_nnf,[status(thm)],[fact_22_Pair__eq]) ).

fof(f_112_2,plain,
    ! [U_194,U_193,U_192,U_191,U_190,U_189] :
      ( ( hAPP(U_194,product_prod(U_193,U_194),hAPP(U_193,fun(U_194,product_prod(U_193,U_194)),product_Pair(U_193,U_194),U_192),U_191) = hAPP(U_194,product_prod(U_193,U_194),hAPP(U_193,fun(U_194,product_prod(U_193,U_194)),product_Pair(U_193,U_194),U_190),U_189)
        | ti(U_194,U_191) != ti(U_194,U_189)
        | ti(U_193,U_192) != ti(U_193,U_190) )
      & ( ( ti(U_194,U_191) = ti(U_194,U_189)
          & ti(U_193,U_192) = ti(U_193,U_190) )
        | hAPP(U_194,product_prod(U_193,U_194),hAPP(U_193,fun(U_194,product_prod(U_193,U_194)),product_Pair(U_193,U_194),U_192),U_191) != hAPP(U_194,product_prod(U_193,U_194),hAPP(U_193,fun(U_194,product_prod(U_193,U_194)),product_Pair(U_193,U_194),U_190),U_189) ) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ( ! [U_206,U_204,U_202,U_200,U_198,U_196] :
        ( hAPP(U_206,product_prod(U_204,U_206),hAPP(U_204,fun(U_206,product_prod(U_204,U_206)),product_Pair(U_204,U_206),U_202),U_200) = hAPP(U_206,product_prod(U_204,U_206),hAPP(U_204,fun(U_206,product_prod(U_204,U_206)),product_Pair(U_204,U_206),U_198),U_196)
        | ti(U_206,U_200) != ti(U_206,U_196)
        | ti(U_204,U_202) != ti(U_204,U_198) )
    & ! [U_205,U_203,U_201,U_199,U_197,U_195] :
        ( ( ti(U_205,U_199) = ti(U_205,U_195)
          & ti(U_203,U_201) = ti(U_203,U_197) )
        | hAPP(U_205,product_prod(U_203,U_205),hAPP(U_203,fun(U_205,product_prod(U_203,U_205)),product_Pair(U_203,U_205),U_201),U_199) != hAPP(U_205,product_prod(U_203,U_205),hAPP(U_203,fun(U_205,product_prod(U_203,U_205)),product_Pair(U_203,U_205),U_197),U_195) ) ),
    inference(miniscope,[status(thm)],[f_112_2]) ).

cnf(f_112_4,plain,
    ( ti(U_203,U_201) = ti(U_203,U_197)
    | hAPP(U_205,product_prod(U_203,U_205),hAPP(U_203,fun(U_205,product_prod(U_203,U_205)),product_Pair(U_203,U_205),U_201),U_199) != hAPP(U_205,product_prod(U_203,U_205),hAPP(U_203,fun(U_205,product_prod(U_203,U_205)),product_Pair(U_203,U_205),U_197),U_195) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

cnf(f_112_5,plain,
    ( ti(U_205,U_199) = ti(U_205,U_195)
    | hAPP(U_205,product_prod(U_203,U_205),hAPP(U_203,fun(U_205,product_prod(U_203,U_205)),product_Pair(U_203,U_205),U_201),U_199) != hAPP(U_205,product_prod(U_203,U_205),hAPP(U_203,fun(U_205,product_prod(U_203,U_205)),product_Pair(U_203,U_205),U_197),U_195) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

cnf(f_112_6,plain,
    ( hAPP(U_206,product_prod(U_204,U_206),hAPP(U_204,fun(U_206,product_prod(U_204,U_206)),product_Pair(U_204,U_206),U_202),U_200) = hAPP(U_206,product_prod(U_204,U_206),hAPP(U_204,fun(U_206,product_prod(U_204,U_206)),product_Pair(U_204,U_206),U_198),U_196)
    | ti(U_206,U_200) != ti(U_206,U_196)
    | ti(U_204,U_202) != ti(U_204,U_198) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_1,plain,
    ! [Fa] :
      ( ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,Fa))
        | ? [X_1] :
            ( ? [Xa] :
                ( ? [A_4,B_3] :
                    ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,Xa))) )
                      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,Xa)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1))) ) )
                    & ! [I_1] :
                        ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I_1)))
                          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Xa,I_1))) )
                        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Xa,I_1)))
                          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I_1))) ) ) )
                & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Xa),arrow_301600364e_Prof)) )
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof)) ) )
      & ( ! [X_1] :
            ( ! [Xa] :
                ( ! [A_4,B_3] :
                    ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,Xa))) )
                      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,Xa)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1))) ) )
                    | ? [I_1] :
                        ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I_1)))
                          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Xa,I_1))) )
                        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Xa,I_1)))
                          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I_1))) ) ) )
                | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Xa),arrow_301600364e_Prof)) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,Fa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_23_IIA__def]) ).

fof(f_113_2,plain,
    ! [U_217] :
      ( ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_217))
        | ? [U_216] :
            ( ? [U_215] :
                ( ? [U_214,U_213] :
                    ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_217,U_216)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_217,U_215))) )
                      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_217,U_215)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_217,U_216))) ) )
                    & ! [U_212] :
                        ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_216,U_212)))
                          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_215,U_212))) )
                        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_215,U_212)))
                          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_216,U_212))) ) ) )
                & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_215),arrow_301600364e_Prof)) )
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_216),arrow_301600364e_Prof)) ) )
      & ( ! [U_211] :
            ( ! [U_210] :
                ( ! [U_209,U_208] :
                    ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_217,U_211)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_217,U_210))) )
                      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_217,U_210)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_217,U_211))) ) )
                    | ? [U_207] :
                        ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,U_207)))
                          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,U_207))) )
                        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,U_207)))
                          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,U_207))) ) ) )
                | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof)) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_217)) ) ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ( ! [U_223] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223))
        | ? [U_216] :
            ( ? [U_215] :
                ( ? [U_214,U_213] :
                    ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_216)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_215))) )
                      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_215)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_216))) ) )
                    & ! [U_221] :
                        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_216,U_221)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_215,U_221))) )
                    & ! [U_220] :
                        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_215,U_220)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_216,U_220))) ) )
                & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_215),arrow_301600364e_Prof)) )
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_216),arrow_301600364e_Prof)) ) )
    & ! [U_222] :
        ( ! [U_211] :
            ( ! [U_210] :
                ( ! [U_209,U_208] :
                    ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210))) )
                      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211))) ) )
                    | ? [U_219] :
                        ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,U_219)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,U_219))) )
                    | ? [U_218] :
                        ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,U_218)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,U_218))) ) )
                | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof)) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ) ),
    inference(miniscope,[status(thm)],[f_113_2]) ).

fof(f_113_4,plain,
    ( ! [U_223] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223))
        | ? [U_216] :
            ( ? [U_215] :
                ( ? [U_214,U_213] :
                    ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_216)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_215))) )
                      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_215)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_216))) ) )
                    & ! [U_221] :
                        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_216,U_221)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_215,U_221))) )
                    & ! [U_220] :
                        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_215,U_220)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_216,U_220))) ) )
                & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_215),arrow_301600364e_Prof)) )
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_216),arrow_301600364e_Prof)) ) )
    & ! [U_222] :
        ( ! [U_211] :
            ( ! [U_210] :
                ( ! [U_209,U_208] :
                    ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210))) )
                      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211))) ) )
                    | ? [U_219] :
                        ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,U_219)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,U_219))) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK14(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK14(U_222,U_211,U_210,U_209,U_208)))) ) )
                | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof)) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_218,sK14(U_222,U_211,U_210,U_209,U_208))],[f_113_3]) ).

fof(f_113_5,plain,
    ( ! [U_223] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223))
        | ? [U_216] :
            ( ? [U_215] :
                ( ? [U_214,U_213] :
                    ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_216)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_215))) )
                      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_215)))
                        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_216))) ) )
                    & ! [U_221] :
                        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_216,U_221)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_215,U_221))) )
                    & ! [U_220] :
                        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_215,U_220)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_216,U_220))) ) )
                & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_215),arrow_301600364e_Prof)) )
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_216),arrow_301600364e_Prof)) ) )
    & ! [U_222] :
        ( ! [U_211] :
            ( ! [U_210] :
                ( ! [U_209,U_208] :
                    ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210))) )
                      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211))) ) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK15(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK15(U_222,U_211,U_210,U_209,U_208)))) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK14(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK14(U_222,U_211,U_210,U_209,U_208)))) ) )
                | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof)) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_219,sK15(U_222,U_211,U_210,U_209,U_208))],[f_113_4]) ).

fof(f_113_6,plain,
    ( ! [U_223] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223))
        | ( ? [U_215] :
              ( ? [U_214,U_213] :
                  ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_215))) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,U_215)))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223)))) ) )
                  & ! [U_221] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK16(U_223),U_221)))
                      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_215,U_221))) )
                  & ! [U_220] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_215,U_220)))
                      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK16(U_223),U_220))) ) )
              & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_215),arrow_301600364e_Prof)) )
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK16(U_223)),arrow_301600364e_Prof)) ) )
    & ! [U_222] :
        ( ! [U_211] :
            ( ! [U_210] :
                ( ! [U_209,U_208] :
                    ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210))) )
                      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211))) ) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK15(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK15(U_222,U_211,U_210,U_209,U_208)))) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK14(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK14(U_222,U_211,U_210,U_209,U_208)))) ) )
                | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof)) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_216,sK16(U_223))],[f_113_5]) ).

fof(f_113_7,plain,
    ( ! [U_223] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223))
        | ( ? [U_214,U_213] :
              ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223))))
                  & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK17(U_223)))) )
                | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK17(U_223))))
                  & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223)))) ) )
              & ! [U_221] :
                  ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK16(U_223),U_221)))
                  | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK17(U_223),U_221))) )
              & ! [U_220] :
                  ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK17(U_223),U_220)))
                  | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_214),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK16(U_223),U_220))) ) )
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK17(U_223)),arrow_301600364e_Prof))
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK16(U_223)),arrow_301600364e_Prof)) ) )
    & ! [U_222] :
        ( ! [U_211] :
            ( ! [U_210] :
                ( ! [U_209,U_208] :
                    ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210))) )
                      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211))) ) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK15(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK15(U_222,U_211,U_210,U_209,U_208)))) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK14(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK14(U_222,U_211,U_210,U_209,U_208)))) ) )
                | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof)) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_215,sK17(U_223))],[f_113_6]) ).

fof(f_113_8,plain,
    ( ! [U_223] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223))
        | ( ? [U_213] :
              ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223))))
                  & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK17(U_223)))) )
                | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK17(U_223))))
                  & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),U_213)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223)))) ) )
              & ! [U_221] :
                  ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK16(U_223),U_221)))
                  | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK17(U_223),U_221))) )
              & ! [U_220] :
                  ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK17(U_223),U_220)))
                  | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),U_213)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK16(U_223),U_220))) ) )
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK17(U_223)),arrow_301600364e_Prof))
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK16(U_223)),arrow_301600364e_Prof)) ) )
    & ! [U_222] :
        ( ! [U_211] :
            ( ! [U_210] :
                ( ! [U_209,U_208] :
                    ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210))) )
                      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211))) ) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK15(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK15(U_222,U_211,U_210,U_209,U_208)))) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK14(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK14(U_222,U_211,U_210,U_209,U_208)))) ) )
                | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof)) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_214,sK18(U_223))],[f_113_7]) ).

fof(f_113_9,plain,
    ( ! [U_223] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223))
        | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223))))
              & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK17(U_223)))) )
            | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK17(U_223))))
              & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223)))) ) )
          & ! [U_221] :
              ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK16(U_223),U_221)))
              | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK17(U_223),U_221))) )
          & ! [U_220] :
              ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK17(U_223),U_220)))
              | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK16(U_223),U_220))) )
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK17(U_223)),arrow_301600364e_Prof))
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK16(U_223)),arrow_301600364e_Prof)) ) )
    & ! [U_222] :
        ( ! [U_211] :
            ( ! [U_210] :
                ( ! [U_209,U_208] :
                    ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210))) )
                      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
                        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211))) ) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK15(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK15(U_222,U_211,U_210,U_209,U_208)))) )
                    | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK14(U_222,U_211,U_210,U_209,U_208))))
                      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK14(U_222,U_211,U_210,U_209,U_208)))) ) )
                | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof)) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_213,sK19(U_223))],[f_113_8]) ).

cnf(f_113_10,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK15(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK14(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK15(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK14(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_12,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK15(U_222,U_211,U_210,U_209,U_208))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK14(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_13,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK15(U_222,U_211,U_210,U_209,U_208))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK14(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_14,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK15(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK14(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_15,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK15(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK14(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_16,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK15(U_222,U_211,U_210,U_209,U_208))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK14(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_17,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_211,sK15(U_222,U_211,U_210,U_209,U_208))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_210,sK14(U_222,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_211)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_209),U_208)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_222,U_210)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_210),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_211),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_222)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_18,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK16(U_223)),arrow_301600364e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_19,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK17(U_223)),arrow_301600364e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_20,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK17(U_223),U_220)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK16(U_223),U_220)))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_21,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK16(U_223),U_221)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK17(U_223),U_221)))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_22,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK17(U_223))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223))))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_23,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223))))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_24,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK17(U_223))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK17(U_223))))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

cnf(f_113_25,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK16(U_223))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK18(U_223)),sK19(U_223))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_223,sK17(U_223))))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,U_223)) ),
    inference(clausify,[status(thm)],[f_113_9]) ).

fof(f_114_1,plain,
    ! [Fa] :
      ( ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,Fa))
        | ? [X_1] :
            ( ? [A_4,B_3] :
                ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1)))
                & ! [I_1] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I_1))) )
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof)) ) )
      & ( ! [X_1] :
            ( ! [A_4,B_3] :
                ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1)))
                | ? [I_1] : ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I_1))) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,Fa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_24_unanimity__def]) ).

fof(f_114_2,plain,
    ! [U_232] :
      ( ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_232))
        | ? [U_231] :
            ( ? [U_230,U_229] :
                ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_230),U_229)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_232,U_231)))
                & ! [U_228] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_230),U_229)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_231,U_228))) )
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_231),arrow_301600364e_Prof)) ) )
      & ( ! [U_227] :
            ( ! [U_226,U_225] :
                ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_232,U_227)))
                | ? [U_224] : ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_227,U_224))) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_227),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_232)) ) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ( ! [U_234] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_234))
        | ? [U_231] :
            ( ? [U_230,U_229] :
                ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_230),U_229)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_234,U_231)))
                & ! [U_228] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_230),U_229)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_231,U_228))) )
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_231),arrow_301600364e_Prof)) ) )
    & ! [U_233] :
        ( ! [U_227] :
            ( ! [U_226,U_225] :
                ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_233,U_227)))
                | ? [U_224] : ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_227,U_224))) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_227),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_233)) ) ),
    inference(miniscope,[status(thm)],[f_114_2]) ).

fof(f_114_4,plain,
    ( ! [U_234] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_234))
        | ? [U_231] :
            ( ? [U_230,U_229] :
                ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_230),U_229)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_234,U_231)))
                & ! [U_228] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_230),U_229)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_231,U_228))) )
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_231),arrow_301600364e_Prof)) ) )
    & ! [U_233] :
        ( ! [U_227] :
            ( ! [U_226,U_225] :
                ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_233,U_227)))
                | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_227,sK20(U_233,U_227,U_226,U_225)))) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_227),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_233)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_224,sK20(U_233,U_227,U_226,U_225))],[f_114_3]) ).

fof(f_114_5,plain,
    ( ! [U_234] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_234))
        | ( ? [U_230,U_229] :
              ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_230),U_229)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_234,sK21(U_234))))
              & ! [U_228] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_230),U_229)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK21(U_234),U_228))) )
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK21(U_234)),arrow_301600364e_Prof)) ) )
    & ! [U_233] :
        ( ! [U_227] :
            ( ! [U_226,U_225] :
                ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_233,U_227)))
                | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_227,sK20(U_233,U_227,U_226,U_225)))) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_227),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_233)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_231,sK21(U_234))],[f_114_4]) ).

fof(f_114_6,plain,
    ( ! [U_234] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_234))
        | ( ? [U_229] :
              ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK22(U_234)),U_229)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_234,sK21(U_234))))
              & ! [U_228] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK22(U_234)),U_229)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK21(U_234),U_228))) )
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK21(U_234)),arrow_301600364e_Prof)) ) )
    & ! [U_233] :
        ( ! [U_227] :
            ( ! [U_226,U_225] :
                ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_233,U_227)))
                | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_227,sK20(U_233,U_227,U_226,U_225)))) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_227),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_233)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_230,sK22(U_234))],[f_114_5]) ).

fof(f_114_7,plain,
    ( ! [U_234] :
        ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_234))
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK22(U_234)),sK23(U_234))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_234,sK21(U_234))))
          & ! [U_228] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK22(U_234)),sK23(U_234))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK21(U_234),U_228)))
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK21(U_234)),arrow_301600364e_Prof)) ) )
    & ! [U_233] :
        ( ! [U_227] :
            ( ! [U_226,U_225] :
                ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_233,U_227)))
                | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_227,sK20(U_233,U_227,U_226,U_225)))) )
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_227),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_233)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_229,sK23(U_234))],[f_114_6]) ).

cnf(f_114_8,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_233,U_227)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_226),U_225)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_227,sK20(U_233,U_227,U_226,U_225))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_227),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_233)) ),
    inference(clausify,[status(thm)],[f_114_7]) ).

cnf(f_114_9,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK21(U_234)),arrow_301600364e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_234)) ),
    inference(clausify,[status(thm)],[f_114_7]) ).

cnf(f_114_10,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK22(U_234)),sK23(U_234))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK21(U_234),U_228)))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_234)) ),
    inference(clausify,[status(thm)],[f_114_7]) ).

cnf(f_114_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK22(U_234)),sK23(U_234))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_234,sK21(U_234))))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,U_234)) ),
    inference(clausify,[status(thm)],[f_114_7]) ).

fof(f_115_1,plain,
    ! [X_a,X_2] : hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_2)),
    inference(fof_nnf,[status(thm)],[fact_25_top1I]) ).

fof(f_115_2,plain,
    ! [U_236,U_235] : hBOOL(hAPP(U_236,bool,top_top(fun(U_236,bool)),U_235)),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

cnf(f_115_3,plain,
    hBOOL(hAPP(U_236,bool,top_top(fun(U_236,bool)),U_235)),
    inference(clausify,[status(thm)],[f_115_2]) ).

fof(f_116_1,plain,
    ! [X_a,X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool)))),
    inference(fof_nnf,[status(thm)],[fact_26_UNIV__I]) ).

fof(f_116_2,plain,
    ! [U_238,U_237] : hBOOL(hAPP(fun(U_238,bool),bool,hAPP(U_238,fun(fun(U_238,bool),bool),member(U_238),U_237),top_top(fun(U_238,bool)))),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

cnf(f_116_3,plain,
    hBOOL(hAPP(fun(U_238,bool),bool,hAPP(U_238,fun(fun(U_238,bool),bool),member(U_238),U_237),top_top(fun(U_238,bool)))),
    inference(clausify,[status(thm)],[f_116_2]) ).

fof(f_117_1,plain,
    ! [X_a,X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool)))),
    inference(fof_nnf,[status(thm)],[fact_27_iso__tuple__UNIV__I]) ).

fof(f_117_2,plain,
    ! [U_240,U_239] : hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_239),top_top(fun(U_240,bool)))),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

cnf(f_117_3,plain,
    hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_239),top_top(fun(U_240,bool)))),
    inference(clausify,[status(thm)],[f_117_2]) ).

fof(f_118_1,plain,
    ! [X_b,X_c,X_a,F1,Aa,Ba] : hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba),
    inference(fof_nnf,[status(thm)],[fact_28_prod_Orecs]) ).

fof(f_118_2,plain,
    ! [U_246,U_245,U_244,U_243,U_242,U_241] : hAPP(product_prod(U_246,U_245),U_244,hAPP(fun(U_246,fun(U_245,U_244)),fun(product_prod(U_246,U_245),U_244),product_prod_rec(U_246,U_245,U_244),U_243),hAPP(U_245,product_prod(U_246,U_245),hAPP(U_246,fun(U_245,product_prod(U_246,U_245)),product_Pair(U_246,U_245),U_242),U_241)) = hAPP(U_245,U_244,hAPP(U_246,fun(U_245,U_244),U_243,U_242),U_241),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

cnf(f_118_3,plain,
    hAPP(product_prod(U_246,U_245),U_244,hAPP(fun(U_246,fun(U_245,U_244)),fun(product_prod(U_246,U_245),U_244),product_prod_rec(U_246,U_245,U_244),U_243),hAPP(U_245,product_prod(U_246,U_245),hAPP(U_246,fun(U_245,product_prod(U_246,U_245)),product_Pair(U_246,U_245),U_242),U_241)) = hAPP(U_245,U_244,hAPP(U_246,fun(U_245,U_244),U_243,U_242),U_241),
    inference(clausify,[status(thm)],[f_118_2]) ).

fof(f_119_1,plain,
    ! [X_b,X_a] :
      ( ! [X_2] : hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_2) = top_top(X_a)
      | ~ top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_29_top__apply]) ).

fof(f_119_2,plain,
    ! [U_249,U_248] :
      ( ! [U_247] : hAPP(U_249,U_248,top_top(fun(U_249,U_248)),U_247) = top_top(U_248)
      | ~ top(U_248) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

cnf(f_119_3,plain,
    ( hAPP(U_249,U_248,top_top(fun(U_249,U_248)),U_247) = top_top(U_248)
    | ~ top(U_248) ),
    inference(clausify,[status(thm)],[f_119_2]) ).

fof(f_120_1,plain,
    ! [X_a] :
      ( ! [A_2] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),top_top(X_a)),A_2))
      | ~ top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_30_not__top__less]) ).

fof(f_120_2,plain,
    ! [U_251] :
      ( ! [U_250] : ~ hBOOL(hAPP(U_251,bool,hAPP(U_251,fun(U_251,bool),ord_less(U_251),top_top(U_251)),U_250))
      | ~ top(U_251) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

cnf(f_120_3,plain,
    ( ~ hBOOL(hAPP(U_251,bool,hAPP(U_251,fun(U_251,bool),ord_less(U_251),top_top(U_251)),U_250))
    | ~ top(U_251) ),
    inference(clausify,[status(thm)],[f_120_2]) ).

fof(f_121_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( ti(X_a,Aa) != top_top(X_a)
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),top_top(X_a))) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),top_top(X_a)))
            | ti(X_a,Aa) = top_top(X_a) ) )
      | ~ top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_31_less__top]) ).

fof(f_121_2,plain,
    ! [U_253] :
      ( ! [U_252] :
          ( ( ti(U_253,U_252) != top_top(U_253)
            | ~ hBOOL(hAPP(U_253,bool,hAPP(U_253,fun(U_253,bool),ord_less(U_253),U_252),top_top(U_253))) )
          & ( hBOOL(hAPP(U_253,bool,hAPP(U_253,fun(U_253,bool),ord_less(U_253),U_252),top_top(U_253)))
            | ti(U_253,U_252) = top_top(U_253) ) )
      | ~ top(U_253) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ! [U_253] :
      ( ( ! [U_255] :
            ( ti(U_253,U_255) != top_top(U_253)
            | ~ hBOOL(hAPP(U_253,bool,hAPP(U_253,fun(U_253,bool),ord_less(U_253),U_255),top_top(U_253))) )
        & ! [U_254] :
            ( hBOOL(hAPP(U_253,bool,hAPP(U_253,fun(U_253,bool),ord_less(U_253),U_254),top_top(U_253)))
            | ti(U_253,U_254) = top_top(U_253) ) )
      | ~ top(U_253) ),
    inference(miniscope,[status(thm)],[f_121_2]) ).

cnf(f_121_4,plain,
    ( hBOOL(hAPP(U_253,bool,hAPP(U_253,fun(U_253,bool),ord_less(U_253),U_254),top_top(U_253)))
    | ti(U_253,U_254) = top_top(U_253)
    | ~ top(U_253) ),
    inference(clausify,[status(thm)],[f_121_3]) ).

cnf(f_121_5,plain,
    ( ti(U_253,U_255) != top_top(U_253)
    | ~ hBOOL(hAPP(U_253,bool,hAPP(U_253,fun(U_253,bool),ord_less(U_253),U_255),top_top(U_253)))
    | ~ top(U_253) ),
    inference(clausify,[status(thm)],[f_121_3]) ).

fof(f_122_1,plain,
    hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
    inference(fof_nnf,[status(thm)],[fact_32_assms_I1_J]) ).

cnf(f_122_2,plain,
    hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
    inference(clausify,[status(thm)],[f_122_1]) ).

fof(f_123_1,plain,
    ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) )
    & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba))))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_33__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk]) ).

cnf(f_123_2,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
    inference(clausify,[status(thm)],[f_123_1]) ).

cnf(f_123_3,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    inference(clausify,[status(thm)],[f_123_1]) ).

fof(f_124_1,plain,
    ! [Fa,I] :
      ( ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,Fa),I))
        | ? [X_1] :
            ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I)
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof)) ) )
      & ( ! [X_1] :
            ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I)
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,Fa),I)) ) ),
    inference(fof_nnf,[status(thm)],[fact_34_dictator__def]) ).

fof(f_124_2,plain,
    ! [U_259,U_258] :
      ( ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_259),U_258))
        | ? [U_257] :
            ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_259,U_257) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_257,U_258)
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_257),arrow_301600364e_Prof)) ) )
      & ( ! [U_256] :
            ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_259,U_256) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_256,U_258)
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_256),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_259),U_258)) ) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ( ! [U_263,U_261] :
        ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_263),U_261))
        | ? [U_257] :
            ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_263,U_257) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_257,U_261)
            & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_257),arrow_301600364e_Prof)) ) )
    & ! [U_262,U_260] :
        ( ! [U_256] :
            ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_262,U_256) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_256,U_260)
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_256),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_262),U_260)) ) ),
    inference(miniscope,[status(thm)],[f_124_2]) ).

fof(f_124_4,plain,
    ( ! [U_263,U_261] :
        ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_263),U_261))
        | ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_263,sK24(U_263,U_261)) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK24(U_263,U_261),U_261)
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK24(U_263,U_261)),arrow_301600364e_Prof)) ) )
    & ! [U_262,U_260] :
        ( ! [U_256] :
            ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_262,U_256) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_256,U_260)
            | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_256),arrow_301600364e_Prof)) )
        | ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_262),U_260)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_257,sK24(U_263,U_261))],[f_124_3]) ).

cnf(f_124_5,plain,
    ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_262,U_256) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_256,U_260)
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_256),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_262),U_260)) ),
    inference(clausify,[status(thm)],[f_124_4]) ).

cnf(f_124_6,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK24(U_263,U_261)),arrow_301600364e_Prof))
    | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_263),U_261)) ),
    inference(clausify,[status(thm)],[f_124_4]) ).

cnf(f_124_7,plain,
    ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_263,sK24(U_263,U_261)) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK24(U_263,U_261),U_261)
    | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_263),U_261)) ),
    inference(clausify,[status(thm)],[f_124_4]) ).

fof(f_125_1,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
    inference(fof_nnf,[status(thm)],[fact_35__096Lab_A_058_ALin_096]) ).

cnf(f_125_2,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
    inference(clausify,[status(thm)],[f_125_1]) ).

fof(f_126_1,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
    inference(fof_nnf,[status(thm)],[fact_36__096Lba_A_058_ALin_096]) ).

cnf(f_126_2,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
    inference(clausify,[status(thm)],[f_126_1]) ).

fof(f_127_1,plain,
    a != b,
    inference(fof_nnf,[status(thm)],[fact_37__096a_A_126_061_Ab_096]) ).

cnf(f_127_2,plain,
    a != b,
    inference(clausify,[status(thm)],[f_127_1]) ).

fof(f_128_1,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
    inference(fof_nnf,[status(thm)],[fact_38__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096]) ).

cnf(f_128_2,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
    inference(clausify,[status(thm)],[f_128_1]) ).

fof(f_129_1,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
    inference(fof_nnf,[status(thm)],[fact_39__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096]) ).

cnf(f_129_2,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
    inference(clausify,[status(thm)],[f_129_1]) ).

fof(f_130_1,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
    inference(fof_nnf,[status(thm)],[fact_40__096_Ia_M_Ab_J_A_126_058_ALba_096]) ).

cnf(f_130_2,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
    inference(clausify,[status(thm)],[f_130_1]) ).

fof(f_131_1,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
    inference(fof_nnf,[status(thm)],[fact_41__096_Ib_M_Aa_J_A_126_058_ALab_096]) ).

cnf(f_131_2,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
    inference(clausify,[status(thm)],[f_131_1]) ).

fof(f_132_1,plain,
    ! [Na] : hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),Na))),lab)),lba)),arrow_301600364e_Prof)),
    inference(fof_nnf,[status(thm)],[fact_42_PiProf]) ).

fof(f_132_2,plain,
    ! [U_264] : hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),U_264))),lab)),lba)),arrow_301600364e_Prof)),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

cnf(f_132_3,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),U_264))),lab)),lba)),arrow_301600364e_Prof)),
    inference(clausify,[status(thm)],[f_132_2]) ).

fof(f_133_1,plain,
    ? [Lab] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),Lab),arrow_1568854078le_Lin))
      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),Lab)) ),
    inference(fof_nnf,[status(thm)],[fact_43__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_]) ).

fof(f_133_2,plain,
    ? [U_265] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_265),arrow_1568854078le_Lin))
      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),U_265)) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sK25),arrow_1568854078le_Lin))
    & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),sK25)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_265,sK25)],[f_133_2]) ).

cnf(f_133_4,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),sK25)),
    inference(clausify,[status(thm)],[f_133_3]) ).

cnf(f_133_5,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sK25),arrow_1568854078le_Lin)),
    inference(clausify,[status(thm)],[f_133_3]) ).

fof(f_134_1,plain,
    ? [Lba] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),Lba),arrow_1568854078le_Lin))
      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),Lba)) ),
    inference(fof_nnf,[status(thm)],[fact_44__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_]) ).

fof(f_134_2,plain,
    ? [U_266] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_266),arrow_1568854078le_Lin))
      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),U_266)) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sK26),arrow_1568854078le_Lin))
    & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),sK26)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_266,sK26)],[f_134_2]) ).

cnf(f_134_4,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),sK26)),
    inference(clausify,[status(thm)],[f_134_3]) ).

cnf(f_134_5,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sK26),arrow_1568854078le_Lin)),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_1,plain,
    ! [I_1] :
      ( ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,I_1) = n )
              & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),c),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,I_1) != n ) )
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) ) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) ) )
      & ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) ) )
        | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,I_1) != n )
            | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),c),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,I_1) = n ) )
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_45__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(f_135_2,plain,
    ! [U_267] :
      ( ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_267)),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_267) = n )
              & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_267)),c),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_267) != n ) )
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_267)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_267)),e)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_267)),n)) ) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_267)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_267)),n)) ) )
      & ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_267)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_267)),n)) ) )
        | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_267)),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_267) != n )
            | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_267)),c),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_267) = n ) )
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_267)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_267)),e)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_267)),n)) ) ) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ( ! [U_269] :
        ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_269) = n )
              & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),c),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_269) != n ) )
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ) )
    & ! [U_268] :
        ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ) )
        | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_268) != n )
            | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_268) = n ) )
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ) ) ),
    inference(miniscope,[status(thm)],[f_135_2]) ).

cnf(f_135_4,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_5,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_268) != n
    | hAPP(arrow_1998540521e_indi,nat,h,U_268) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_6,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_268) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_7,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_268) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_8,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_9,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_10,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_268) != n
    | hAPP(arrow_1998540521e_indi,nat,h,U_268) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_268) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_12,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_268) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_13,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_14,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_15,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_268) != n
    | hAPP(arrow_1998540521e_indi,nat,h,U_268) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_16,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_268) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_17,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_268) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_18,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_19,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_20,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_268) != n
    | hAPP(arrow_1998540521e_indi,nat,h,U_268) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_21,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_268) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_22,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_268) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_23,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_24,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_25,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_26,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_27,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_28,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_269) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_29,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_269) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_30,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_269) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_31,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_269) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_32,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_269) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_33,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_269) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_34,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_269) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_35,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_269) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

fof(f_136_1,plain,
    ! [M_1] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),M_1))),lab)),lba))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),n)) ),
    inference(fof_nnf,[status(thm)],[fact_46_n_I2_J]) ).

fof(f_136_2,plain,
    ! [U_270] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),U_270))),lab)),lba))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_270),n)) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

cnf(f_136_3,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),U_270))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_270),n)) ),
    inference(clausify,[status(thm)],[f_136_2]) ).

fof(f_137_1,plain,
    ! [X_2,Y_1,L_3] :
      ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Y_1),X_2)),L_3)) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Y_1),X_2)),L_3))
          | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3)) ) )
      | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Y_1)
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_47_notin__Lin__iff]) ).

fof(f_137_2,plain,
    ! [U_273,U_272,U_271] :
      ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_273),U_272)),U_271))
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_272),U_273)),U_271)) )
        & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_272),U_273)),U_271))
          | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_273),U_272)),U_271)) ) )
      | ti(arrow_2142409994le_alt,U_273) = ti(arrow_2142409994le_alt,U_272)
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_271),arrow_1568854078le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

cnf(f_137_3,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_272),U_273)),U_271))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_273),U_272)),U_271))
    | ti(arrow_2142409994le_alt,U_273) = ti(arrow_2142409994le_alt,U_272)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_271),arrow_1568854078le_Lin)) ),
    inference(clausify,[status(thm)],[f_137_2]) ).

cnf(f_137_4,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_273),U_272)),U_271))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_272),U_273)),U_271))
    | ti(arrow_2142409994le_alt,U_273) = ti(arrow_2142409994le_alt,U_272)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_271),arrow_1568854078le_Lin)) ),
    inference(clausify,[status(thm)],[f_137_2]) ).

fof(f_138_1,plain,
    ! [Aa,Ba,L_3] :
      ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Aa)),L_3))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),L_3))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_48_Lin__irrefl]) ).

fof(f_138_2,plain,
    ! [U_276,U_275,U_274] :
      ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_275),U_276)),U_274))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_276),U_275)),U_274))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_274),arrow_1568854078le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

cnf(f_138_3,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_275),U_276)),U_274))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_276),U_275)),U_274))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_274),arrow_1568854078le_Lin)) ),
    inference(clausify,[status(thm)],[f_138_2]) ).

fof(f_139_1,plain,
    ! [X_2,L_3] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,L_3),X_2)),arrow_1568854078le_Lin))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_49_mktop__Lin]) ).

fof(f_139_2,plain,
    ! [U_278,U_277] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_277),U_278)),arrow_1568854078le_Lin))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_277),arrow_1568854078le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

cnf(f_139_3,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,U_277),U_278)),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_277),arrow_1568854078le_Lin)) ),
    inference(clausify,[status(thm)],[f_139_2]) ).

fof(f_140_1,plain,
    ! [X_2,L_3] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,L_3),X_2)),arrow_1568854078le_Lin))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_50_mkbot__Lin]) ).

fof(f_140_2,plain,
    ! [U_280,U_279] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_279),U_280)),arrow_1568854078le_Lin))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_279),arrow_1568854078le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

cnf(f_140_3,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,U_279),U_280)),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_279),arrow_1568854078le_Lin)) ),
    inference(clausify,[status(thm)],[f_140_2]) ).

fof(f_141_1,plain,
    ! [L_3,X_2,Y_1] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,L_3),X_2),Y_1)),arrow_1568854078le_Lin))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
      | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Y_1) ),
    inference(fof_nnf,[status(thm)],[fact_51_above__Lin]) ).

fof(f_141_2,plain,
    ! [U_283,U_282,U_281] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_283),U_282),U_281)),arrow_1568854078le_Lin))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_283),arrow_1568854078le_Lin))
      | ti(arrow_2142409994le_alt,U_282) = ti(arrow_2142409994le_alt,U_281) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

cnf(f_141_3,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_283),U_282),U_281)),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_283),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_282) = ti(arrow_2142409994le_alt,U_281) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

fof(f_142_1,plain,
    ! [L_3] :
      ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),L_3)),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_52_const__Lin__Prof]) ).

fof(f_142_2,plain,
    ! [U_284] :
      ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),U_284)),arrow_301600364e_Prof))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_284),arrow_1568854078le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

cnf(f_142_3,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),U_284)),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_284),arrow_1568854078le_Lin)) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

fof(f_143_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ti(X_a,X) = ti(X_a,Y)
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_53_linorder__cases]) ).

fof(f_143_2,plain,
    ! [U_287] :
      ( ! [U_286,U_285] :
          ( hBOOL(hAPP(U_287,bool,hAPP(U_287,fun(U_287,bool),ord_less(U_287),U_285),U_286))
          | ti(U_287,U_286) = ti(U_287,U_285)
          | hBOOL(hAPP(U_287,bool,hAPP(U_287,fun(U_287,bool),ord_less(U_287),U_286),U_285)) )
      | ~ linorder(U_287) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

cnf(f_143_3,plain,
    ( hBOOL(hAPP(U_287,bool,hAPP(U_287,fun(U_287,bool),ord_less(U_287),U_285),U_286))
    | ti(U_287,U_286) = ti(U_287,U_285)
    | hBOOL(hAPP(U_287,bool,hAPP(U_287,fun(U_287,bool),ord_less(U_287),U_286),U_285))
    | ~ linorder(U_287) ),
    inference(clausify,[status(thm)],[f_143_2]) ).

fof(f_144_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_54_order__less__asym]) ).

fof(f_144_2,plain,
    ! [U_290] :
      ( ! [U_289,U_288] :
          ( ~ hBOOL(hAPP(U_290,bool,hAPP(U_290,fun(U_290,bool),ord_less(U_290),U_288),U_289))
          | ~ hBOOL(hAPP(U_290,bool,hAPP(U_290,fun(U_290,bool),ord_less(U_290),U_289),U_288)) )
      | ~ preorder(U_290) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

cnf(f_144_3,plain,
    ( ~ hBOOL(hAPP(U_290,bool,hAPP(U_290,fun(U_290,bool),ord_less(U_290),U_288),U_289))
    | ~ hBOOL(hAPP(U_290,bool,hAPP(U_290,fun(U_290,bool),ord_less(U_290),U_289),U_288))
    | ~ preorder(U_290) ),
    inference(clausify,[status(thm)],[f_144_2]) ).

fof(f_145_1,plain,
    ! [X_a] :
      ( ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_55_xt1_I10_J]) ).

fof(f_145_2,plain,
    ! [U_294] :
      ( ! [U_293,U_292,U_291] :
          ( hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less(U_294),U_293),U_291))
          | ~ hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less(U_294),U_293),U_292))
          | ~ hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less(U_294),U_292),U_291)) )
      | ~ order(U_294) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

cnf(f_145_3,plain,
    ( hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less(U_294),U_293),U_291))
    | ~ hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less(U_294),U_293),U_292))
    | ~ hBOOL(hAPP(U_294,bool,hAPP(U_294,fun(U_294,bool),ord_less(U_294),U_292),U_291))
    | ~ order(U_294) ),
    inference(clausify,[status(thm)],[f_145_2]) ).

fof(f_146_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_56_order__less__trans]) ).

fof(f_146_2,plain,
    ! [U_298] :
      ( ! [U_297,U_296,U_295] :
          ( hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less(U_298),U_296),U_297))
          | ~ hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less(U_298),U_295),U_297))
          | ~ hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less(U_298),U_296),U_295)) )
      | ~ preorder(U_298) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

cnf(f_146_3,plain,
    ( hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less(U_298),U_296),U_297))
    | ~ hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less(U_298),U_295),U_297))
    | ~ hBOOL(hAPP(U_298,bool,hAPP(U_298,fun(U_298,bool),ord_less(U_298),U_296),U_295))
    | ~ preorder(U_298) ),
    inference(clausify,[status(thm)],[f_146_2]) ).

fof(f_147_1,plain,
    ! [X_a] :
      ( ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2))
          | ti(X_a,B_1) != ti(X_a,C_1)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_57_xt1_I2_J]) ).

fof(f_147_2,plain,
    ! [U_302] :
      ( ! [U_301,U_300,U_299] :
          ( hBOOL(hAPP(U_302,bool,hAPP(U_302,fun(U_302,bool),ord_less(U_302),U_301),U_299))
          | ti(U_302,U_300) != ti(U_302,U_301)
          | ~ hBOOL(hAPP(U_302,bool,hAPP(U_302,fun(U_302,bool),ord_less(U_302),U_300),U_299)) )
      | ~ order(U_302) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

cnf(f_147_3,plain,
    ( hBOOL(hAPP(U_302,bool,hAPP(U_302,fun(U_302,bool),ord_less(U_302),U_301),U_299))
    | ti(U_302,U_300) != ti(U_302,U_301)
    | ~ hBOOL(hAPP(U_302,bool,hAPP(U_302,fun(U_302,bool),ord_less(U_302),U_300),U_299))
    | ~ order(U_302) ),
    inference(clausify,[status(thm)],[f_147_2]) ).

fof(f_148_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_1))
          | B_1 != C_1
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_58_ord__less__eq__trans]) ).

fof(f_148_2,plain,
    ! [U_306] :
      ( ! [U_305,U_304,U_303] :
          ( hBOOL(hAPP(U_306,bool,hAPP(U_306,fun(U_306,bool),ord_less(U_306),U_304),U_305))
          | U_303 != U_305
          | ~ hBOOL(hAPP(U_306,bool,hAPP(U_306,fun(U_306,bool),ord_less(U_306),U_304),U_303)) )
      | ~ ord(U_306) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

cnf(f_148_3,plain,
    ( hBOOL(hAPP(U_306,bool,hAPP(U_306,fun(U_306,bool),ord_less(U_306),U_304),U_305))
    | U_303 != U_305
    | ~ hBOOL(hAPP(U_306,bool,hAPP(U_306,fun(U_306,bool),ord_less(U_306),U_304),U_303))
    | ~ ord(U_306) ),
    inference(clausify,[status(thm)],[f_148_2]) ).

fof(f_149_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),B_1))
          | ti(X_a,A_2) != ti(X_a,B_1) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_59_xt1_I1_J]) ).

fof(f_149_2,plain,
    ! [U_310] :
      ( ! [U_309,U_308,U_307] :
          ( hBOOL(hAPP(U_310,bool,hAPP(U_310,fun(U_310,bool),ord_less(U_310),U_309),U_308))
          | ~ hBOOL(hAPP(U_310,bool,hAPP(U_310,fun(U_310,bool),ord_less(U_310),U_309),U_307))
          | ti(U_310,U_308) != ti(U_310,U_307) )
      | ~ order(U_310) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

cnf(f_149_3,plain,
    ( hBOOL(hAPP(U_310,bool,hAPP(U_310,fun(U_310,bool),ord_less(U_310),U_309),U_308))
    | ~ hBOOL(hAPP(U_310,bool,hAPP(U_310,fun(U_310,bool),ord_less(U_310),U_309),U_307))
    | ti(U_310,U_308) != ti(U_310,U_307)
    | ~ order(U_310) ),
    inference(clausify,[status(thm)],[f_149_2]) ).

fof(f_150_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_1))
          | A_2 != B_1 )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_60_ord__eq__less__trans]) ).

fof(f_150_2,plain,
    ! [U_314] :
      ( ! [U_313,U_312,U_311] :
          ( hBOOL(hAPP(U_314,bool,hAPP(U_314,fun(U_314,bool),ord_less(U_314),U_312),U_313))
          | ~ hBOOL(hAPP(U_314,bool,hAPP(U_314,fun(U_314,bool),ord_less(U_314),U_311),U_313))
          | U_312 != U_311 )
      | ~ ord(U_314) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

cnf(f_150_3,plain,
    ( hBOOL(hAPP(U_314,bool,hAPP(U_314,fun(U_314,bool),ord_less(U_314),U_312),U_313))
    | ~ hBOOL(hAPP(U_314,bool,hAPP(U_314,fun(U_314,bool),ord_less(U_314),U_311),U_313))
    | U_312 != U_311
    | ~ ord(U_314) ),
    inference(clausify,[status(thm)],[f_150_2]) ).

fof(f_151_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_61_xt1_I9_J]) ).

fof(f_151_2,plain,
    ! [U_317] :
      ( ! [U_316,U_315] :
          ( ~ hBOOL(hAPP(U_317,bool,hAPP(U_317,fun(U_317,bool),ord_less(U_317),U_315),U_316))
          | ~ hBOOL(hAPP(U_317,bool,hAPP(U_317,fun(U_317,bool),ord_less(U_317),U_316),U_315)) )
      | ~ order(U_317) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

cnf(f_151_3,plain,
    ( ~ hBOOL(hAPP(U_317,bool,hAPP(U_317,fun(U_317,bool),ord_less(U_317),U_315),U_316))
    | ~ hBOOL(hAPP(U_317,bool,hAPP(U_317,fun(U_317,bool),ord_less(U_317),U_316),U_315))
    | ~ order(U_317) ),
    inference(clausify,[status(thm)],[f_151_2]) ).

fof(f_152_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_62_order__less__asym_H]) ).

fof(f_152_2,plain,
    ! [U_320] :
      ( ! [U_319,U_318] :
          ( ~ hBOOL(hAPP(U_320,bool,hAPP(U_320,fun(U_320,bool),ord_less(U_320),U_318),U_319))
          | ~ hBOOL(hAPP(U_320,bool,hAPP(U_320,fun(U_320,bool),ord_less(U_320),U_319),U_318)) )
      | ~ preorder(U_320) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

cnf(f_152_3,plain,
    ( ~ hBOOL(hAPP(U_320,bool,hAPP(U_320,fun(U_320,bool),ord_less(U_320),U_318),U_319))
    | ~ hBOOL(hAPP(U_320,bool,hAPP(U_320,fun(U_320,bool),ord_less(U_320),U_319),U_318))
    | ~ preorder(U_320) ),
    inference(clausify,[status(thm)],[f_152_2]) ).

fof(f_153_1,plain,
    ! [X_a] :
      ( ! [Pa,X_2,Y_1] :
          ( hBOOL(Pa)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_63_order__less__imp__triv]) ).

fof(f_153_2,plain,
    ! [U_324] :
      ( ! [U_323,U_322,U_321] :
          ( hBOOL(U_323)
          | ~ hBOOL(hAPP(U_324,bool,hAPP(U_324,fun(U_324,bool),ord_less(U_324),U_321),U_322))
          | ~ hBOOL(hAPP(U_324,bool,hAPP(U_324,fun(U_324,bool),ord_less(U_324),U_322),U_321)) )
      | ~ preorder(U_324) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

cnf(f_153_3,plain,
    ( hBOOL(U_323)
    | ~ hBOOL(hAPP(U_324,bool,hAPP(U_324,fun(U_324,bool),ord_less(U_324),U_321),U_322))
    | ~ hBOOL(hAPP(U_324,bool,hAPP(U_324,fun(U_324,bool),ord_less(U_324),U_322),U_321))
    | ~ preorder(U_324) ),
    inference(clausify,[status(thm)],[f_153_2]) ).

fof(f_154_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ti(X_a,Y) != ti(X_a,X)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_64_order__less__imp__not__eq2]) ).

fof(f_154_2,plain,
    ! [U_327] :
      ( ! [U_326,U_325] :
          ( ti(U_327,U_325) != ti(U_327,U_326)
          | ~ hBOOL(hAPP(U_327,bool,hAPP(U_327,fun(U_327,bool),ord_less(U_327),U_326),U_325)) )
      | ~ order(U_327) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

cnf(f_154_3,plain,
    ( ti(U_327,U_325) != ti(U_327,U_326)
    | ~ hBOOL(hAPP(U_327,bool,hAPP(U_327,fun(U_327,bool),ord_less(U_327),U_326),U_325))
    | ~ order(U_327) ),
    inference(clausify,[status(thm)],[f_154_2]) ).

fof(f_155_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ti(X_a,X) != ti(X_a,Y)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_65_order__less__imp__not__eq]) ).

fof(f_155_2,plain,
    ! [U_330] :
      ( ! [U_329,U_328] :
          ( ti(U_330,U_329) != ti(U_330,U_328)
          | ~ hBOOL(hAPP(U_330,bool,hAPP(U_330,fun(U_330,bool),ord_less(U_330),U_329),U_328)) )
      | ~ order(U_330) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

cnf(f_155_3,plain,
    ( ti(U_330,U_329) != ti(U_330,U_328)
    | ~ hBOOL(hAPP(U_330,bool,hAPP(U_330,fun(U_330,bool),ord_less(U_330),U_329),U_328))
    | ~ order(U_330) ),
    inference(clausify,[status(thm)],[f_155_2]) ).

fof(f_156_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_66_order__less__imp__not__less]) ).

fof(f_156_2,plain,
    ! [U_333] :
      ( ! [U_332,U_331] :
          ( ~ hBOOL(hAPP(U_333,bool,hAPP(U_333,fun(U_333,bool),ord_less(U_333),U_331),U_332))
          | ~ hBOOL(hAPP(U_333,bool,hAPP(U_333,fun(U_333,bool),ord_less(U_333),U_332),U_331)) )
      | ~ preorder(U_333) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

cnf(f_156_3,plain,
    ( ~ hBOOL(hAPP(U_333,bool,hAPP(U_333,fun(U_333,bool),ord_less(U_333),U_331),U_332))
    | ~ hBOOL(hAPP(U_333,bool,hAPP(U_333,fun(U_333,bool),ord_less(U_333),U_332),U_331))
    | ~ preorder(U_333) ),
    inference(clausify,[status(thm)],[f_156_2]) ).

fof(f_157_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_67_order__less__not__sym]) ).

fof(f_157_2,plain,
    ! [U_336] :
      ( ! [U_335,U_334] :
          ( ~ hBOOL(hAPP(U_336,bool,hAPP(U_336,fun(U_336,bool),ord_less(U_336),U_334),U_335))
          | ~ hBOOL(hAPP(U_336,bool,hAPP(U_336,fun(U_336,bool),ord_less(U_336),U_335),U_334)) )
      | ~ preorder(U_336) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

cnf(f_157_3,plain,
    ( ~ hBOOL(hAPP(U_336,bool,hAPP(U_336,fun(U_336,bool),ord_less(U_336),U_334),U_335))
    | ~ hBOOL(hAPP(U_336,bool,hAPP(U_336,fun(U_336,bool),ord_less(U_336),U_335),U_334))
    | ~ preorder(U_336) ),
    inference(clausify,[status(thm)],[f_157_2]) ).

fof(f_158_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ti(X_a,X) != ti(X_a,Y)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_68_less__imp__neq]) ).

fof(f_158_2,plain,
    ! [U_339] :
      ( ! [U_338,U_337] :
          ( ti(U_339,U_338) != ti(U_339,U_337)
          | ~ hBOOL(hAPP(U_339,bool,hAPP(U_339,fun(U_339,bool),ord_less(U_339),U_338),U_337)) )
      | ~ order(U_339) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

cnf(f_158_3,plain,
    ( ti(U_339,U_338) != ti(U_339,U_337)
    | ~ hBOOL(hAPP(U_339,bool,hAPP(U_339,fun(U_339,bool),ord_less(U_339),U_338),U_337))
    | ~ order(U_339) ),
    inference(clausify,[status(thm)],[f_158_2]) ).

fof(f_159_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
          | ti(X_a,X) = ti(X_a,Y) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_69_linorder__neqE]) ).

fof(f_159_2,plain,
    ! [U_342] :
      ( ! [U_341,U_340] :
          ( hBOOL(hAPP(U_342,bool,hAPP(U_342,fun(U_342,bool),ord_less(U_342),U_340),U_341))
          | hBOOL(hAPP(U_342,bool,hAPP(U_342,fun(U_342,bool),ord_less(U_342),U_341),U_340))
          | ti(U_342,U_341) = ti(U_342,U_340) )
      | ~ linorder(U_342) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

cnf(f_159_3,plain,
    ( hBOOL(hAPP(U_342,bool,hAPP(U_342,fun(U_342,bool),ord_less(U_342),U_340),U_341))
    | hBOOL(hAPP(U_342,bool,hAPP(U_342,fun(U_342,bool),ord_less(U_342),U_341),U_340))
    | ti(U_342,U_341) = ti(U_342,U_340)
    | ~ linorder(U_342) ),
    inference(clausify,[status(thm)],[f_159_2]) ).

fof(f_160_1,plain,
    ! [X_a] :
      ( ! [Y_1,X_2] :
          ( ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
              | ti(X_a,X_2) != ti(X_a,Y_1) )
            & ( ti(X_a,X_2) = ti(X_a,Y_1)
              | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_70_linorder__antisym__conv3]) ).

fof(f_160_2,plain,
    ! [U_345] :
      ( ! [U_344,U_343] :
          ( ( ( ~ hBOOL(hAPP(U_345,bool,hAPP(U_345,fun(U_345,bool),ord_less(U_345),U_343),U_344))
              | ti(U_345,U_343) != ti(U_345,U_344) )
            & ( ti(U_345,U_343) = ti(U_345,U_344)
              | hBOOL(hAPP(U_345,bool,hAPP(U_345,fun(U_345,bool),ord_less(U_345),U_343),U_344)) ) )
          | hBOOL(hAPP(U_345,bool,hAPP(U_345,fun(U_345,bool),ord_less(U_345),U_344),U_343)) )
      | ~ linorder(U_345) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

cnf(f_160_3,plain,
    ( ti(U_345,U_343) = ti(U_345,U_344)
    | hBOOL(hAPP(U_345,bool,hAPP(U_345,fun(U_345,bool),ord_less(U_345),U_343),U_344))
    | hBOOL(hAPP(U_345,bool,hAPP(U_345,fun(U_345,bool),ord_less(U_345),U_344),U_343))
    | ~ linorder(U_345) ),
    inference(clausify,[status(thm)],[f_160_2]) ).

cnf(f_160_4,plain,
    ( ~ hBOOL(hAPP(U_345,bool,hAPP(U_345,fun(U_345,bool),ord_less(U_345),U_343),U_344))
    | ti(U_345,U_343) != ti(U_345,U_344)
    | hBOOL(hAPP(U_345,bool,hAPP(U_345,fun(U_345,bool),ord_less(U_345),U_344),U_343))
    | ~ linorder(U_345) ),
    inference(clausify,[status(thm)],[f_160_2]) ).

fof(f_161_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ti(X_a,X) = ti(X_a,Y)
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_71_linorder__less__linear]) ).

fof(f_161_2,plain,
    ! [U_348] :
      ( ! [U_347,U_346] :
          ( hBOOL(hAPP(U_348,bool,hAPP(U_348,fun(U_348,bool),ord_less(U_348),U_346),U_347))
          | ti(U_348,U_347) = ti(U_348,U_346)
          | hBOOL(hAPP(U_348,bool,hAPP(U_348,fun(U_348,bool),ord_less(U_348),U_347),U_346)) )
      | ~ linorder(U_348) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

cnf(f_161_3,plain,
    ( hBOOL(hAPP(U_348,bool,hAPP(U_348,fun(U_348,bool),ord_less(U_348),U_346),U_347))
    | ti(U_348,U_347) = ti(U_348,U_346)
    | hBOOL(hAPP(U_348,bool,hAPP(U_348,fun(U_348,bool),ord_less(U_348),U_347),U_346))
    | ~ linorder(U_348) ),
    inference(clausify,[status(thm)],[f_161_2]) ).

fof(f_162_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
            | ( ti(X_a,X_2) != ti(X_a,Y_1)
              & ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) ) )
          & ( ti(X_a,X_2) = ti(X_a,Y_1)
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_72_not__less__iff__gr__or__eq]) ).

fof(f_162_2,plain,
    ! [U_351] :
      ( ! [U_350,U_349] :
          ( ( ~ hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_350),U_349))
            | ( ti(U_351,U_350) != ti(U_351,U_349)
              & ~ hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_349),U_350)) ) )
          & ( ti(U_351,U_350) = ti(U_351,U_349)
            | hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_349),U_350))
            | hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_350),U_349)) ) )
      | ~ linorder(U_351) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ! [U_351] :
      ( ( ! [U_355,U_353] :
            ( ~ hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_355),U_353))
            | ( ti(U_351,U_355) != ti(U_351,U_353)
              & ~ hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_353),U_355)) ) )
        & ! [U_354,U_352] :
            ( ti(U_351,U_354) = ti(U_351,U_352)
            | hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_352),U_354))
            | hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_354),U_352)) ) )
      | ~ linorder(U_351) ),
    inference(miniscope,[status(thm)],[f_162_2]) ).

cnf(f_162_4,plain,
    ( ti(U_351,U_354) = ti(U_351,U_352)
    | hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_352),U_354))
    | hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_354),U_352))
    | ~ linorder(U_351) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

cnf(f_162_5,plain,
    ( ~ hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_353),U_355))
    | ~ hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_355),U_353))
    | ~ linorder(U_351) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

cnf(f_162_6,plain,
    ( ti(U_351,U_355) != ti(U_351,U_353)
    | ~ hBOOL(hAPP(U_351,bool,hAPP(U_351,fun(U_351,bool),ord_less(U_351),U_355),U_353))
    | ~ linorder(U_351) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

fof(f_163_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( ti(X_a,X_2) != ti(X_a,Y_1)
            | ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
              & ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
            | ti(X_a,X_2) = ti(X_a,Y_1) ) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_73_linorder__neq__iff]) ).

fof(f_163_2,plain,
    ! [U_358] :
      ( ! [U_357,U_356] :
          ( ( ti(U_358,U_357) != ti(U_358,U_356)
            | ( ~ hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_356),U_357))
              & ~ hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_357),U_356)) ) )
          & ( hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_356),U_357))
            | hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_357),U_356))
            | ti(U_358,U_357) = ti(U_358,U_356) ) )
      | ~ linorder(U_358) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ! [U_358] :
      ( ( ! [U_362,U_360] :
            ( ti(U_358,U_362) != ti(U_358,U_360)
            | ( ~ hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_360),U_362))
              & ~ hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_362),U_360)) ) )
        & ! [U_361,U_359] :
            ( hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_359),U_361))
            | hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_361),U_359))
            | ti(U_358,U_361) = ti(U_358,U_359) ) )
      | ~ linorder(U_358) ),
    inference(miniscope,[status(thm)],[f_163_2]) ).

cnf(f_163_4,plain,
    ( hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_359),U_361))
    | hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_361),U_359))
    | ti(U_358,U_361) = ti(U_358,U_359)
    | ~ linorder(U_358) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

cnf(f_163_5,plain,
    ( ~ hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_362),U_360))
    | ti(U_358,U_362) != ti(U_358,U_360)
    | ~ linorder(U_358) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

cnf(f_163_6,plain,
    ( ~ hBOOL(hAPP(U_358,bool,hAPP(U_358,fun(U_358,bool),ord_less(U_358),U_360),U_362))
    | ti(U_358,U_362) != ti(U_358,U_360)
    | ~ linorder(U_358) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

fof(f_164_1,plain,
    ! [X_a] :
      ( ! [X] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_74_order__less__irrefl]) ).

fof(f_164_2,plain,
    ! [U_364] :
      ( ! [U_363] : ~ hBOOL(hAPP(U_364,bool,hAPP(U_364,fun(U_364,bool),ord_less(U_364),U_363),U_363))
      | ~ preorder(U_364) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

cnf(f_164_3,plain,
    ( ~ hBOOL(hAPP(U_364,bool,hAPP(U_364,fun(U_364,bool),ord_less(U_364),U_363),U_363))
    | ~ preorder(U_364) ),
    inference(clausify,[status(thm)],[f_164_2]) ).

fof(f_165_1,plain,
    ! [X_a,X_b,F,G] :
      ( ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G)
      | ? [X_1] : hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,G,X_1) ),
    inference(fof_nnf,[status(thm)],[fact_75_ext]) ).

fof(f_165_2,plain,
    ! [U_369,U_368,U_367,U_366] :
      ( ti(fun(U_369,U_368),U_367) = ti(fun(U_369,U_368),U_366)
      | ? [U_365] : hAPP(U_369,U_368,U_367,U_365) != hAPP(U_369,U_368,U_366,U_365) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ! [U_369,U_368,U_367,U_366] :
      ( ti(fun(U_369,U_368),U_367) = ti(fun(U_369,U_368),U_366)
      | hAPP(U_369,U_368,U_367,sK27(U_369,U_368,U_367,U_366)) != hAPP(U_369,U_368,U_366,sK27(U_369,U_368,U_367,U_366)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_365,sK27(U_369,U_368,U_367,U_366))],[f_165_2]) ).

cnf(f_165_4,plain,
    ( ti(fun(U_369,U_368),U_367) = ti(fun(U_369,U_368),U_366)
    | hAPP(U_369,U_368,U_367,sK27(U_369,U_368,U_367,U_366)) != hAPP(U_369,U_368,U_366,sK27(U_369,U_368,U_367,U_366)) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

fof(f_166_1,plain,
    ! [X_a,X_2,A_1] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
        | ~ hBOOL(hAPP(X_a,bool,A_1,X_2)) )
      & ( hBOOL(hAPP(X_a,bool,A_1,X_2))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_76_mem__def]) ).

fof(f_166_2,plain,
    ! [U_372,U_371,U_370] :
      ( ( hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_371),U_370))
        | ~ hBOOL(hAPP(U_372,bool,U_370,U_371)) )
      & ( hBOOL(hAPP(U_372,bool,U_370,U_371))
        | ~ hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_371),U_370)) ) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ( ! [U_378,U_376,U_374] :
        ( hBOOL(hAPP(fun(U_378,bool),bool,hAPP(U_378,fun(fun(U_378,bool),bool),member(U_378),U_376),U_374))
        | ~ hBOOL(hAPP(U_378,bool,U_374,U_376)) )
    & ! [U_377,U_375,U_373] :
        ( hBOOL(hAPP(U_377,bool,U_373,U_375))
        | ~ hBOOL(hAPP(fun(U_377,bool),bool,hAPP(U_377,fun(fun(U_377,bool),bool),member(U_377),U_375),U_373)) ) ),
    inference(miniscope,[status(thm)],[f_166_2]) ).

cnf(f_166_4,plain,
    ( hBOOL(hAPP(U_377,bool,U_373,U_375))
    | ~ hBOOL(hAPP(fun(U_377,bool),bool,hAPP(U_377,fun(fun(U_377,bool),bool),member(U_377),U_375),U_373)) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

cnf(f_166_5,plain,
    ( hBOOL(hAPP(fun(U_378,bool),bool,hAPP(U_378,fun(fun(U_378,bool),bool),member(U_378),U_376),U_374))
    | ~ hBOOL(hAPP(U_378,bool,U_374,U_376)) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

fof(f_167_1,plain,
    ! [X_a,Pa] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = ti(fun(X_a,bool),Pa),
    inference(fof_nnf,[status(thm)],[fact_77_Collect__def]) ).

fof(f_167_2,plain,
    ! [U_380,U_379] : hAPP(fun(U_380,bool),fun(U_380,bool),collect(U_380),U_379) = ti(fun(U_380,bool),U_379),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

cnf(f_167_3,plain,
    hAPP(fun(U_380,bool),fun(U_380,bool),collect(U_380),U_379) = ti(fun(U_380,bool),U_379),
    inference(clausify,[status(thm)],[f_167_2]) ).

fof(f_168_1,plain,
    ! [X_a] : top_top(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fTrue)),
    inference(fof_nnf,[status(thm)],[fact_78_UNIV__def]) ).

fof(f_168_2,plain,
    ! [U_381] : top_top(fun(U_381,bool)) = hAPP(fun(U_381,bool),fun(U_381,bool),collect(U_381),hAPP(bool,fun(U_381,bool),combk(bool,U_381),fTrue)),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

cnf(f_168_3,plain,
    top_top(fun(U_381,bool)) = hAPP(fun(U_381,bool),fun(U_381,bool),collect(U_381),hAPP(bool,fun(U_381,bool),combk(bool,U_381),fTrue)),
    inference(clausify,[status(thm)],[f_168_2]) ).

fof(f_169_1,plain,
    ! [X_2,Y_1,L_3,Aa,Ba] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,L_3),Aa),Ba)))
          | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3))
                & ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Ba) )
              | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Aa)),L_3))
                & ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Aa)
                & ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Ba) ) )
            & ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Ba) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Y_1)),L_3))
            & ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Ba) )
          | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Y_1) )
        & ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3))
                  | ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Ba) )
                & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Aa)),L_3))
                  | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Aa)
                  | ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Ba) ) )
              | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Ba) )
            & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Y_1)),L_3))
              | ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Ba) )
            & ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1) )
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,L_3),Aa),Ba))) ) )
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,Ba) ),
    inference(fof_nnf,[status(thm)],[fact_79_in__above]) ).

fof(f_169_2,plain,
    ! [U_386,U_385,U_384,U_383,U_382] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
          | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),U_384))
                & ti(arrow_2142409994le_alt,U_385) != ti(arrow_2142409994le_alt,U_382) )
              | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_383)),U_384))
                & ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_383)
                & ti(arrow_2142409994le_alt,U_385) = ti(arrow_2142409994le_alt,U_382) ) )
            & ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_382) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_383),U_385)),U_384))
            & ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382) )
          | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385) )
        & ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),U_384))
                  | ti(arrow_2142409994le_alt,U_385) = ti(arrow_2142409994le_alt,U_382) )
                & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_383)),U_384))
                  | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_383)
                  | ti(arrow_2142409994le_alt,U_385) != ti(arrow_2142409994le_alt,U_382) ) )
              | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382) )
            & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_383),U_385)),U_384))
              | ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_382) )
            & ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_385) )
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382))) ) )
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
      | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

cnf(f_169_3,plain,
    ( ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_385)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_4,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_383),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_382)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_5,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_383)),U_384))
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_383)
    | ti(arrow_2142409994le_alt,U_385) != ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_6,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_385) = ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_7,plain,
    ( ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_8,plain,
    ( ti(arrow_2142409994le_alt,U_385) != ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_385) = ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_9,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_385) = ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_10,plain,
    ( ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_383)
    | ti(arrow_2142409994le_alt,U_385) != ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_383)),U_384))
    | ti(arrow_2142409994le_alt,U_385) != ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_12,plain,
    ( ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_383)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_13,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_383)),U_384))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_14,plain,
    ( ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_382)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_383),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_15,plain,
    ( ti(arrow_2142409994le_alt,U_385) != ti(arrow_2142409994le_alt,U_382)
    | ti(arrow_2142409994le_alt,U_385) = ti(arrow_2142409994le_alt,U_382)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_383),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_16,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_385) = ti(arrow_2142409994le_alt,U_382)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_383),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_17,plain,
    ( ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_383)
    | ti(arrow_2142409994le_alt,U_385) != ti(arrow_2142409994le_alt,U_382)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_383),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_18,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_383)),U_384))
    | ti(arrow_2142409994le_alt,U_385) != ti(arrow_2142409994le_alt,U_382)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_383),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_19,plain,
    ( ti(arrow_2142409994le_alt,U_386) != ti(arrow_2142409994le_alt,U_383)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),U_384))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_383),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

cnf(f_169_20,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_383)),U_384))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),U_384))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_383),U_385)),U_384))
    | ti(arrow_2142409994le_alt,U_386) = ti(arrow_2142409994le_alt,U_385)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_386),U_385)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,U_384),U_383),U_382)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_384),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_383) = ti(arrow_2142409994le_alt,U_382) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

fof(f_170_1,plain,
    ! [X_a,X_b,S,R_2] :
      ( ( ! [X_1,Xa] :
            ( ( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),R_2))
              | ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),S)) )
            & ( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),S))
              | ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),R_2)) ) )
        | ti(fun(product_prod(X_a,X_b),bool),R_2) != ti(fun(product_prod(X_a,X_b),bool),S) )
      & ( ti(fun(product_prod(X_a,X_b),bool),R_2) = ti(fun(product_prod(X_a,X_b),bool),S)
        | ? [X_1,Xa] :
            ( ( ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),R_2))
              & hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),S)) )
            | ( ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),S))
              & hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),R_2)) ) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_80_pred__equals__eq2]) ).

fof(f_170_2,plain,
    ! [U_394,U_393,U_392,U_391] :
      ( ( ! [U_390,U_389] :
            ( ( hBOOL(hAPP(fun(product_prod(U_394,U_393),bool),bool,hAPP(product_prod(U_394,U_393),fun(fun(product_prod(U_394,U_393),bool),bool),member(product_prod(U_394,U_393)),hAPP(U_393,product_prod(U_394,U_393),hAPP(U_394,fun(U_393,product_prod(U_394,U_393)),product_Pair(U_394,U_393),U_390),U_389)),U_391))
              | ~ hBOOL(hAPP(fun(product_prod(U_394,U_393),bool),bool,hAPP(product_prod(U_394,U_393),fun(fun(product_prod(U_394,U_393),bool),bool),member(product_prod(U_394,U_393)),hAPP(U_393,product_prod(U_394,U_393),hAPP(U_394,fun(U_393,product_prod(U_394,U_393)),product_Pair(U_394,U_393),U_390),U_389)),U_392)) )
            & ( hBOOL(hAPP(fun(product_prod(U_394,U_393),bool),bool,hAPP(product_prod(U_394,U_393),fun(fun(product_prod(U_394,U_393),bool),bool),member(product_prod(U_394,U_393)),hAPP(U_393,product_prod(U_394,U_393),hAPP(U_394,fun(U_393,product_prod(U_394,U_393)),product_Pair(U_394,U_393),U_390),U_389)),U_392))
              | ~ hBOOL(hAPP(fun(product_prod(U_394,U_393),bool),bool,hAPP(product_prod(U_394,U_393),fun(fun(product_prod(U_394,U_393),bool),bool),member(product_prod(U_394,U_393)),hAPP(U_393,product_prod(U_394,U_393),hAPP(U_394,fun(U_393,product_prod(U_394,U_393)),product_Pair(U_394,U_393),U_390),U_389)),U_391)) ) )
        | ti(fun(product_prod(U_394,U_393),bool),U_391) != ti(fun(product_prod(U_394,U_393),bool),U_392) )
      & ( ti(fun(product_prod(U_394,U_393),bool),U_391) = ti(fun(product_prod(U_394,U_393),bool),U_392)
        | ? [U_388,U_387] :
            ( ( ~ hBOOL(hAPP(fun(product_prod(U_394,U_393),bool),bool,hAPP(product_prod(U_394,U_393),fun(fun(product_prod(U_394,U_393),bool),bool),member(product_prod(U_394,U_393)),hAPP(U_393,product_prod(U_394,U_393),hAPP(U_394,fun(U_393,product_prod(U_394,U_393)),product_Pair(U_394,U_393),U_388),U_387)),U_391))
              & hBOOL(hAPP(fun(product_prod(U_394,U_393),bool),bool,hAPP(product_prod(U_394,U_393),fun(fun(product_prod(U_394,U_393),bool),bool),member(product_prod(U_394,U_393)),hAPP(U_393,product_prod(U_394,U_393),hAPP(U_394,fun(U_393,product_prod(U_394,U_393)),product_Pair(U_394,U_393),U_388),U_387)),U_392)) )
            | ( ~ hBOOL(hAPP(fun(product_prod(U_394,U_393),bool),bool,hAPP(product_prod(U_394,U_393),fun(fun(product_prod(U_394,U_393),bool),bool),member(product_prod(U_394,U_393)),hAPP(U_393,product_prod(U_394,U_393),hAPP(U_394,fun(U_393,product_prod(U_394,U_393)),product_Pair(U_394,U_393),U_388),U_387)),U_392))
              & hBOOL(hAPP(fun(product_prod(U_394,U_393),bool),bool,hAPP(product_prod(U_394,U_393),fun(fun(product_prod(U_394,U_393),bool),bool),member(product_prod(U_394,U_393)),hAPP(U_393,product_prod(U_394,U_393),hAPP(U_394,fun(U_393,product_prod(U_394,U_393)),product_Pair(U_394,U_393),U_388),U_387)),U_391)) ) ) ) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ( ! [U_410,U_408,U_406,U_404] :
        ( ( ! [U_402,U_400] :
              ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_404))
              | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_406)) )
          & ! [U_401,U_399] :
              ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_406))
              | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_404)) ) )
        | ti(fun(product_prod(U_410,U_408),bool),U_404) != ti(fun(product_prod(U_410,U_408),bool),U_406) )
    & ! [U_409,U_407,U_405,U_403] :
        ( ti(fun(product_prod(U_409,U_407),bool),U_403) = ti(fun(product_prod(U_409,U_407),bool),U_405)
        | ? [U_398,U_396] :
            ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),U_398),U_396)),U_403))
            & hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),U_398),U_396)),U_405)) )
        | ? [U_397,U_395] :
            ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),U_397),U_395)),U_405))
            & hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),U_397),U_395)),U_403)) ) ) ),
    inference(miniscope,[status(thm)],[f_170_2]) ).

fof(f_170_4,plain,
    ( ! [U_410,U_408,U_406,U_404] :
        ( ( ! [U_402,U_400] :
              ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_404))
              | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_406)) )
          & ! [U_401,U_399] :
              ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_406))
              | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_404)) ) )
        | ti(fun(product_prod(U_410,U_408),bool),U_404) != ti(fun(product_prod(U_410,U_408),bool),U_406) )
    & ! [U_409,U_407,U_405,U_403] :
        ( ti(fun(product_prod(U_409,U_407),bool),U_403) = ti(fun(product_prod(U_409,U_407),bool),U_405)
        | ? [U_398,U_396] :
            ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),U_398),U_396)),U_403))
            & hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),U_398),U_396)),U_405)) )
        | ? [U_395] :
            ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),U_395)),U_405))
            & hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),U_395)),U_403)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_397,sK28(U_409,U_407,U_405,U_403))],[f_170_3]) ).

fof(f_170_5,plain,
    ( ! [U_410,U_408,U_406,U_404] :
        ( ( ! [U_402,U_400] :
              ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_404))
              | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_406)) )
          & ! [U_401,U_399] :
              ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_406))
              | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_404)) ) )
        | ti(fun(product_prod(U_410,U_408),bool),U_404) != ti(fun(product_prod(U_410,U_408),bool),U_406) )
    & ! [U_409,U_407,U_405,U_403] :
        ( ti(fun(product_prod(U_409,U_407),bool),U_403) = ti(fun(product_prod(U_409,U_407),bool),U_405)
        | ? [U_398,U_396] :
            ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),U_398),U_396)),U_403))
            & hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),U_398),U_396)),U_405)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),sK29(U_409,U_407,U_405,U_403))),U_405))
          & hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),sK29(U_409,U_407,U_405,U_403))),U_403)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_395,sK29(U_409,U_407,U_405,U_403))],[f_170_4]) ).

fof(f_170_6,plain,
    ( ! [U_410,U_408,U_406,U_404] :
        ( ( ! [U_402,U_400] :
              ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_404))
              | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_406)) )
          & ! [U_401,U_399] :
              ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_406))
              | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_404)) ) )
        | ti(fun(product_prod(U_410,U_408),bool),U_404) != ti(fun(product_prod(U_410,U_408),bool),U_406) )
    & ! [U_409,U_407,U_405,U_403] :
        ( ti(fun(product_prod(U_409,U_407),bool),U_403) = ti(fun(product_prod(U_409,U_407),bool),U_405)
        | ? [U_396] :
            ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK30(U_409,U_407,U_405,U_403)),U_396)),U_403))
            & hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK30(U_409,U_407,U_405,U_403)),U_396)),U_405)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),sK29(U_409,U_407,U_405,U_403))),U_405))
          & hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),sK29(U_409,U_407,U_405,U_403))),U_403)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_398,sK30(U_409,U_407,U_405,U_403))],[f_170_5]) ).

fof(f_170_7,plain,
    ( ! [U_410,U_408,U_406,U_404] :
        ( ( ! [U_402,U_400] :
              ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_404))
              | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_406)) )
          & ! [U_401,U_399] :
              ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_406))
              | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_404)) ) )
        | ti(fun(product_prod(U_410,U_408),bool),U_404) != ti(fun(product_prod(U_410,U_408),bool),U_406) )
    & ! [U_409,U_407,U_405,U_403] :
        ( ti(fun(product_prod(U_409,U_407),bool),U_403) = ti(fun(product_prod(U_409,U_407),bool),U_405)
        | ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK30(U_409,U_407,U_405,U_403)),sK31(U_409,U_407,U_405,U_403))),U_403))
          & hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK30(U_409,U_407,U_405,U_403)),sK31(U_409,U_407,U_405,U_403))),U_405)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),sK29(U_409,U_407,U_405,U_403))),U_405))
          & hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),sK29(U_409,U_407,U_405,U_403))),U_403)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_396,sK31(U_409,U_407,U_405,U_403))],[f_170_6]) ).

cnf(f_170_8,plain,
    ( hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK30(U_409,U_407,U_405,U_403)),sK31(U_409,U_407,U_405,U_403))),U_405))
    | hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),sK29(U_409,U_407,U_405,U_403))),U_403))
    | ti(fun(product_prod(U_409,U_407),bool),U_403) = ti(fun(product_prod(U_409,U_407),bool),U_405) ),
    inference(clausify,[status(thm)],[f_170_7]) ).

cnf(f_170_9,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK30(U_409,U_407,U_405,U_403)),sK31(U_409,U_407,U_405,U_403))),U_403))
    | hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),sK29(U_409,U_407,U_405,U_403))),U_403))
    | ti(fun(product_prod(U_409,U_407),bool),U_403) = ti(fun(product_prod(U_409,U_407),bool),U_405) ),
    inference(clausify,[status(thm)],[f_170_7]) ).

cnf(f_170_10,plain,
    ( hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK30(U_409,U_407,U_405,U_403)),sK31(U_409,U_407,U_405,U_403))),U_405))
    | ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),sK29(U_409,U_407,U_405,U_403))),U_405))
    | ti(fun(product_prod(U_409,U_407),bool),U_403) = ti(fun(product_prod(U_409,U_407),bool),U_405) ),
    inference(clausify,[status(thm)],[f_170_7]) ).

cnf(f_170_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK30(U_409,U_407,U_405,U_403)),sK31(U_409,U_407,U_405,U_403))),U_403))
    | ~ hBOOL(hAPP(fun(product_prod(U_409,U_407),bool),bool,hAPP(product_prod(U_409,U_407),fun(fun(product_prod(U_409,U_407),bool),bool),member(product_prod(U_409,U_407)),hAPP(U_407,product_prod(U_409,U_407),hAPP(U_409,fun(U_407,product_prod(U_409,U_407)),product_Pair(U_409,U_407),sK28(U_409,U_407,U_405,U_403)),sK29(U_409,U_407,U_405,U_403))),U_405))
    | ti(fun(product_prod(U_409,U_407),bool),U_403) = ti(fun(product_prod(U_409,U_407),bool),U_405) ),
    inference(clausify,[status(thm)],[f_170_7]) ).

cnf(f_170_12,plain,
    ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_406))
    | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_401),U_399)),U_404))
    | ti(fun(product_prod(U_410,U_408),bool),U_404) != ti(fun(product_prod(U_410,U_408),bool),U_406) ),
    inference(clausify,[status(thm)],[f_170_7]) ).

cnf(f_170_13,plain,
    ( hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_404))
    | ~ hBOOL(hAPP(fun(product_prod(U_410,U_408),bool),bool,hAPP(product_prod(U_410,U_408),fun(fun(product_prod(U_410,U_408),bool),bool),member(product_prod(U_410,U_408)),hAPP(U_408,product_prod(U_410,U_408),hAPP(U_410,fun(U_408,product_prod(U_410,U_408)),product_Pair(U_410,U_408),U_402),U_400)),U_406))
    | ti(fun(product_prod(U_410,U_408),bool),U_404) != ti(fun(product_prod(U_410,U_408),bool),U_406) ),
    inference(clausify,[status(thm)],[f_170_7]) ).

fof(f_171_1,plain,
    ! [I,Fa] :
      ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,Fa),I))
      | ? [X_1] :
          ( ? [A_4,B_3] :
              ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),Fa,X_1)))
              & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),A_4),B_3)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X_1,I)))
              & ti(arrow_2142409994le_alt,A_4) != ti(arrow_2142409994le_alt,B_3) )
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X_1),arrow_301600364e_Prof)) )
      | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),Fa),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(fof_nnf,[status(thm)],[fact_81_dictatorI]) ).

fof(f_171_2,plain,
    ! [U_415,U_414] :
      ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_414),U_415))
      | ? [U_413] :
          ( ? [U_412,U_411] :
              ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_412),U_411)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_414,U_413)))
              & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_412),U_411)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_413,U_415)))
              & ti(arrow_2142409994le_alt,U_412) != ti(arrow_2142409994le_alt,U_411) )
          & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_413),arrow_301600364e_Prof)) )
      | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_414),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ! [U_415,U_414] :
      ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_414),U_415))
      | ( ? [U_412,U_411] :
            ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_412),U_411)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_414,sK32(U_415,U_414))))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_412),U_411)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK32(U_415,U_414),U_415)))
            & ti(arrow_2142409994le_alt,U_412) != ti(arrow_2142409994le_alt,U_411) )
        & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK32(U_415,U_414)),arrow_301600364e_Prof)) )
      | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_414),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_413,sK32(U_415,U_414))],[f_171_2]) ).

fof(f_171_4,plain,
    ! [U_415,U_414] :
      ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_414),U_415))
      | ( ? [U_411] :
            ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK33(U_415,U_414)),U_411)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_414,sK32(U_415,U_414))))
            & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK33(U_415,U_414)),U_411)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK32(U_415,U_414),U_415)))
            & ti(arrow_2142409994le_alt,sK33(U_415,U_414)) != ti(arrow_2142409994le_alt,U_411) )
        & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK32(U_415,U_414)),arrow_301600364e_Prof)) )
      | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_414),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_412,sK33(U_415,U_414))],[f_171_3]) ).

fof(f_171_5,plain,
    ! [U_415,U_414] :
      ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_414),U_415))
      | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK33(U_415,U_414)),sK34(U_415,U_414))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_414,sK32(U_415,U_414))))
        & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK33(U_415,U_414)),sK34(U_415,U_414))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK32(U_415,U_414),U_415)))
        & ti(arrow_2142409994le_alt,sK33(U_415,U_414)) != ti(arrow_2142409994le_alt,sK34(U_415,U_414))
        & hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK32(U_415,U_414)),arrow_301600364e_Prof)) )
      | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_414),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_411,sK34(U_415,U_414))],[f_171_4]) ).

cnf(f_171_6,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),sK32(U_415,U_414)),arrow_301600364e_Prof))
    | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_414),U_415))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_414),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(clausify,[status(thm)],[f_171_5]) ).

cnf(f_171_7,plain,
    ( ti(arrow_2142409994le_alt,sK33(U_415,U_414)) != ti(arrow_2142409994le_alt,sK34(U_415,U_414))
    | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_414),U_415))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_414),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(clausify,[status(thm)],[f_171_5]) ).

cnf(f_171_8,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK33(U_415,U_414)),sK34(U_415,U_414))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),sK32(U_415,U_414),U_415)))
    | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_414),U_415))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_414),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(clausify,[status(thm)],[f_171_5]) ).

cnf(f_171_9,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),sK33(U_415,U_414)),sK34(U_415,U_414))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),U_414,sK32(U_415,U_414))))
    | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,U_414),U_415))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),U_414),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(clausify,[status(thm)],[f_171_5]) ).

fof(f_172_1,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_82_n_I3_J]) ).

cnf(f_172_2,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_172_1]) ).

fof(f_173_1,plain,
    ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) )
    & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba))))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_83__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk]) ).

cnf(f_173_2,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
    inference(clausify,[status(thm)],[f_173_1]) ).

cnf(f_173_3,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_173_1]) ).

fof(f_174_1,plain,
    ! [I_1] :
      ( ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,I_1) = n )
              & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),c),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,I_1) != n ) )
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) ) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
      & ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
        | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,I_1) != n )
            | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),c),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,I_1) = n ) )
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,I_1)),e)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,I_1)),n)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_84__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(f_174_2,plain,
    ! [U_416] :
      ( ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_416)),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_416) = n )
              & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_416)),c),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_416) != n ) )
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_416)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_416)),e)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_416)),n)) ) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_416)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_416)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
      & ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_416)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_416)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
        | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_416)),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_416) != n )
            | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_416)),c),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_416) = n ) )
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_416)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_416)),e)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_416)),n)) ) ) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ( ! [U_418] :
        ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_418) = n )
              & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),c),e)))
                | hAPP(arrow_1998540521e_indi,nat,h,U_418) != n ) )
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),e)))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
    & ! [U_417] :
        ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
          & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
        | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_417) != n )
            | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),c),e)))
              & hAPP(arrow_1998540521e_indi,nat,h,U_417) = n ) )
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n)) )
        | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n)) ) ) ),
    inference(miniscope,[status(thm)],[f_174_2]) ).

cnf(f_174_4,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_5,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_417) != n
    | hAPP(arrow_1998540521e_indi,nat,h,U_417) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_6,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_417) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_7,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_417) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_8,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_9,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_10,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_417) != n
    | hAPP(arrow_1998540521e_indi,nat,h,U_417) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_417) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_12,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_417) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_13,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_14,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_15,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_417) != n
    | hAPP(arrow_1998540521e_indi,nat,h,U_417) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_16,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_417) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_17,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_417) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_18,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_19,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_20,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_417) != n
    | hAPP(arrow_1998540521e_indi,nat,h,U_417) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_21,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_417) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_22,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_417) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_23,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_417)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_417)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_24,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_25,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_26,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_27,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_28,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_418) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_29,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_418) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_30,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_418) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_31,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_418) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_32,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_418) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_33,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_418) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_34,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_418) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_35,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_418)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_418) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_418)),n)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

fof(f_175_1,plain,
    ! [X_a,X_b,X_2,Y_1,F] :
      ( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),Y_1) = ti(X_a,X_2)
      | hAPP(X_a,X_b,F,X_2) != ti(X_b,Y_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_85_inv__f__eq]) ).

fof(f_175_2,plain,
    ! [U_423,U_422,U_421,U_420,U_419] :
      ( hAPP(U_422,U_423,hAPP(fun(U_423,U_422),fun(U_422,U_423),hAPP(fun(U_423,bool),fun(fun(U_423,U_422),fun(U_422,U_423)),hilbert_inv_into(U_423,U_422),top_top(fun(U_423,bool))),U_419),U_420) = ti(U_423,U_421)
      | hAPP(U_423,U_422,U_419,U_421) != ti(U_422,U_420)
      | ~ hBOOL(hAPP(fun(U_423,bool),bool,hAPP(fun(U_423,U_422),fun(fun(U_423,bool),bool),inj_on(U_423,U_422),U_419),top_top(fun(U_423,bool)))) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

cnf(f_175_3,plain,
    ( hAPP(U_422,U_423,hAPP(fun(U_423,U_422),fun(U_422,U_423),hAPP(fun(U_423,bool),fun(fun(U_423,U_422),fun(U_422,U_423)),hilbert_inv_into(U_423,U_422),top_top(fun(U_423,bool))),U_419),U_420) = ti(U_423,U_421)
    | hAPP(U_423,U_422,U_419,U_421) != ti(U_422,U_420)
    | ~ hBOOL(hAPP(fun(U_423,bool),bool,hAPP(fun(U_423,U_422),fun(fun(U_423,bool),bool),inj_on(U_423,U_422),U_419),top_top(fun(U_423,bool)))) ),
    inference(clausify,[status(thm)],[f_175_2]) ).

fof(f_176_1,plain,
    ! [X_a,X_b,X_2,F] :
      ( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_86_inv__f__f]) ).

fof(f_176_2,plain,
    ! [U_427,U_426,U_425,U_424] :
      ( hAPP(U_426,U_427,hAPP(fun(U_427,U_426),fun(U_426,U_427),hAPP(fun(U_427,bool),fun(fun(U_427,U_426),fun(U_426,U_427)),hilbert_inv_into(U_427,U_426),top_top(fun(U_427,bool))),U_424),hAPP(U_427,U_426,U_424,U_425)) = ti(U_427,U_425)
      | ~ hBOOL(hAPP(fun(U_427,bool),bool,hAPP(fun(U_427,U_426),fun(fun(U_427,bool),bool),inj_on(U_427,U_426),U_424),top_top(fun(U_427,bool)))) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

cnf(f_176_3,plain,
    ( hAPP(U_426,U_427,hAPP(fun(U_427,U_426),fun(U_426,U_427),hAPP(fun(U_427,bool),fun(fun(U_427,U_426),fun(U_426,U_427)),hilbert_inv_into(U_427,U_426),top_top(fun(U_427,bool))),U_424),hAPP(U_427,U_426,U_424,U_425)) = ti(U_427,U_425)
    | ~ hBOOL(hAPP(fun(U_427,bool),bool,hAPP(fun(U_427,U_426),fun(fun(U_427,bool),bool),inj_on(U_427,U_426),U_424),top_top(fun(U_427,bool)))) ),
    inference(clausify,[status(thm)],[f_176_2]) ).

fof(f_177_1,plain,
    ! [X_a,X_b,X_2,F,A_1,B] :
      ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2)))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ),
    inference(fof_nnf,[status(thm)],[fact_87_PiE]) ).

fof(f_177_2,plain,
    ! [U_433,U_432,U_431,U_430,U_429,U_428] :
      ( ~ hBOOL(hAPP(fun(U_433,bool),bool,hAPP(U_433,fun(fun(U_433,bool),bool),member(U_433),U_431),U_429))
      | hBOOL(hAPP(fun(U_432,bool),bool,hAPP(U_432,fun(fun(U_432,bool),bool),member(U_432),hAPP(U_433,U_432,U_430,U_431)),hAPP(U_433,fun(U_432,bool),U_428,U_431)))
      | ~ hBOOL(hAPP(fun(fun(U_433,U_432),bool),bool,hAPP(fun(U_433,U_432),fun(fun(fun(U_433,U_432),bool),bool),member(fun(U_433,U_432)),U_430),hAPP(fun(U_433,fun(U_432,bool)),fun(fun(U_433,U_432),bool),hAPP(fun(U_433,bool),fun(fun(U_433,fun(U_432,bool)),fun(fun(U_433,U_432),bool)),pi(U_433,U_432),U_429),U_428))) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

cnf(f_177_3,plain,
    ( ~ hBOOL(hAPP(fun(U_433,bool),bool,hAPP(U_433,fun(fun(U_433,bool),bool),member(U_433),U_431),U_429))
    | hBOOL(hAPP(fun(U_432,bool),bool,hAPP(U_432,fun(fun(U_432,bool),bool),member(U_432),hAPP(U_433,U_432,U_430,U_431)),hAPP(U_433,fun(U_432,bool),U_428,U_431)))
    | ~ hBOOL(hAPP(fun(fun(U_433,U_432),bool),bool,hAPP(fun(U_433,U_432),fun(fun(fun(U_433,U_432),bool),bool),member(fun(U_433,U_432)),U_430),hAPP(fun(U_433,fun(U_432,bool)),fun(fun(U_433,U_432),bool),hAPP(fun(U_433,bool),fun(fun(U_433,fun(U_432,bool)),fun(fun(U_433,U_432),bool)),pi(U_433,U_432),U_429),U_428))) ),
    inference(clausify,[status(thm)],[f_177_2]) ).

fof(f_178_1,plain,
    ! [Aa,Ba] :
      ( ? [X_1] :
          ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Aa),Ba)),X_1))
          & hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X_1),arrow_1568854078le_Lin)) )
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,Ba) ),
    inference(fof_nnf,[status(thm)],[fact_88_complete__Lin]) ).

fof(f_178_2,plain,
    ! [U_436,U_435] :
      ( ? [U_434] :
          ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_436),U_435)),U_434))
          & hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_434),arrow_1568854078le_Lin)) )
      | ti(arrow_2142409994le_alt,U_436) = ti(arrow_2142409994le_alt,U_435) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ! [U_436,U_435] :
      ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_436),U_435)),sK35(U_436,U_435)))
        & hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sK35(U_436,U_435)),arrow_1568854078le_Lin)) )
      | ti(arrow_2142409994le_alt,U_436) = ti(arrow_2142409994le_alt,U_435) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_434,sK35(U_436,U_435))],[f_178_2]) ).

cnf(f_178_4,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sK35(U_436,U_435)),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_436) = ti(arrow_2142409994le_alt,U_435) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

cnf(f_178_5,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_436),U_435)),sK35(U_436,U_435)))
    | ti(arrow_2142409994le_alt,U_436) = ti(arrow_2142409994le_alt,U_435) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

fof(f_179_1,plain,
    ! [X_a,X_b,A_1] : hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),top_top(fun(X_b,bool)))) = top_top(fun(fun(X_a,X_b),bool)),
    inference(fof_nnf,[status(thm)],[fact_89_Pi__UNIV]) ).

fof(f_179_2,plain,
    ! [U_439,U_438,U_437] : hAPP(fun(U_439,fun(U_438,bool)),fun(fun(U_439,U_438),bool),hAPP(fun(U_439,bool),fun(fun(U_439,fun(U_438,bool)),fun(fun(U_439,U_438),bool)),pi(U_439,U_438),U_437),hAPP(fun(U_438,bool),fun(U_439,fun(U_438,bool)),combk(fun(U_438,bool),U_439),top_top(fun(U_438,bool)))) = top_top(fun(fun(U_439,U_438),bool)),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

cnf(f_179_3,plain,
    hAPP(fun(U_439,fun(U_438,bool)),fun(fun(U_439,U_438),bool),hAPP(fun(U_439,bool),fun(fun(U_439,fun(U_438,bool)),fun(fun(U_439,U_438),bool)),pi(U_439,U_438),U_437),hAPP(fun(U_438,bool),fun(U_439,fun(U_438,bool)),combk(fun(U_438,bool),U_439),top_top(fun(U_438,bool)))) = top_top(fun(fun(U_439,U_438),bool)),
    inference(clausify,[status(thm)],[f_179_2]) ).

fof(f_180_1,plain,
    ! [X_c,X_a,X_b,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,fun(X_c,X_b)),fun(fun(X_a,bool),bool),inj_on(X_a,fun(X_c,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_c,X_b)),hAPP(fun(X_b,fun(X_c,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_c,X_b))),combb(X_b,fun(X_c,X_b),X_a),combk(X_b,X_c)),F)),top_top(fun(X_a,bool))))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_90_inj__fun]) ).

fof(f_180_2,plain,
    ! [U_443,U_442,U_441,U_440] :
      ( hBOOL(hAPP(fun(U_442,bool),bool,hAPP(fun(U_442,fun(U_443,U_441)),fun(fun(U_442,bool),bool),inj_on(U_442,fun(U_443,U_441)),hAPP(fun(U_442,U_441),fun(U_442,fun(U_443,U_441)),hAPP(fun(U_441,fun(U_443,U_441)),fun(fun(U_442,U_441),fun(U_442,fun(U_443,U_441))),combb(U_441,fun(U_443,U_441),U_442),combk(U_441,U_443)),U_440)),top_top(fun(U_442,bool))))
      | ~ hBOOL(hAPP(fun(U_442,bool),bool,hAPP(fun(U_442,U_441),fun(fun(U_442,bool),bool),inj_on(U_442,U_441),U_440),top_top(fun(U_442,bool)))) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

cnf(f_180_3,plain,
    ( hBOOL(hAPP(fun(U_442,bool),bool,hAPP(fun(U_442,fun(U_443,U_441)),fun(fun(U_442,bool),bool),inj_on(U_442,fun(U_443,U_441)),hAPP(fun(U_442,U_441),fun(U_442,fun(U_443,U_441)),hAPP(fun(U_441,fun(U_443,U_441)),fun(fun(U_442,U_441),fun(U_442,fun(U_443,U_441))),combb(U_441,fun(U_443,U_441),U_442),combk(U_441,U_443)),U_440)),top_top(fun(U_442,bool))))
    | ~ hBOOL(hAPP(fun(U_442,bool),bool,hAPP(fun(U_442,U_441),fun(fun(U_442,bool),bool),inj_on(U_442,U_441),U_440),top_top(fun(U_442,bool)))) ),
    inference(clausify,[status(thm)],[f_180_2]) ).

fof(f_181_1,plain,
    ! [X_2,Y_1,L_3,Aa,Ba] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,L_3),Aa),Ba)))
          | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3))
                & ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Aa) )
              | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Y_1)),L_3))
                & ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Ba)
                & ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Aa) ) )
            & ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Aa) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Ba)),L_3))
            & ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Aa) )
          | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Y_1) )
        & ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),L_3))
                  | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Aa) )
                & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),Ba),Y_1)),L_3))
                  | ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Ba)
                  | ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Aa) ) )
              | ti(arrow_2142409994le_alt,Y_1) = ti(arrow_2142409994le_alt,Aa) )
            & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Ba)),L_3))
              | ti(arrow_2142409994le_alt,Y_1) != ti(arrow_2142409994le_alt,Aa) )
            & ti(arrow_2142409994le_alt,X_2) != ti(arrow_2142409994le_alt,Y_1) )
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X_2),Y_1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,L_3),Aa),Ba))) ) )
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
      | ti(arrow_2142409994le_alt,Aa) = ti(arrow_2142409994le_alt,Ba) ),
    inference(fof_nnf,[status(thm)],[fact_91_in__below]) ).

fof(f_181_2,plain,
    ! [U_448,U_447,U_446,U_445,U_444] :
      ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
          | ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),U_446))
                & ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_445) )
              | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_444),U_447)),U_446))
                & ti(arrow_2142409994le_alt,U_447) != ti(arrow_2142409994le_alt,U_444)
                & ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_445) ) )
            & ti(arrow_2142409994le_alt,U_447) != ti(arrow_2142409994le_alt,U_445) )
          | ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_444)),U_446))
            & ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445) )
          | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447) )
        & ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),U_446))
                  | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_445) )
                & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_444),U_447)),U_446))
                  | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_444)
                  | ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_445) ) )
              | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445) )
            & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_444)),U_446))
              | ti(arrow_2142409994le_alt,U_447) != ti(arrow_2142409994le_alt,U_445) )
            & ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_447) )
          | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444))) ) )
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
      | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

cnf(f_181_3,plain,
    ( ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_447)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_4,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_444)),U_446))
    | ti(arrow_2142409994le_alt,U_447) != ti(arrow_2142409994le_alt,U_445)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_5,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_444),U_447)),U_446))
    | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_444)
    | ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_6,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),U_446))
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_7,plain,
    ( ti(arrow_2142409994le_alt,U_447) != ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_8,plain,
    ( ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_9,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),U_446))
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_10,plain,
    ( ti(arrow_2142409994le_alt,U_447) != ti(arrow_2142409994le_alt,U_444)
    | ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_11,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_444),U_447)),U_446))
    | ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_12,plain,
    ( ti(arrow_2142409994le_alt,U_447) != ti(arrow_2142409994le_alt,U_444)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),U_446))
    | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_13,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_444),U_447)),U_446))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),U_446))
    | ti(arrow_2142409994le_alt,U_447) = ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_14,plain,
    ( ti(arrow_2142409994le_alt,U_447) != ti(arrow_2142409994le_alt,U_445)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_444)),U_446))
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_15,plain,
    ( ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_445)
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_445)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_444)),U_446))
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_16,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),U_446))
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_445)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_444)),U_446))
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_17,plain,
    ( ti(arrow_2142409994le_alt,U_447) != ti(arrow_2142409994le_alt,U_444)
    | ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_445)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_444)),U_446))
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_18,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_444),U_447)),U_446))
    | ti(arrow_2142409994le_alt,U_448) != ti(arrow_2142409994le_alt,U_445)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_444)),U_446))
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_19,plain,
    ( ti(arrow_2142409994le_alt,U_447) != ti(arrow_2142409994le_alt,U_444)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),U_446))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_444)),U_446))
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_20,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_444),U_447)),U_446))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),U_446))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_444)),U_446))
    | ti(arrow_2142409994le_alt,U_448) = ti(arrow_2142409994le_alt,U_447)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),U_448),U_447)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_446),U_445),U_444)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_446),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_445) = ti(arrow_2142409994le_alt,U_444) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

fof(f_182_1,plain,
    ! [X_a] :
      ( ! [X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_92_order__refl]) ).

fof(f_182_2,plain,
    ! [U_450] :
      ( ! [U_449] : hBOOL(hAPP(U_450,bool,hAPP(U_450,fun(U_450,bool),ord_less_eq(U_450),U_449),U_449))
      | ~ preorder(U_450) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

cnf(f_182_3,plain,
    ( hBOOL(hAPP(U_450,bool,hAPP(U_450,fun(U_450,bool),ord_less_eq(U_450),U_449),U_449))
    | ~ preorder(U_450) ),
    inference(clausify,[status(thm)],[f_182_2]) ).

fof(f_183_1,plain,
    ? [N_2] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),one_one(nat))))),lab)),lba))))
      & ! [M_1] :
          ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),M_1))),lab)),lba))))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)) )
      & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))) ),
    inference(fof_nnf,[status(thm)],[fact_93__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_]) ).

fof(f_183_2,plain,
    ? [U_452] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_452),one_one(nat))))),lab)),lba))))
      & ! [U_451] :
          ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),U_451))),lab)),lba))))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_451),U_452)) )
      & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_452),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK36),one_one(nat))))),lab)),lba))))
    & ! [U_451] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),U_451))),lab)),lba))))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_451),sK36)) )
    & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK36),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_452,sK36)],[f_183_2]) ).

cnf(f_183_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK36),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
    inference(clausify,[status(thm)],[f_183_3]) ).

cnf(f_183_5,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),U_451))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_451),sK36)) ),
    inference(clausify,[status(thm)],[f_183_3]) ).

cnf(f_183_6,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK36),one_one(nat))))),lab)),lba)))),
    inference(clausify,[status(thm)],[f_183_3]) ).

fof(f_184_1,plain,
    ? [N_2] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),one_one(nat))))),lab)),lba))))
      & ! [M_1] :
          ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),M_1))),lab)),lba))))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)) )
      & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))) ),
    inference(fof_nnf,[status(thm)],[fact_94__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O]) ).

fof(f_184_2,plain,
    ? [U_454] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_454),one_one(nat))))),lab)),lba))))
      & ! [U_453] :
          ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),U_453))),lab)),lba))))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_453),U_454)) )
      & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_454),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK37),one_one(nat))))),lab)),lba))))
    & ! [U_453] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),U_453))),lab)),lba))))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_453),sK37)) )
    & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK37),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_454,sK37)],[f_184_2]) ).

cnf(f_184_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK37),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
    inference(clausify,[status(thm)],[f_184_3]) ).

cnf(f_184_5,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),U_453))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_453),sK37)) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

cnf(f_184_6,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK37),one_one(nat))))),lab)),lba)))),
    inference(clausify,[status(thm)],[f_184_3]) ).

fof(f_185_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_95_linorder__le__cases]) ).

fof(f_185_2,plain,
    ! [U_457] :
      ( ! [U_456,U_455] :
          ( hBOOL(hAPP(U_457,bool,hAPP(U_457,fun(U_457,bool),ord_less_eq(U_457),U_455),U_456))
          | hBOOL(hAPP(U_457,bool,hAPP(U_457,fun(U_457,bool),ord_less_eq(U_457),U_456),U_455)) )
      | ~ linorder(U_457) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

cnf(f_185_3,plain,
    ( hBOOL(hAPP(U_457,bool,hAPP(U_457,fun(U_457,bool),ord_less_eq(U_457),U_455),U_456))
    | hBOOL(hAPP(U_457,bool,hAPP(U_457,fun(U_457,bool),ord_less_eq(U_457),U_456),U_455))
    | ~ linorder(U_457) ),
    inference(clausify,[status(thm)],[f_185_2]) ).

fof(f_186_1,plain,
    ! [X_a,X_b] :
      ( ! [X_2,F,G] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))
          | ~ hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) )
      | ~ ord(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_96_le__funE]) ).

fof(f_186_2,plain,
    ! [U_462,U_461] :
      ( ! [U_460,U_459,U_458] :
          ( hBOOL(hAPP(U_461,bool,hAPP(U_461,fun(U_461,bool),ord_less_eq(U_461),hAPP(U_462,U_461,U_459,U_460)),hAPP(U_462,U_461,U_458,U_460)))
          | ~ hBOOL(hAPP(fun(U_462,U_461),bool,hAPP(fun(U_462,U_461),fun(fun(U_462,U_461),bool),ord_less_eq(fun(U_462,U_461)),U_459),U_458)) )
      | ~ ord(U_461) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

cnf(f_186_3,plain,
    ( hBOOL(hAPP(U_461,bool,hAPP(U_461,fun(U_461,bool),ord_less_eq(U_461),hAPP(U_462,U_461,U_459,U_460)),hAPP(U_462,U_461,U_458,U_460)))
    | ~ hBOOL(hAPP(fun(U_462,U_461),bool,hAPP(fun(U_462,U_461),fun(fun(U_462,U_461),bool),ord_less_eq(fun(U_462,U_461)),U_459),U_458))
    | ~ ord(U_461) ),
    inference(clausify,[status(thm)],[f_186_2]) ).

fof(f_187_1,plain,
    ! [X_a] :
      ( ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_97_xt1_I6_J]) ).

fof(f_187_2,plain,
    ! [U_466] :
      ( ! [U_465,U_464,U_463] :
          ( hBOOL(hAPP(U_466,bool,hAPP(U_466,fun(U_466,bool),ord_less_eq(U_466),U_465),U_463))
          | ~ hBOOL(hAPP(U_466,bool,hAPP(U_466,fun(U_466,bool),ord_less_eq(U_466),U_465),U_464))
          | ~ hBOOL(hAPP(U_466,bool,hAPP(U_466,fun(U_466,bool),ord_less_eq(U_466),U_464),U_463)) )
      | ~ order(U_466) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

cnf(f_187_3,plain,
    ( hBOOL(hAPP(U_466,bool,hAPP(U_466,fun(U_466,bool),ord_less_eq(U_466),U_465),U_463))
    | ~ hBOOL(hAPP(U_466,bool,hAPP(U_466,fun(U_466,bool),ord_less_eq(U_466),U_465),U_464))
    | ~ hBOOL(hAPP(U_466,bool,hAPP(U_466,fun(U_466,bool),ord_less_eq(U_466),U_464),U_463))
    | ~ order(U_466) ),
    inference(clausify,[status(thm)],[f_187_2]) ).

fof(f_188_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( ti(X_a,X) = ti(X_a,Y)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_98_xt1_I5_J]) ).

fof(f_188_2,plain,
    ! [U_469] :
      ( ! [U_468,U_467] :
          ( ti(U_469,U_467) = ti(U_469,U_468)
          | ~ hBOOL(hAPP(U_469,bool,hAPP(U_469,fun(U_469,bool),ord_less_eq(U_469),U_467),U_468))
          | ~ hBOOL(hAPP(U_469,bool,hAPP(U_469,fun(U_469,bool),ord_less_eq(U_469),U_468),U_467)) )
      | ~ order(U_469) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

cnf(f_188_3,plain,
    ( ti(U_469,U_467) = ti(U_469,U_468)
    | ~ hBOOL(hAPP(U_469,bool,hAPP(U_469,fun(U_469,bool),ord_less_eq(U_469),U_467),U_468))
    | ~ hBOOL(hAPP(U_469,bool,hAPP(U_469,fun(U_469,bool),ord_less_eq(U_469),U_468),U_467))
    | ~ order(U_469) ),
    inference(clausify,[status(thm)],[f_188_2]) ).

fof(f_189_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_99_order__trans]) ).

fof(f_189_2,plain,
    ! [U_473] :
      ( ! [U_472,U_471,U_470] :
          ( hBOOL(hAPP(U_473,bool,hAPP(U_473,fun(U_473,bool),ord_less_eq(U_473),U_471),U_472))
          | ~ hBOOL(hAPP(U_473,bool,hAPP(U_473,fun(U_473,bool),ord_less_eq(U_473),U_470),U_472))
          | ~ hBOOL(hAPP(U_473,bool,hAPP(U_473,fun(U_473,bool),ord_less_eq(U_473),U_471),U_470)) )
      | ~ preorder(U_473) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

cnf(f_189_3,plain,
    ( hBOOL(hAPP(U_473,bool,hAPP(U_473,fun(U_473,bool),ord_less_eq(U_473),U_471),U_472))
    | ~ hBOOL(hAPP(U_473,bool,hAPP(U_473,fun(U_473,bool),ord_less_eq(U_473),U_470),U_472))
    | ~ hBOOL(hAPP(U_473,bool,hAPP(U_473,fun(U_473,bool),ord_less_eq(U_473),U_471),U_470))
    | ~ preorder(U_473) ),
    inference(clausify,[status(thm)],[f_189_2]) ).

fof(f_190_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ti(X_a,X) = ti(X_a,Y)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_100_order__antisym]) ).

fof(f_190_2,plain,
    ! [U_476] :
      ( ! [U_475,U_474] :
          ( ti(U_476,U_475) = ti(U_476,U_474)
          | ~ hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),U_474),U_475))
          | ~ hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),U_475),U_474)) )
      | ~ order(U_476) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

cnf(f_190_3,plain,
    ( ti(U_476,U_475) = ti(U_476,U_474)
    | ~ hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),U_474),U_475))
    | ~ hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),U_475),U_474))
    | ~ order(U_476) ),
    inference(clausify,[status(thm)],[f_190_2]) ).

fof(f_191_1,plain,
    ! [X_a] :
      ( ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))
          | ti(X_a,B_1) != ti(X_a,C_1)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_101_xt1_I4_J]) ).

fof(f_191_2,plain,
    ! [U_480] :
      ( ! [U_479,U_478,U_477] :
          ( hBOOL(hAPP(U_480,bool,hAPP(U_480,fun(U_480,bool),ord_less_eq(U_480),U_479),U_477))
          | ti(U_480,U_478) != ti(U_480,U_479)
          | ~ hBOOL(hAPP(U_480,bool,hAPP(U_480,fun(U_480,bool),ord_less_eq(U_480),U_478),U_477)) )
      | ~ order(U_480) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

cnf(f_191_3,plain,
    ( hBOOL(hAPP(U_480,bool,hAPP(U_480,fun(U_480,bool),ord_less_eq(U_480),U_479),U_477))
    | ti(U_480,U_478) != ti(U_480,U_479)
    | ~ hBOOL(hAPP(U_480,bool,hAPP(U_480,fun(U_480,bool),ord_less_eq(U_480),U_478),U_477))
    | ~ order(U_480) ),
    inference(clausify,[status(thm)],[f_191_2]) ).

fof(f_192_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1))
          | B_1 != C_1
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_102_ord__le__eq__trans]) ).

fof(f_192_2,plain,
    ! [U_484] :
      ( ! [U_483,U_482,U_481] :
          ( hBOOL(hAPP(U_484,bool,hAPP(U_484,fun(U_484,bool),ord_less_eq(U_484),U_482),U_483))
          | U_481 != U_483
          | ~ hBOOL(hAPP(U_484,bool,hAPP(U_484,fun(U_484,bool),ord_less_eq(U_484),U_482),U_481)) )
      | ~ ord(U_484) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

cnf(f_192_3,plain,
    ( hBOOL(hAPP(U_484,bool,hAPP(U_484,fun(U_484,bool),ord_less_eq(U_484),U_482),U_483))
    | U_481 != U_483
    | ~ hBOOL(hAPP(U_484,bool,hAPP(U_484,fun(U_484,bool),ord_less_eq(U_484),U_482),U_481))
    | ~ ord(U_484) ),
    inference(clausify,[status(thm)],[f_192_2]) ).

fof(f_193_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),B_1))
          | ti(X_a,A_2) != ti(X_a,B_1) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_103_xt1_I3_J]) ).

fof(f_193_2,plain,
    ! [U_488] :
      ( ! [U_487,U_486,U_485] :
          ( hBOOL(hAPP(U_488,bool,hAPP(U_488,fun(U_488,bool),ord_less_eq(U_488),U_487),U_486))
          | ~ hBOOL(hAPP(U_488,bool,hAPP(U_488,fun(U_488,bool),ord_less_eq(U_488),U_487),U_485))
          | ti(U_488,U_486) != ti(U_488,U_485) )
      | ~ order(U_488) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

cnf(f_193_3,plain,
    ( hBOOL(hAPP(U_488,bool,hAPP(U_488,fun(U_488,bool),ord_less_eq(U_488),U_487),U_486))
    | ~ hBOOL(hAPP(U_488,bool,hAPP(U_488,fun(U_488,bool),ord_less_eq(U_488),U_487),U_485))
    | ti(U_488,U_486) != ti(U_488,U_485)
    | ~ order(U_488) ),
    inference(clausify,[status(thm)],[f_193_2]) ).

fof(f_194_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C_1))
          | A_2 != B_1 )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_104_ord__eq__le__trans]) ).

fof(f_194_2,plain,
    ! [U_492] :
      ( ! [U_491,U_490,U_489] :
          ( hBOOL(hAPP(U_492,bool,hAPP(U_492,fun(U_492,bool),ord_less_eq(U_492),U_490),U_491))
          | ~ hBOOL(hAPP(U_492,bool,hAPP(U_492,fun(U_492,bool),ord_less_eq(U_492),U_489),U_491))
          | U_490 != U_489 )
      | ~ ord(U_492) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

cnf(f_194_3,plain,
    ( hBOOL(hAPP(U_492,bool,hAPP(U_492,fun(U_492,bool),ord_less_eq(U_492),U_490),U_491))
    | ~ hBOOL(hAPP(U_492,bool,hAPP(U_492,fun(U_492,bool),ord_less_eq(U_492),U_489),U_491))
    | U_490 != U_489
    | ~ ord(U_492) ),
    inference(clausify,[status(thm)],[f_194_2]) ).

fof(f_195_1,plain,
    ! [X_a] :
      ( ! [Y_1,X_2] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
              | ti(X_a,X_2) != ti(X_a,Y_1) )
            & ( ti(X_a,X_2) = ti(X_a,Y_1)
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) ) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_105_order__antisym__conv]) ).

fof(f_195_2,plain,
    ! [U_495] :
      ( ! [U_494,U_493] :
          ( ( ( hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_493),U_494))
              | ti(U_495,U_493) != ti(U_495,U_494) )
            & ( ti(U_495,U_493) = ti(U_495,U_494)
              | ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_493),U_494)) ) )
          | ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_494),U_493)) )
      | ~ order(U_495) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

cnf(f_195_3,plain,
    ( ti(U_495,U_493) = ti(U_495,U_494)
    | ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_493),U_494))
    | ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_494),U_493))
    | ~ order(U_495) ),
    inference(clausify,[status(thm)],[f_195_2]) ).

cnf(f_195_4,plain,
    ( hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_493),U_494))
    | ti(U_495,U_493) != ti(U_495,U_494)
    | ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_494),U_493))
    | ~ order(U_495) ),
    inference(clausify,[status(thm)],[f_195_2]) ).

fof(f_196_1,plain,
    ! [X_a,X_b] :
      ( ! [X_2,F,G] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))
          | ~ hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) )
      | ~ ord(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_106_le__funD]) ).

fof(f_196_2,plain,
    ! [U_500,U_499] :
      ( ! [U_498,U_497,U_496] :
          ( hBOOL(hAPP(U_499,bool,hAPP(U_499,fun(U_499,bool),ord_less_eq(U_499),hAPP(U_500,U_499,U_497,U_498)),hAPP(U_500,U_499,U_496,U_498)))
          | ~ hBOOL(hAPP(fun(U_500,U_499),bool,hAPP(fun(U_500,U_499),fun(fun(U_500,U_499),bool),ord_less_eq(fun(U_500,U_499)),U_497),U_496)) )
      | ~ ord(U_499) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

cnf(f_196_3,plain,
    ( hBOOL(hAPP(U_499,bool,hAPP(U_499,fun(U_499,bool),ord_less_eq(U_499),hAPP(U_500,U_499,U_497,U_498)),hAPP(U_500,U_499,U_496,U_498)))
    | ~ hBOOL(hAPP(fun(U_500,U_499),bool,hAPP(fun(U_500,U_499),fun(fun(U_500,U_499),bool),ord_less_eq(fun(U_500,U_499)),U_497),U_496))
    | ~ ord(U_499) ),
    inference(clausify,[status(thm)],[f_196_2]) ).

fof(f_197_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
          | X != Y )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_107_order__eq__refl]) ).

fof(f_197_2,plain,
    ! [U_503] :
      ( ! [U_502,U_501] :
          ( hBOOL(hAPP(U_503,bool,hAPP(U_503,fun(U_503,bool),ord_less_eq(U_503),U_502),U_501))
          | U_502 != U_501 )
      | ~ preorder(U_503) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

cnf(f_197_3,plain,
    ( hBOOL(hAPP(U_503,bool,hAPP(U_503,fun(U_503,bool),ord_less_eq(U_503),U_502),U_501))
    | U_502 != U_501
    | ~ preorder(U_503) ),
    inference(clausify,[status(thm)],[f_197_2]) ).

fof(f_198_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( ti(X_a,X_2) = ti(X_a,Y_1)
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) )
            | ti(X_a,X_2) != ti(X_a,Y_1) ) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_108_order__eq__iff]) ).

fof(f_198_2,plain,
    ! [U_506] :
      ( ! [U_505,U_504] :
          ( ( ti(U_506,U_505) = ti(U_506,U_504)
            | ~ hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_504),U_505))
            | ~ hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_505),U_504)) )
          & ( ( hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_504),U_505))
              & hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_505),U_504)) )
            | ti(U_506,U_505) != ti(U_506,U_504) ) )
      | ~ order(U_506) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ! [U_506] :
      ( ( ! [U_510,U_508] :
            ( ti(U_506,U_510) = ti(U_506,U_508)
            | ~ hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_508),U_510))
            | ~ hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_510),U_508)) )
        & ! [U_509,U_507] :
            ( ( hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_507),U_509))
              & hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_509),U_507)) )
            | ti(U_506,U_509) != ti(U_506,U_507) ) )
      | ~ order(U_506) ),
    inference(miniscope,[status(thm)],[f_198_2]) ).

cnf(f_198_4,plain,
    ( hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_509),U_507))
    | ti(U_506,U_509) != ti(U_506,U_507)
    | ~ order(U_506) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

cnf(f_198_5,plain,
    ( hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_507),U_509))
    | ti(U_506,U_509) != ti(U_506,U_507)
    | ~ order(U_506) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

cnf(f_198_6,plain,
    ( ti(U_506,U_510) = ti(U_506,U_508)
    | ~ hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_508),U_510))
    | ~ hBOOL(hAPP(U_506,bool,hAPP(U_506,fun(U_506,bool),ord_less_eq(U_506),U_510),U_508))
    | ~ order(U_506) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

fof(f_199_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_109_linorder__linear]) ).

fof(f_199_2,plain,
    ! [U_513] :
      ( ! [U_512,U_511] :
          ( hBOOL(hAPP(U_513,bool,hAPP(U_513,fun(U_513,bool),ord_less_eq(U_513),U_511),U_512))
          | hBOOL(hAPP(U_513,bool,hAPP(U_513,fun(U_513,bool),ord_less_eq(U_513),U_512),U_511)) )
      | ~ linorder(U_513) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

cnf(f_199_3,plain,
    ( hBOOL(hAPP(U_513,bool,hAPP(U_513,fun(U_513,bool),ord_less_eq(U_513),U_511),U_512))
    | hBOOL(hAPP(U_513,bool,hAPP(U_513,fun(U_513,bool),ord_less_eq(U_513),U_512),U_511))
    | ~ linorder(U_513) ),
    inference(clausify,[status(thm)],[f_199_2]) ).

fof(f_200_1,plain,
    ! [X_a,X_b] :
      ( ! [F,G] :
          ( ( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G))
            | ? [X_1] : ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))) )
          & ( ! [X_1] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))
            | ~ hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) ) )
      | ~ ord(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_110_le__fun__def]) ).

fof(f_200_2,plain,
    ! [U_519,U_518] :
      ( ! [U_517,U_516] :
          ( ( hBOOL(hAPP(fun(U_519,U_518),bool,hAPP(fun(U_519,U_518),fun(fun(U_519,U_518),bool),ord_less_eq(fun(U_519,U_518)),U_517),U_516))
            | ? [U_515] : ~ hBOOL(hAPP(U_518,bool,hAPP(U_518,fun(U_518,bool),ord_less_eq(U_518),hAPP(U_519,U_518,U_517,U_515)),hAPP(U_519,U_518,U_516,U_515))) )
          & ( ! [U_514] : hBOOL(hAPP(U_518,bool,hAPP(U_518,fun(U_518,bool),ord_less_eq(U_518),hAPP(U_519,U_518,U_517,U_514)),hAPP(U_519,U_518,U_516,U_514)))
            | ~ hBOOL(hAPP(fun(U_519,U_518),bool,hAPP(fun(U_519,U_518),fun(fun(U_519,U_518),bool),ord_less_eq(fun(U_519,U_518)),U_517),U_516)) ) )
      | ~ ord(U_518) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ! [U_519,U_518] :
      ( ( ! [U_523,U_521] :
            ( hBOOL(hAPP(fun(U_519,U_518),bool,hAPP(fun(U_519,U_518),fun(fun(U_519,U_518),bool),ord_less_eq(fun(U_519,U_518)),U_523),U_521))
            | ? [U_515] : ~ hBOOL(hAPP(U_518,bool,hAPP(U_518,fun(U_518,bool),ord_less_eq(U_518),hAPP(U_519,U_518,U_523,U_515)),hAPP(U_519,U_518,U_521,U_515))) )
        & ! [U_522,U_520] :
            ( ! [U_514] : hBOOL(hAPP(U_518,bool,hAPP(U_518,fun(U_518,bool),ord_less_eq(U_518),hAPP(U_519,U_518,U_522,U_514)),hAPP(U_519,U_518,U_520,U_514)))
            | ~ hBOOL(hAPP(fun(U_519,U_518),bool,hAPP(fun(U_519,U_518),fun(fun(U_519,U_518),bool),ord_less_eq(fun(U_519,U_518)),U_522),U_520)) ) )
      | ~ ord(U_518) ),
    inference(miniscope,[status(thm)],[f_200_2]) ).

fof(f_200_4,plain,
    ! [U_519,U_518] :
      ( ( ! [U_523,U_521] :
            ( hBOOL(hAPP(fun(U_519,U_518),bool,hAPP(fun(U_519,U_518),fun(fun(U_519,U_518),bool),ord_less_eq(fun(U_519,U_518)),U_523),U_521))
            | ~ hBOOL(hAPP(U_518,bool,hAPP(U_518,fun(U_518,bool),ord_less_eq(U_518),hAPP(U_519,U_518,U_523,sK38(U_519,U_518,U_523,U_521))),hAPP(U_519,U_518,U_521,sK38(U_519,U_518,U_523,U_521)))) )
        & ! [U_522,U_520] :
            ( ! [U_514] : hBOOL(hAPP(U_518,bool,hAPP(U_518,fun(U_518,bool),ord_less_eq(U_518),hAPP(U_519,U_518,U_522,U_514)),hAPP(U_519,U_518,U_520,U_514)))
            | ~ hBOOL(hAPP(fun(U_519,U_518),bool,hAPP(fun(U_519,U_518),fun(fun(U_519,U_518),bool),ord_less_eq(fun(U_519,U_518)),U_522),U_520)) ) )
      | ~ ord(U_518) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_515,sK38(U_519,U_518,U_523,U_521))],[f_200_3]) ).

cnf(f_200_5,plain,
    ( hBOOL(hAPP(U_518,bool,hAPP(U_518,fun(U_518,bool),ord_less_eq(U_518),hAPP(U_519,U_518,U_522,U_514)),hAPP(U_519,U_518,U_520,U_514)))
    | ~ hBOOL(hAPP(fun(U_519,U_518),bool,hAPP(fun(U_519,U_518),fun(fun(U_519,U_518),bool),ord_less_eq(fun(U_519,U_518)),U_522),U_520))
    | ~ ord(U_518) ),
    inference(clausify,[status(thm)],[f_200_4]) ).

cnf(f_200_6,plain,
    ( hBOOL(hAPP(fun(U_519,U_518),bool,hAPP(fun(U_519,U_518),fun(fun(U_519,U_518),bool),ord_less_eq(fun(U_519,U_518)),U_523),U_521))
    | ~ hBOOL(hAPP(U_518,bool,hAPP(U_518,fun(U_518,bool),ord_less_eq(U_518),hAPP(U_519,U_518,U_523,sK38(U_519,U_518,U_523,U_521))),hAPP(U_519,U_518,U_521,sK38(U_519,U_518,U_523,U_521))))
    | ~ ord(U_518) ),
    inference(clausify,[status(thm)],[f_200_4]) ).

fof(f_201_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2))
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_111_linorder__not__less]) ).

fof(f_201_2,plain,
    ! [U_526] :
      ( ! [U_525,U_524] :
          ( ( ~ hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less(U_526),U_525),U_524))
            | ~ hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less_eq(U_526),U_524),U_525)) )
          & ( hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less_eq(U_526),U_524),U_525))
            | hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less(U_526),U_525),U_524)) ) )
      | ~ linorder(U_526) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ! [U_526] :
      ( ( ! [U_530,U_528] :
            ( ~ hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less(U_526),U_530),U_528))
            | ~ hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less_eq(U_526),U_528),U_530)) )
        & ! [U_529,U_527] :
            ( hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less_eq(U_526),U_527),U_529))
            | hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less(U_526),U_529),U_527)) ) )
      | ~ linorder(U_526) ),
    inference(miniscope,[status(thm)],[f_201_2]) ).

cnf(f_201_4,plain,
    ( hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less_eq(U_526),U_527),U_529))
    | hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less(U_526),U_529),U_527))
    | ~ linorder(U_526) ),
    inference(clausify,[status(thm)],[f_201_3]) ).

cnf(f_201_5,plain,
    ( ~ hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less(U_526),U_530),U_528))
    | ~ hBOOL(hAPP(U_526,bool,hAPP(U_526,fun(U_526,bool),ord_less_eq(U_526),U_528),U_530))
    | ~ linorder(U_526) ),
    inference(clausify,[status(thm)],[f_201_3]) ).

fof(f_202_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) ) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_112_linorder__not__le]) ).

fof(f_202_2,plain,
    ! [U_533] :
      ( ! [U_532,U_531] :
          ( ( ~ hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less_eq(U_533),U_532),U_531))
            | ~ hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less(U_533),U_531),U_532)) )
          & ( hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less(U_533),U_531),U_532))
            | hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less_eq(U_533),U_532),U_531)) ) )
      | ~ linorder(U_533) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ! [U_533] :
      ( ( ! [U_537,U_535] :
            ( ~ hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less_eq(U_533),U_537),U_535))
            | ~ hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less(U_533),U_535),U_537)) )
        & ! [U_536,U_534] :
            ( hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less(U_533),U_534),U_536))
            | hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less_eq(U_533),U_536),U_534)) ) )
      | ~ linorder(U_533) ),
    inference(miniscope,[status(thm)],[f_202_2]) ).

cnf(f_202_4,plain,
    ( hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less(U_533),U_534),U_536))
    | hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less_eq(U_533),U_536),U_534))
    | ~ linorder(U_533) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_5,plain,
    ( ~ hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less_eq(U_533),U_537),U_535))
    | ~ hBOOL(hAPP(U_533,bool,hAPP(U_533,fun(U_533,bool),ord_less(U_533),U_535),U_537))
    | ~ linorder(U_533) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_113_linorder__le__less__linear]) ).

fof(f_203_2,plain,
    ! [U_540] :
      ( ! [U_539,U_538] :
          ( hBOOL(hAPP(U_540,bool,hAPP(U_540,fun(U_540,bool),ord_less(U_540),U_538),U_539))
          | hBOOL(hAPP(U_540,bool,hAPP(U_540,fun(U_540,bool),ord_less_eq(U_540),U_539),U_538)) )
      | ~ linorder(U_540) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

cnf(f_203_3,plain,
    ( hBOOL(hAPP(U_540,bool,hAPP(U_540,fun(U_540,bool),ord_less(U_540),U_538),U_539))
    | hBOOL(hAPP(U_540,bool,hAPP(U_540,fun(U_540,bool),ord_less_eq(U_540),U_539),U_538))
    | ~ linorder(U_540) ),
    inference(clausify,[status(thm)],[f_203_2]) ).

fof(f_204_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
            | ti(X_a,X_2) = ti(X_a,Y_1)
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) )
          & ( ( ti(X_a,X_2) != ti(X_a,Y_1)
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_114_order__less__le]) ).

fof(f_204_2,plain,
    ! [U_543] :
      ( ! [U_542,U_541] :
          ( ( hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less(U_543),U_542),U_541))
            | ti(U_543,U_542) = ti(U_543,U_541)
            | ~ hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less_eq(U_543),U_542),U_541)) )
          & ( ( ti(U_543,U_542) != ti(U_543,U_541)
              & hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less_eq(U_543),U_542),U_541)) )
            | ~ hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less(U_543),U_542),U_541)) ) )
      | ~ order(U_543) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ! [U_543] :
      ( ( ! [U_547,U_545] :
            ( hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less(U_543),U_547),U_545))
            | ti(U_543,U_547) = ti(U_543,U_545)
            | ~ hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less_eq(U_543),U_547),U_545)) )
        & ! [U_546,U_544] :
            ( ( ti(U_543,U_546) != ti(U_543,U_544)
              & hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less_eq(U_543),U_546),U_544)) )
            | ~ hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less(U_543),U_546),U_544)) ) )
      | ~ order(U_543) ),
    inference(miniscope,[status(thm)],[f_204_2]) ).

cnf(f_204_4,plain,
    ( hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less_eq(U_543),U_546),U_544))
    | ~ hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less(U_543),U_546),U_544))
    | ~ order(U_543) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

cnf(f_204_5,plain,
    ( ti(U_543,U_546) != ti(U_543,U_544)
    | ~ hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less(U_543),U_546),U_544))
    | ~ order(U_543) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

cnf(f_204_6,plain,
    ( hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less(U_543),U_547),U_545))
    | ti(U_543,U_547) = ti(U_543,U_545)
    | ~ hBOOL(hAPP(U_543,bool,hAPP(U_543,fun(U_543,bool),ord_less_eq(U_543),U_547),U_545))
    | ~ order(U_543) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

fof(f_205_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) )
          & ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_115_less__le__not__le]) ).

fof(f_205_2,plain,
    ! [U_550] :
      ( ! [U_549,U_548] :
          ( ( hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_549),U_548))
            | hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_548),U_549))
            | ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_549),U_548)) )
          & ( ( ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_548),U_549))
              & hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_549),U_548)) )
            | ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_549),U_548)) ) )
      | ~ preorder(U_550) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ! [U_550] :
      ( ( ! [U_554,U_552] :
            ( hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_554),U_552))
            | hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_552),U_554))
            | ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_554),U_552)) )
        & ! [U_553,U_551] :
            ( ( ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_551),U_553))
              & hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_553),U_551)) )
            | ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_553),U_551)) ) )
      | ~ preorder(U_550) ),
    inference(miniscope,[status(thm)],[f_205_2]) ).

cnf(f_205_4,plain,
    ( hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_553),U_551))
    | ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_553),U_551))
    | ~ preorder(U_550) ),
    inference(clausify,[status(thm)],[f_205_3]) ).

cnf(f_205_5,plain,
    ( ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_551),U_553))
    | ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_553),U_551))
    | ~ preorder(U_550) ),
    inference(clausify,[status(thm)],[f_205_3]) ).

cnf(f_205_6,plain,
    ( hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_554),U_552))
    | hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_552),U_554))
    | ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_554),U_552))
    | ~ preorder(U_550) ),
    inference(clausify,[status(thm)],[f_205_3]) ).

fof(f_206_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
            | ( ti(X_a,X_2) != ti(X_a,Y_1)
              & ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
          & ( ti(X_a,X_2) = ti(X_a,Y_1)
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) ) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_116_order__le__less]) ).

fof(f_206_2,plain,
    ! [U_557] :
      ( ! [U_556,U_555] :
          ( ( hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less_eq(U_557),U_556),U_555))
            | ( ti(U_557,U_556) != ti(U_557,U_555)
              & ~ hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less(U_557),U_556),U_555)) ) )
          & ( ti(U_557,U_556) = ti(U_557,U_555)
            | hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less(U_557),U_556),U_555))
            | ~ hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less_eq(U_557),U_556),U_555)) ) )
      | ~ order(U_557) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ! [U_557] :
      ( ( ! [U_561,U_559] :
            ( hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less_eq(U_557),U_561),U_559))
            | ( ti(U_557,U_561) != ti(U_557,U_559)
              & ~ hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less(U_557),U_561),U_559)) ) )
        & ! [U_560,U_558] :
            ( ti(U_557,U_560) = ti(U_557,U_558)
            | hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less(U_557),U_560),U_558))
            | ~ hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less_eq(U_557),U_560),U_558)) ) )
      | ~ order(U_557) ),
    inference(miniscope,[status(thm)],[f_206_2]) ).

cnf(f_206_4,plain,
    ( ti(U_557,U_560) = ti(U_557,U_558)
    | hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less(U_557),U_560),U_558))
    | ~ hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less_eq(U_557),U_560),U_558))
    | ~ order(U_557) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_5,plain,
    ( ~ hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less(U_557),U_561),U_559))
    | hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less_eq(U_557),U_561),U_559))
    | ~ order(U_557) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_6,plain,
    ( ti(U_557,U_561) != ti(U_557,U_559)
    | hBOOL(hAPP(U_557,bool,hAPP(U_557,fun(U_557,bool),ord_less_eq(U_557),U_561),U_559))
    | ~ order(U_557) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

fof(f_207_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_117_leI]) ).

fof(f_207_2,plain,
    ! [U_564] :
      ( ! [U_563,U_562] :
          ( hBOOL(hAPP(U_564,bool,hAPP(U_564,fun(U_564,bool),ord_less_eq(U_564),U_562),U_563))
          | hBOOL(hAPP(U_564,bool,hAPP(U_564,fun(U_564,bool),ord_less(U_564),U_563),U_562)) )
      | ~ linorder(U_564) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

cnf(f_207_3,plain,
    ( hBOOL(hAPP(U_564,bool,hAPP(U_564,fun(U_564,bool),ord_less_eq(U_564),U_562),U_563))
    | hBOOL(hAPP(U_564,bool,hAPP(U_564,fun(U_564,bool),ord_less(U_564),U_563),U_562))
    | ~ linorder(U_564) ),
    inference(clausify,[status(thm)],[f_207_2]) ).

fof(f_208_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_118_not__leE]) ).

fof(f_208_2,plain,
    ! [U_567] :
      ( ! [U_566,U_565] :
          ( hBOOL(hAPP(U_567,bool,hAPP(U_567,fun(U_567,bool),ord_less(U_567),U_565),U_566))
          | hBOOL(hAPP(U_567,bool,hAPP(U_567,fun(U_567,bool),ord_less_eq(U_567),U_566),U_565)) )
      | ~ linorder(U_567) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

cnf(f_208_3,plain,
    ( hBOOL(hAPP(U_567,bool,hAPP(U_567,fun(U_567,bool),ord_less(U_567),U_565),U_566))
    | hBOOL(hAPP(U_567,bool,hAPP(U_567,fun(U_567,bool),ord_less_eq(U_567),U_566),U_565))
    | ~ linorder(U_567) ),
    inference(clausify,[status(thm)],[f_208_2]) ).

fof(f_209_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
              | ti(X_a,X_2) != ti(X_a,Y_1) )
            & ( ti(X_a,X_2) = ti(X_a,Y_1)
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) ) )
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_119_linorder__antisym__conv1]) ).

fof(f_209_2,plain,
    ! [U_570] :
      ( ! [U_569,U_568] :
          ( ( ( hBOOL(hAPP(U_570,bool,hAPP(U_570,fun(U_570,bool),ord_less_eq(U_570),U_569),U_568))
              | ti(U_570,U_569) != ti(U_570,U_568) )
            & ( ti(U_570,U_569) = ti(U_570,U_568)
              | ~ hBOOL(hAPP(U_570,bool,hAPP(U_570,fun(U_570,bool),ord_less_eq(U_570),U_569),U_568)) ) )
          | hBOOL(hAPP(U_570,bool,hAPP(U_570,fun(U_570,bool),ord_less(U_570),U_569),U_568)) )
      | ~ linorder(U_570) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

cnf(f_209_3,plain,
    ( ti(U_570,U_569) = ti(U_570,U_568)
    | ~ hBOOL(hAPP(U_570,bool,hAPP(U_570,fun(U_570,bool),ord_less_eq(U_570),U_569),U_568))
    | hBOOL(hAPP(U_570,bool,hAPP(U_570,fun(U_570,bool),ord_less(U_570),U_569),U_568))
    | ~ linorder(U_570) ),
    inference(clausify,[status(thm)],[f_209_2]) ).

cnf(f_209_4,plain,
    ( hBOOL(hAPP(U_570,bool,hAPP(U_570,fun(U_570,bool),ord_less_eq(U_570),U_569),U_568))
    | ti(U_570,U_569) != ti(U_570,U_568)
    | hBOOL(hAPP(U_570,bool,hAPP(U_570,fun(U_570,bool),ord_less(U_570),U_569),U_568))
    | ~ linorder(U_570) ),
    inference(clausify,[status(thm)],[f_209_2]) ).

fof(f_210_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
          | ti(X_a,A_2) = ti(X_a,B_1) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_120_order__neq__le__trans]) ).

fof(f_210_2,plain,
    ! [U_573] :
      ( ! [U_572,U_571] :
          ( hBOOL(hAPP(U_573,bool,hAPP(U_573,fun(U_573,bool),ord_less(U_573),U_572),U_571))
          | ~ hBOOL(hAPP(U_573,bool,hAPP(U_573,fun(U_573,bool),ord_less_eq(U_573),U_572),U_571))
          | ti(U_573,U_572) = ti(U_573,U_571) )
      | ~ order(U_573) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

cnf(f_210_3,plain,
    ( hBOOL(hAPP(U_573,bool,hAPP(U_573,fun(U_573,bool),ord_less(U_573),U_572),U_571))
    | ~ hBOOL(hAPP(U_573,bool,hAPP(U_573,fun(U_573,bool),ord_less_eq(U_573),U_572),U_571))
    | ti(U_573,U_572) = ti(U_573,U_571)
    | ~ order(U_573) ),
    inference(clausify,[status(thm)],[f_210_2]) ).

fof(f_211_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
          | ti(X_a,A_2) = ti(X_a,B_1) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_121_xt1_I12_J]) ).

fof(f_211_2,plain,
    ! [U_576] :
      ( ! [U_575,U_574] :
          ( hBOOL(hAPP(U_576,bool,hAPP(U_576,fun(U_576,bool),ord_less(U_576),U_574),U_575))
          | ~ hBOOL(hAPP(U_576,bool,hAPP(U_576,fun(U_576,bool),ord_less_eq(U_576),U_574),U_575))
          | ti(U_576,U_575) = ti(U_576,U_574) )
      | ~ order(U_576) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

cnf(f_211_3,plain,
    ( hBOOL(hAPP(U_576,bool,hAPP(U_576,fun(U_576,bool),ord_less(U_576),U_574),U_575))
    | ~ hBOOL(hAPP(U_576,bool,hAPP(U_576,fun(U_576,bool),ord_less_eq(U_576),U_574),U_575))
    | ti(U_576,U_575) = ti(U_576,U_574)
    | ~ order(U_576) ),
    inference(clausify,[status(thm)],[f_211_2]) ).

fof(f_212_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_122_leD]) ).

fof(f_212_2,plain,
    ! [U_579] :
      ( ! [U_578,U_577] :
          ( ~ hBOOL(hAPP(U_579,bool,hAPP(U_579,fun(U_579,bool),ord_less(U_579),U_577),U_578))
          | ~ hBOOL(hAPP(U_579,bool,hAPP(U_579,fun(U_579,bool),ord_less_eq(U_579),U_578),U_577)) )
      | ~ linorder(U_579) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

cnf(f_212_3,plain,
    ( ~ hBOOL(hAPP(U_579,bool,hAPP(U_579,fun(U_579,bool),ord_less(U_579),U_577),U_578))
    | ~ hBOOL(hAPP(U_579,bool,hAPP(U_579,fun(U_579,bool),ord_less_eq(U_579),U_578),U_577))
    | ~ linorder(U_579) ),
    inference(clausify,[status(thm)],[f_212_2]) ).

fof(f_213_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_123_order__less__imp__le]) ).

fof(f_213_2,plain,
    ! [U_582] :
      ( ! [U_581,U_580] :
          ( hBOOL(hAPP(U_582,bool,hAPP(U_582,fun(U_582,bool),ord_less_eq(U_582),U_581),U_580))
          | ~ hBOOL(hAPP(U_582,bool,hAPP(U_582,fun(U_582,bool),ord_less(U_582),U_581),U_580)) )
      | ~ preorder(U_582) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

cnf(f_213_3,plain,
    ( hBOOL(hAPP(U_582,bool,hAPP(U_582,fun(U_582,bool),ord_less_eq(U_582),U_581),U_580))
    | ~ hBOOL(hAPP(U_582,bool,hAPP(U_582,fun(U_582,bool),ord_less(U_582),U_581),U_580))
    | ~ preorder(U_582) ),
    inference(clausify,[status(thm)],[f_213_2]) ).

fof(f_214_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
              | ti(X_a,X_2) != ti(X_a,Y_1) )
            & ( ti(X_a,X_2) = ti(X_a,Y_1)
              | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_124_linorder__antisym__conv2]) ).

fof(f_214_2,plain,
    ! [U_585] :
      ( ! [U_584,U_583] :
          ( ( ( ~ hBOOL(hAPP(U_585,bool,hAPP(U_585,fun(U_585,bool),ord_less(U_585),U_584),U_583))
              | ti(U_585,U_584) != ti(U_585,U_583) )
            & ( ti(U_585,U_584) = ti(U_585,U_583)
              | hBOOL(hAPP(U_585,bool,hAPP(U_585,fun(U_585,bool),ord_less(U_585),U_584),U_583)) ) )
          | ~ hBOOL(hAPP(U_585,bool,hAPP(U_585,fun(U_585,bool),ord_less_eq(U_585),U_584),U_583)) )
      | ~ linorder(U_585) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

cnf(f_214_3,plain,
    ( ti(U_585,U_584) = ti(U_585,U_583)
    | hBOOL(hAPP(U_585,bool,hAPP(U_585,fun(U_585,bool),ord_less(U_585),U_584),U_583))
    | ~ hBOOL(hAPP(U_585,bool,hAPP(U_585,fun(U_585,bool),ord_less_eq(U_585),U_584),U_583))
    | ~ linorder(U_585) ),
    inference(clausify,[status(thm)],[f_214_2]) ).

cnf(f_214_4,plain,
    ( ~ hBOOL(hAPP(U_585,bool,hAPP(U_585,fun(U_585,bool),ord_less(U_585),U_584),U_583))
    | ti(U_585,U_584) != ti(U_585,U_583)
    | ~ hBOOL(hAPP(U_585,bool,hAPP(U_585,fun(U_585,bool),ord_less_eq(U_585),U_584),U_583))
    | ~ linorder(U_585) ),
    inference(clausify,[status(thm)],[f_214_2]) ).

fof(f_215_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ti(X_a,X) = ti(X_a,Y)
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_125_order__le__imp__less__or__eq]) ).

fof(f_215_2,plain,
    ! [U_588] :
      ( ! [U_587,U_586] :
          ( ti(U_588,U_587) = ti(U_588,U_586)
          | hBOOL(hAPP(U_588,bool,hAPP(U_588,fun(U_588,bool),ord_less(U_588),U_587),U_586))
          | ~ hBOOL(hAPP(U_588,bool,hAPP(U_588,fun(U_588,bool),ord_less_eq(U_588),U_587),U_586)) )
      | ~ order(U_588) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

cnf(f_215_3,plain,
    ( ti(U_588,U_587) = ti(U_588,U_586)
    | hBOOL(hAPP(U_588,bool,hAPP(U_588,fun(U_588,bool),ord_less(U_588),U_587),U_586))
    | ~ hBOOL(hAPP(U_588,bool,hAPP(U_588,fun(U_588,bool),ord_less_eq(U_588),U_587),U_586))
    | ~ order(U_588) ),
    inference(clausify,[status(thm)],[f_215_2]) ).

fof(f_216_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
          | ti(X_a,A_2) = ti(X_a,B_1)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_126_order__le__neq__trans]) ).

fof(f_216_2,plain,
    ! [U_591] :
      ( ! [U_590,U_589] :
          ( hBOOL(hAPP(U_591,bool,hAPP(U_591,fun(U_591,bool),ord_less(U_591),U_590),U_589))
          | ti(U_591,U_590) = ti(U_591,U_589)
          | ~ hBOOL(hAPP(U_591,bool,hAPP(U_591,fun(U_591,bool),ord_less_eq(U_591),U_590),U_589)) )
      | ~ order(U_591) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

cnf(f_216_3,plain,
    ( hBOOL(hAPP(U_591,bool,hAPP(U_591,fun(U_591,bool),ord_less(U_591),U_590),U_589))
    | ti(U_591,U_590) = ti(U_591,U_589)
    | ~ hBOOL(hAPP(U_591,bool,hAPP(U_591,fun(U_591,bool),ord_less_eq(U_591),U_590),U_589))
    | ~ order(U_591) ),
    inference(clausify,[status(thm)],[f_216_2]) ).

fof(f_217_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))
          | ti(X_a,A_2) = ti(X_a,B_1)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_127_xt1_I11_J]) ).

fof(f_217_2,plain,
    ! [U_594] :
      ( ! [U_593,U_592] :
          ( hBOOL(hAPP(U_594,bool,hAPP(U_594,fun(U_594,bool),ord_less(U_594),U_593),U_592))
          | ti(U_594,U_592) = ti(U_594,U_593)
          | ~ hBOOL(hAPP(U_594,bool,hAPP(U_594,fun(U_594,bool),ord_less_eq(U_594),U_593),U_592)) )
      | ~ order(U_594) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

cnf(f_217_3,plain,
    ( hBOOL(hAPP(U_594,bool,hAPP(U_594,fun(U_594,bool),ord_less(U_594),U_593),U_592))
    | ti(U_594,U_592) = ti(U_594,U_593)
    | ~ hBOOL(hAPP(U_594,bool,hAPP(U_594,fun(U_594,bool),ord_less_eq(U_594),U_593),U_592))
    | ~ order(U_594) ),
    inference(clausify,[status(thm)],[f_217_2]) ).

fof(f_218_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_128_order__less__le__trans]) ).

fof(f_218_2,plain,
    ! [U_598] :
      ( ! [U_597,U_596,U_595] :
          ( hBOOL(hAPP(U_598,bool,hAPP(U_598,fun(U_598,bool),ord_less(U_598),U_596),U_597))
          | ~ hBOOL(hAPP(U_598,bool,hAPP(U_598,fun(U_598,bool),ord_less_eq(U_598),U_595),U_597))
          | ~ hBOOL(hAPP(U_598,bool,hAPP(U_598,fun(U_598,bool),ord_less(U_598),U_596),U_595)) )
      | ~ preorder(U_598) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

cnf(f_218_3,plain,
    ( hBOOL(hAPP(U_598,bool,hAPP(U_598,fun(U_598,bool),ord_less(U_598),U_596),U_597))
    | ~ hBOOL(hAPP(U_598,bool,hAPP(U_598,fun(U_598,bool),ord_less_eq(U_598),U_595),U_597))
    | ~ hBOOL(hAPP(U_598,bool,hAPP(U_598,fun(U_598,bool),ord_less(U_598),U_596),U_595))
    | ~ preorder(U_598) ),
    inference(clausify,[status(thm)],[f_218_2]) ).

fof(f_219_1,plain,
    ! [X_a] :
      ( ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_129_xt1_I7_J]) ).

fof(f_219_2,plain,
    ! [U_602] :
      ( ! [U_601,U_600,U_599] :
          ( hBOOL(hAPP(U_602,bool,hAPP(U_602,fun(U_602,bool),ord_less(U_602),U_601),U_599))
          | ~ hBOOL(hAPP(U_602,bool,hAPP(U_602,fun(U_602,bool),ord_less_eq(U_602),U_601),U_600))
          | ~ hBOOL(hAPP(U_602,bool,hAPP(U_602,fun(U_602,bool),ord_less(U_602),U_600),U_599)) )
      | ~ order(U_602) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

cnf(f_219_3,plain,
    ( hBOOL(hAPP(U_602,bool,hAPP(U_602,fun(U_602,bool),ord_less(U_602),U_601),U_599))
    | ~ hBOOL(hAPP(U_602,bool,hAPP(U_602,fun(U_602,bool),ord_less_eq(U_602),U_601),U_600))
    | ~ hBOOL(hAPP(U_602,bool,hAPP(U_602,fun(U_602,bool),ord_less(U_602),U_600),U_599))
    | ~ order(U_602) ),
    inference(clausify,[status(thm)],[f_219_2]) ).

fof(f_220_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_130_order__le__less__trans]) ).

fof(f_220_2,plain,
    ! [U_606] :
      ( ! [U_605,U_604,U_603] :
          ( hBOOL(hAPP(U_606,bool,hAPP(U_606,fun(U_606,bool),ord_less(U_606),U_604),U_605))
          | ~ hBOOL(hAPP(U_606,bool,hAPP(U_606,fun(U_606,bool),ord_less(U_606),U_603),U_605))
          | ~ hBOOL(hAPP(U_606,bool,hAPP(U_606,fun(U_606,bool),ord_less_eq(U_606),U_604),U_603)) )
      | ~ preorder(U_606) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

cnf(f_220_3,plain,
    ( hBOOL(hAPP(U_606,bool,hAPP(U_606,fun(U_606,bool),ord_less(U_606),U_604),U_605))
    | ~ hBOOL(hAPP(U_606,bool,hAPP(U_606,fun(U_606,bool),ord_less(U_606),U_603),U_605))
    | ~ hBOOL(hAPP(U_606,bool,hAPP(U_606,fun(U_606,bool),ord_less_eq(U_606),U_604),U_603))
    | ~ preorder(U_606) ),
    inference(clausify,[status(thm)],[f_220_2]) ).

fof(f_221_1,plain,
    ! [X_a] :
      ( ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_131_xt1_I8_J]) ).

fof(f_221_2,plain,
    ! [U_610] :
      ( ! [U_609,U_608,U_607] :
          ( hBOOL(hAPP(U_610,bool,hAPP(U_610,fun(U_610,bool),ord_less(U_610),U_609),U_607))
          | ~ hBOOL(hAPP(U_610,bool,hAPP(U_610,fun(U_610,bool),ord_less(U_610),U_609),U_608))
          | ~ hBOOL(hAPP(U_610,bool,hAPP(U_610,fun(U_610,bool),ord_less_eq(U_610),U_608),U_607)) )
      | ~ order(U_610) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

cnf(f_221_3,plain,
    ( hBOOL(hAPP(U_610,bool,hAPP(U_610,fun(U_610,bool),ord_less(U_610),U_609),U_607))
    | ~ hBOOL(hAPP(U_610,bool,hAPP(U_610,fun(U_610,bool),ord_less(U_610),U_609),U_608))
    | ~ hBOOL(hAPP(U_610,bool,hAPP(U_610,fun(U_610,bool),ord_less_eq(U_610),U_608),U_607))
    | ~ order(U_610) ),
    inference(clausify,[status(thm)],[f_221_2]) ).

fof(f_222_1,plain,
    ! [X_a] :
      ( ! [A_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),top_top(X_a)))
      | ~ top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_132_top__greatest]) ).

fof(f_222_2,plain,
    ! [U_612] :
      ( ! [U_611] : hBOOL(hAPP(U_612,bool,hAPP(U_612,fun(U_612,bool),ord_less_eq(U_612),U_611),top_top(U_612)))
      | ~ top(U_612) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

cnf(f_222_3,plain,
    ( hBOOL(hAPP(U_612,bool,hAPP(U_612,fun(U_612,bool),ord_less_eq(U_612),U_611),top_top(U_612)))
    | ~ top(U_612) ),
    inference(clausify,[status(thm)],[f_222_2]) ).

fof(f_223_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),Aa))
            | ti(X_a,Aa) != top_top(X_a) )
          & ( ti(X_a,Aa) = top_top(X_a)
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),Aa)) ) )
      | ~ top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_133_top__unique]) ).

fof(f_223_2,plain,
    ! [U_614] :
      ( ! [U_613] :
          ( ( hBOOL(hAPP(U_614,bool,hAPP(U_614,fun(U_614,bool),ord_less_eq(U_614),top_top(U_614)),U_613))
            | ti(U_614,U_613) != top_top(U_614) )
          & ( ti(U_614,U_613) = top_top(U_614)
            | ~ hBOOL(hAPP(U_614,bool,hAPP(U_614,fun(U_614,bool),ord_less_eq(U_614),top_top(U_614)),U_613)) ) )
      | ~ top(U_614) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ! [U_614] :
      ( ( ! [U_616] :
            ( hBOOL(hAPP(U_614,bool,hAPP(U_614,fun(U_614,bool),ord_less_eq(U_614),top_top(U_614)),U_616))
            | ti(U_614,U_616) != top_top(U_614) )
        & ! [U_615] :
            ( ti(U_614,U_615) = top_top(U_614)
            | ~ hBOOL(hAPP(U_614,bool,hAPP(U_614,fun(U_614,bool),ord_less_eq(U_614),top_top(U_614)),U_615)) ) )
      | ~ top(U_614) ),
    inference(miniscope,[status(thm)],[f_223_2]) ).

cnf(f_223_4,plain,
    ( ti(U_614,U_615) = top_top(U_614)
    | ~ hBOOL(hAPP(U_614,bool,hAPP(U_614,fun(U_614,bool),ord_less_eq(U_614),top_top(U_614)),U_615))
    | ~ top(U_614) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_5,plain,
    ( hBOOL(hAPP(U_614,bool,hAPP(U_614,fun(U_614,bool),ord_less_eq(U_614),top_top(U_614)),U_616))
    | ti(U_614,U_616) != top_top(U_614)
    | ~ top(U_614) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

fof(f_224_1,plain,
    ! [X_a] :
      ( ! [A_2] :
          ( ti(X_a,A_2) = top_top(X_a)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),A_2)) )
      | ~ top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_134_top__le]) ).

fof(f_224_2,plain,
    ! [U_618] :
      ( ! [U_617] :
          ( ti(U_618,U_617) = top_top(U_618)
          | ~ hBOOL(hAPP(U_618,bool,hAPP(U_618,fun(U_618,bool),ord_less_eq(U_618),top_top(U_618)),U_617)) )
      | ~ top(U_618) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

cnf(f_224_3,plain,
    ( ti(U_618,U_617) = top_top(U_618)
    | ~ hBOOL(hAPP(U_618,bool,hAPP(U_618,fun(U_618,bool),ord_less_eq(U_618),top_top(U_618)),U_617))
    | ~ top(U_618) ),
    inference(clausify,[status(thm)],[f_224_2]) ).

fof(f_225_1,plain,
    ! [X_a,X_b,F,A_1] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
        | ? [X_1] :
            ( ? [Xa] :
                ( ti(X_a,X_1) != ti(X_a,Xa)
                & hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Xa)
                & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) )
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) )
      & ( ! [X_1] :
            ( ! [Xa] :
                ( ti(X_a,X_1) = ti(X_a,Xa)
                | hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,F,Xa)
                | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) )
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) )
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_135_inj__on__def]) ).

fof(f_225_2,plain,
    ! [U_626,U_625,U_624,U_623] :
      ( ( hBOOL(hAPP(fun(U_626,bool),bool,hAPP(fun(U_626,U_625),fun(fun(U_626,bool),bool),inj_on(U_626,U_625),U_624),U_623))
        | ? [U_622] :
            ( ? [U_621] :
                ( ti(U_626,U_622) != ti(U_626,U_621)
                & hAPP(U_626,U_625,U_624,U_622) = hAPP(U_626,U_625,U_624,U_621)
                & hBOOL(hAPP(fun(U_626,bool),bool,hAPP(U_626,fun(fun(U_626,bool),bool),member(U_626),U_621),U_623)) )
            & hBOOL(hAPP(fun(U_626,bool),bool,hAPP(U_626,fun(fun(U_626,bool),bool),member(U_626),U_622),U_623)) ) )
      & ( ! [U_620] :
            ( ! [U_619] :
                ( ti(U_626,U_620) = ti(U_626,U_619)
                | hAPP(U_626,U_625,U_624,U_620) != hAPP(U_626,U_625,U_624,U_619)
                | ~ hBOOL(hAPP(fun(U_626,bool),bool,hAPP(U_626,fun(fun(U_626,bool),bool),member(U_626),U_619),U_623)) )
            | ~ hBOOL(hAPP(fun(U_626,bool),bool,hAPP(U_626,fun(fun(U_626,bool),bool),member(U_626),U_620),U_623)) )
        | ~ hBOOL(hAPP(fun(U_626,bool),bool,hAPP(fun(U_626,U_625),fun(fun(U_626,bool),bool),inj_on(U_626,U_625),U_624),U_623)) ) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ( ! [U_634,U_632,U_630,U_628] :
        ( hBOOL(hAPP(fun(U_634,bool),bool,hAPP(fun(U_634,U_632),fun(fun(U_634,bool),bool),inj_on(U_634,U_632),U_630),U_628))
        | ? [U_622] :
            ( ? [U_621] :
                ( ti(U_634,U_622) != ti(U_634,U_621)
                & hAPP(U_634,U_632,U_630,U_622) = hAPP(U_634,U_632,U_630,U_621)
                & hBOOL(hAPP(fun(U_634,bool),bool,hAPP(U_634,fun(fun(U_634,bool),bool),member(U_634),U_621),U_628)) )
            & hBOOL(hAPP(fun(U_634,bool),bool,hAPP(U_634,fun(fun(U_634,bool),bool),member(U_634),U_622),U_628)) ) )
    & ! [U_633,U_631,U_629,U_627] :
        ( ! [U_620] :
            ( ! [U_619] :
                ( ti(U_633,U_620) = ti(U_633,U_619)
                | hAPP(U_633,U_631,U_629,U_620) != hAPP(U_633,U_631,U_629,U_619)
                | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(U_633,fun(fun(U_633,bool),bool),member(U_633),U_619),U_627)) )
            | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(U_633,fun(fun(U_633,bool),bool),member(U_633),U_620),U_627)) )
        | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(fun(U_633,U_631),fun(fun(U_633,bool),bool),inj_on(U_633,U_631),U_629),U_627)) ) ),
    inference(miniscope,[status(thm)],[f_225_2]) ).

fof(f_225_4,plain,
    ( ! [U_634,U_632,U_630,U_628] :
        ( hBOOL(hAPP(fun(U_634,bool),bool,hAPP(fun(U_634,U_632),fun(fun(U_634,bool),bool),inj_on(U_634,U_632),U_630),U_628))
        | ( ? [U_621] :
              ( ti(U_634,sK39(U_634,U_632,U_630,U_628)) != ti(U_634,U_621)
              & hAPP(U_634,U_632,U_630,sK39(U_634,U_632,U_630,U_628)) = hAPP(U_634,U_632,U_630,U_621)
              & hBOOL(hAPP(fun(U_634,bool),bool,hAPP(U_634,fun(fun(U_634,bool),bool),member(U_634),U_621),U_628)) )
          & hBOOL(hAPP(fun(U_634,bool),bool,hAPP(U_634,fun(fun(U_634,bool),bool),member(U_634),sK39(U_634,U_632,U_630,U_628)),U_628)) ) )
    & ! [U_633,U_631,U_629,U_627] :
        ( ! [U_620] :
            ( ! [U_619] :
                ( ti(U_633,U_620) = ti(U_633,U_619)
                | hAPP(U_633,U_631,U_629,U_620) != hAPP(U_633,U_631,U_629,U_619)
                | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(U_633,fun(fun(U_633,bool),bool),member(U_633),U_619),U_627)) )
            | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(U_633,fun(fun(U_633,bool),bool),member(U_633),U_620),U_627)) )
        | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(fun(U_633,U_631),fun(fun(U_633,bool),bool),inj_on(U_633,U_631),U_629),U_627)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_622,sK39(U_634,U_632,U_630,U_628))],[f_225_3]) ).

fof(f_225_5,plain,
    ( ! [U_634,U_632,U_630,U_628] :
        ( hBOOL(hAPP(fun(U_634,bool),bool,hAPP(fun(U_634,U_632),fun(fun(U_634,bool),bool),inj_on(U_634,U_632),U_630),U_628))
        | ( ti(U_634,sK39(U_634,U_632,U_630,U_628)) != ti(U_634,sK40(U_634,U_632,U_630,U_628))
          & hAPP(U_634,U_632,U_630,sK39(U_634,U_632,U_630,U_628)) = hAPP(U_634,U_632,U_630,sK40(U_634,U_632,U_630,U_628))
          & hBOOL(hAPP(fun(U_634,bool),bool,hAPP(U_634,fun(fun(U_634,bool),bool),member(U_634),sK40(U_634,U_632,U_630,U_628)),U_628))
          & hBOOL(hAPP(fun(U_634,bool),bool,hAPP(U_634,fun(fun(U_634,bool),bool),member(U_634),sK39(U_634,U_632,U_630,U_628)),U_628)) ) )
    & ! [U_633,U_631,U_629,U_627] :
        ( ! [U_620] :
            ( ! [U_619] :
                ( ti(U_633,U_620) = ti(U_633,U_619)
                | hAPP(U_633,U_631,U_629,U_620) != hAPP(U_633,U_631,U_629,U_619)
                | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(U_633,fun(fun(U_633,bool),bool),member(U_633),U_619),U_627)) )
            | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(U_633,fun(fun(U_633,bool),bool),member(U_633),U_620),U_627)) )
        | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(fun(U_633,U_631),fun(fun(U_633,bool),bool),inj_on(U_633,U_631),U_629),U_627)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_621,sK40(U_634,U_632,U_630,U_628))],[f_225_4]) ).

cnf(f_225_6,plain,
    ( ti(U_633,U_620) = ti(U_633,U_619)
    | hAPP(U_633,U_631,U_629,U_620) != hAPP(U_633,U_631,U_629,U_619)
    | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(U_633,fun(fun(U_633,bool),bool),member(U_633),U_619),U_627))
    | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(U_633,fun(fun(U_633,bool),bool),member(U_633),U_620),U_627))
    | ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(fun(U_633,U_631),fun(fun(U_633,bool),bool),inj_on(U_633,U_631),U_629),U_627)) ),
    inference(clausify,[status(thm)],[f_225_5]) ).

cnf(f_225_7,plain,
    ( hBOOL(hAPP(fun(U_634,bool),bool,hAPP(U_634,fun(fun(U_634,bool),bool),member(U_634),sK39(U_634,U_632,U_630,U_628)),U_628))
    | hBOOL(hAPP(fun(U_634,bool),bool,hAPP(fun(U_634,U_632),fun(fun(U_634,bool),bool),inj_on(U_634,U_632),U_630),U_628)) ),
    inference(clausify,[status(thm)],[f_225_5]) ).

cnf(f_225_8,plain,
    ( hBOOL(hAPP(fun(U_634,bool),bool,hAPP(U_634,fun(fun(U_634,bool),bool),member(U_634),sK40(U_634,U_632,U_630,U_628)),U_628))
    | hBOOL(hAPP(fun(U_634,bool),bool,hAPP(fun(U_634,U_632),fun(fun(U_634,bool),bool),inj_on(U_634,U_632),U_630),U_628)) ),
    inference(clausify,[status(thm)],[f_225_5]) ).

cnf(f_225_9,plain,
    ( hAPP(U_634,U_632,U_630,sK39(U_634,U_632,U_630,U_628)) = hAPP(U_634,U_632,U_630,sK40(U_634,U_632,U_630,U_628))
    | hBOOL(hAPP(fun(U_634,bool),bool,hAPP(fun(U_634,U_632),fun(fun(U_634,bool),bool),inj_on(U_634,U_632),U_630),U_628)) ),
    inference(clausify,[status(thm)],[f_225_5]) ).

cnf(f_225_10,plain,
    ( ti(U_634,sK39(U_634,U_632,U_630,U_628)) != ti(U_634,sK40(U_634,U_632,U_630,U_628))
    | hBOOL(hAPP(fun(U_634,bool),bool,hAPP(fun(U_634,U_632),fun(fun(U_634,bool),bool),inj_on(U_634,U_632),U_630),U_628)) ),
    inference(clausify,[status(thm)],[f_225_5]) ).

fof(f_226_1,plain,
    ! [X_a,X_b,X_2,Y_1,F,A_1] :
      ( hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | ti(X_a,X_2) = ti(X_a,Y_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_136_inj__on__contraD]) ).

fof(f_226_2,plain,
    ! [U_640,U_639,U_638,U_637,U_636,U_635] :
      ( hAPP(U_640,U_639,U_636,U_638) != hAPP(U_640,U_639,U_636,U_637)
      | ~ hBOOL(hAPP(fun(U_640,bool),bool,hAPP(U_640,fun(fun(U_640,bool),bool),member(U_640),U_637),U_635))
      | ~ hBOOL(hAPP(fun(U_640,bool),bool,hAPP(U_640,fun(fun(U_640,bool),bool),member(U_640),U_638),U_635))
      | ti(U_640,U_638) = ti(U_640,U_637)
      | ~ hBOOL(hAPP(fun(U_640,bool),bool,hAPP(fun(U_640,U_639),fun(fun(U_640,bool),bool),inj_on(U_640,U_639),U_636),U_635)) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

cnf(f_226_3,plain,
    ( hAPP(U_640,U_639,U_636,U_638) != hAPP(U_640,U_639,U_636,U_637)
    | ~ hBOOL(hAPP(fun(U_640,bool),bool,hAPP(U_640,fun(fun(U_640,bool),bool),member(U_640),U_637),U_635))
    | ~ hBOOL(hAPP(fun(U_640,bool),bool,hAPP(U_640,fun(fun(U_640,bool),bool),member(U_640),U_638),U_635))
    | ti(U_640,U_638) = ti(U_640,U_637)
    | ~ hBOOL(hAPP(fun(U_640,bool),bool,hAPP(fun(U_640,U_639),fun(fun(U_640,bool),bool),inj_on(U_640,U_639),U_636),U_635)) ),
    inference(clausify,[status(thm)],[f_226_2]) ).

fof(f_227_1,plain,
    ! [X_a,X_b,Y_1,X_2,F,A_1] :
      ( ( ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
          | ti(X_a,X_2) != ti(X_a,Y_1) )
        & ( ti(X_a,X_2) = ti(X_a,Y_1)
          | hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_137_inj__on__iff]) ).

fof(f_227_2,plain,
    ! [U_646,U_645,U_644,U_643,U_642,U_641] :
      ( ( ( hAPP(U_646,U_645,U_642,U_643) = hAPP(U_646,U_645,U_642,U_644)
          | ti(U_646,U_643) != ti(U_646,U_644) )
        & ( ti(U_646,U_643) = ti(U_646,U_644)
          | hAPP(U_646,U_645,U_642,U_643) != hAPP(U_646,U_645,U_642,U_644) ) )
      | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(U_646,fun(fun(U_646,bool),bool),member(U_646),U_644),U_641))
      | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(U_646,fun(fun(U_646,bool),bool),member(U_646),U_643),U_641))
      | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(fun(U_646,U_645),fun(fun(U_646,bool),bool),inj_on(U_646,U_645),U_642),U_641)) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

cnf(f_227_3,plain,
    ( ti(U_646,U_643) = ti(U_646,U_644)
    | hAPP(U_646,U_645,U_642,U_643) != hAPP(U_646,U_645,U_642,U_644)
    | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(U_646,fun(fun(U_646,bool),bool),member(U_646),U_644),U_641))
    | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(U_646,fun(fun(U_646,bool),bool),member(U_646),U_643),U_641))
    | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(fun(U_646,U_645),fun(fun(U_646,bool),bool),inj_on(U_646,U_645),U_642),U_641)) ),
    inference(clausify,[status(thm)],[f_227_2]) ).

cnf(f_227_4,plain,
    ( hAPP(U_646,U_645,U_642,U_643) = hAPP(U_646,U_645,U_642,U_644)
    | ti(U_646,U_643) != ti(U_646,U_644)
    | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(U_646,fun(fun(U_646,bool),bool),member(U_646),U_644),U_641))
    | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(U_646,fun(fun(U_646,bool),bool),member(U_646),U_643),U_641))
    | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(fun(U_646,U_645),fun(fun(U_646,bool),bool),inj_on(U_646,U_645),U_642),U_641)) ),
    inference(clausify,[status(thm)],[f_227_2]) ).

fof(f_228_1,plain,
    ! [X_a,X_b,X_2,Y_1,F,A_1] :
      ( ti(X_a,X_2) = ti(X_a,Y_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_138_inj__onD]) ).

fof(f_228_2,plain,
    ! [U_652,U_651,U_650,U_649,U_648,U_647] :
      ( ti(U_652,U_650) = ti(U_652,U_649)
      | ~ hBOOL(hAPP(fun(U_652,bool),bool,hAPP(U_652,fun(fun(U_652,bool),bool),member(U_652),U_649),U_647))
      | ~ hBOOL(hAPP(fun(U_652,bool),bool,hAPP(U_652,fun(fun(U_652,bool),bool),member(U_652),U_650),U_647))
      | hAPP(U_652,U_651,U_648,U_650) != hAPP(U_652,U_651,U_648,U_649)
      | ~ hBOOL(hAPP(fun(U_652,bool),bool,hAPP(fun(U_652,U_651),fun(fun(U_652,bool),bool),inj_on(U_652,U_651),U_648),U_647)) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

cnf(f_228_3,plain,
    ( ti(U_652,U_650) = ti(U_652,U_649)
    | ~ hBOOL(hAPP(fun(U_652,bool),bool,hAPP(U_652,fun(fun(U_652,bool),bool),member(U_652),U_649),U_647))
    | ~ hBOOL(hAPP(fun(U_652,bool),bool,hAPP(U_652,fun(fun(U_652,bool),bool),member(U_652),U_650),U_647))
    | hAPP(U_652,U_651,U_648,U_650) != hAPP(U_652,U_651,U_648,U_649)
    | ~ hBOOL(hAPP(fun(U_652,bool),bool,hAPP(fun(U_652,U_651),fun(fun(U_652,bool),bool),inj_on(U_652,U_651),U_648),U_647)) ),
    inference(clausify,[status(thm)],[f_228_2]) ).

fof(f_229_1,plain,
    ! [X_a,X_b,X_2,F,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ),
    inference(fof_nnf,[status(thm)],[fact_139_Pi__mem]) ).

fof(f_229_2,plain,
    ! [U_658,U_657,U_656,U_655,U_654,U_653] :
      ( hBOOL(hAPP(fun(U_657,bool),bool,hAPP(U_657,fun(fun(U_657,bool),bool),member(U_657),hAPP(U_658,U_657,U_655,U_656)),hAPP(U_658,fun(U_657,bool),U_653,U_656)))
      | ~ hBOOL(hAPP(fun(U_658,bool),bool,hAPP(U_658,fun(fun(U_658,bool),bool),member(U_658),U_656),U_654))
      | ~ hBOOL(hAPP(fun(fun(U_658,U_657),bool),bool,hAPP(fun(U_658,U_657),fun(fun(fun(U_658,U_657),bool),bool),member(fun(U_658,U_657)),U_655),hAPP(fun(U_658,fun(U_657,bool)),fun(fun(U_658,U_657),bool),hAPP(fun(U_658,bool),fun(fun(U_658,fun(U_657,bool)),fun(fun(U_658,U_657),bool)),pi(U_658,U_657),U_654),U_653))) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

cnf(f_229_3,plain,
    ( hBOOL(hAPP(fun(U_657,bool),bool,hAPP(U_657,fun(fun(U_657,bool),bool),member(U_657),hAPP(U_658,U_657,U_655,U_656)),hAPP(U_658,fun(U_657,bool),U_653,U_656)))
    | ~ hBOOL(hAPP(fun(U_658,bool),bool,hAPP(U_658,fun(fun(U_658,bool),bool),member(U_658),U_656),U_654))
    | ~ hBOOL(hAPP(fun(fun(U_658,U_657),bool),bool,hAPP(fun(U_658,U_657),fun(fun(fun(U_658,U_657),bool),bool),member(fun(U_658,U_657)),U_655),hAPP(fun(U_658,fun(U_657,bool)),fun(fun(U_658,U_657),bool),hAPP(fun(U_658,bool),fun(fun(U_658,fun(U_657,bool)),fun(fun(U_658,U_657),bool)),pi(U_658,U_657),U_654),U_653))) ),
    inference(clausify,[status(thm)],[f_229_2]) ).

fof(f_230_1,plain,
    ! [L_3,X_2,Y_1] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,L_3),X_2),Y_1)),arrow_1568854078le_Lin))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_3),arrow_1568854078le_Lin))
      | ti(arrow_2142409994le_alt,X_2) = ti(arrow_2142409994le_alt,Y_1) ),
    inference(fof_nnf,[status(thm)],[fact_140_below__Lin]) ).

fof(f_230_2,plain,
    ! [U_661,U_660,U_659] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_661),U_660),U_659)),arrow_1568854078le_Lin))
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_661),arrow_1568854078le_Lin))
      | ti(arrow_2142409994le_alt,U_660) = ti(arrow_2142409994le_alt,U_659) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

cnf(f_230_3,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,U_661),U_660),U_659)),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_661),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,U_660) = ti(arrow_2142409994le_alt,U_659) ),
    inference(clausify,[status(thm)],[f_230_2]) ).

fof(f_231_1,plain,
    arrow_301600364e_Prof = hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)),
    inference(fof_nnf,[status(thm)],[fact_141_Prof__def]) ).

cnf(f_231_2,plain,
    arrow_301600364e_Prof = hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)),
    inference(clausify,[status(thm)],[f_231_1]) ).

fof(f_232_1,plain,
    ! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),combi(X_a)),A_1)),
    inference(fof_nnf,[status(thm)],[fact_142_inj__on__id2]) ).

fof(f_232_2,plain,
    ! [U_663,U_662] : hBOOL(hAPP(fun(U_663,bool),bool,hAPP(fun(U_663,U_663),fun(fun(U_663,bool),bool),inj_on(U_663,U_663),combi(U_663)),U_662)),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

cnf(f_232_3,plain,
    hBOOL(hAPP(fun(U_663,bool),bool,hAPP(fun(U_663,U_663),fun(fun(U_663,bool),bool),inj_on(U_663,U_663),combi(U_663)),U_662)),
    inference(clausify,[status(thm)],[f_232_2]) ).

fof(f_233_1,plain,
    ! [X_a,X_b,X_2,F,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
    inference(fof_nnf,[status(thm)],[fact_143_funcset__mem]) ).

fof(f_233_2,plain,
    ! [U_669,U_668,U_667,U_666,U_665,U_664] :
      ( hBOOL(hAPP(fun(U_668,bool),bool,hAPP(U_668,fun(fun(U_668,bool),bool),member(U_668),hAPP(U_669,U_668,U_666,U_667)),U_664))
      | ~ hBOOL(hAPP(fun(U_669,bool),bool,hAPP(U_669,fun(fun(U_669,bool),bool),member(U_669),U_667),U_665))
      | ~ hBOOL(hAPP(fun(fun(U_669,U_668),bool),bool,hAPP(fun(U_669,U_668),fun(fun(fun(U_669,U_668),bool),bool),member(fun(U_669,U_668)),U_666),hAPP(fun(U_669,fun(U_668,bool)),fun(fun(U_669,U_668),bool),hAPP(fun(U_669,bool),fun(fun(U_669,fun(U_668,bool)),fun(fun(U_669,U_668),bool)),pi(U_669,U_668),U_665),hAPP(fun(U_668,bool),fun(U_669,fun(U_668,bool)),combk(fun(U_668,bool),U_669),U_664)))) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

cnf(f_233_3,plain,
    ( hBOOL(hAPP(fun(U_668,bool),bool,hAPP(U_668,fun(fun(U_668,bool),bool),member(U_668),hAPP(U_669,U_668,U_666,U_667)),U_664))
    | ~ hBOOL(hAPP(fun(U_669,bool),bool,hAPP(U_669,fun(fun(U_669,bool),bool),member(U_669),U_667),U_665))
    | ~ hBOOL(hAPP(fun(fun(U_669,U_668),bool),bool,hAPP(fun(U_669,U_668),fun(fun(fun(U_669,U_668),bool),bool),member(fun(U_669,U_668)),U_666),hAPP(fun(U_669,fun(U_668,bool)),fun(fun(U_669,U_668),bool),hAPP(fun(U_669,bool),fun(fun(U_669,fun(U_668,bool)),fun(fun(U_669,U_668),bool)),pi(U_669,U_668),U_665),hAPP(fun(U_668,bool),fun(U_669,fun(U_668,bool)),combk(fun(U_668,bool),U_669),U_664)))) ),
    inference(clausify,[status(thm)],[f_233_2]) ).

fof(f_234_1,plain,
    ! [X_a,A_1] : hBOOL(hAPP(fun(fun(X_a,X_a),bool),bool,hAPP(fun(X_a,X_a),fun(fun(fun(X_a,X_a),bool),bool),member(fun(X_a,X_a)),combi(X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool)),pi(X_a,X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),combk(fun(X_a,bool),X_a),A_1)))),
    inference(fof_nnf,[status(thm)],[fact_144_funcset__id]) ).

fof(f_234_2,plain,
    ! [U_671,U_670] : hBOOL(hAPP(fun(fun(U_671,U_671),bool),bool,hAPP(fun(U_671,U_671),fun(fun(fun(U_671,U_671),bool),bool),member(fun(U_671,U_671)),combi(U_671)),hAPP(fun(U_671,fun(U_671,bool)),fun(fun(U_671,U_671),bool),hAPP(fun(U_671,bool),fun(fun(U_671,fun(U_671,bool)),fun(fun(U_671,U_671),bool)),pi(U_671,U_671),U_670),hAPP(fun(U_671,bool),fun(U_671,fun(U_671,bool)),combk(fun(U_671,bool),U_671),U_670)))),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

cnf(f_234_3,plain,
    hBOOL(hAPP(fun(fun(U_671,U_671),bool),bool,hAPP(fun(U_671,U_671),fun(fun(fun(U_671,U_671),bool),bool),member(fun(U_671,U_671)),combi(U_671)),hAPP(fun(U_671,fun(U_671,bool)),fun(fun(U_671,U_671),bool),hAPP(fun(U_671,bool),fun(fun(U_671,fun(U_671,bool)),fun(fun(U_671,U_671),bool)),pi(U_671,U_671),U_670),hAPP(fun(U_671,bool),fun(U_671,fun(U_671,bool)),combk(fun(U_671,bool),U_671),U_670)))),
    inference(clausify,[status(thm)],[f_234_2]) ).

fof(f_235_1,plain,
    ! [X_a,X_b,X_2,Y_1,F] :
      ( ( ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
          | ti(X_a,X_2) != ti(X_a,Y_1) )
        & ( ti(X_a,X_2) = ti(X_a,Y_1)
          | hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_145_inj__eq]) ).

fof(f_235_2,plain,
    ! [U_676,U_675,U_674,U_673,U_672] :
      ( ( ( hAPP(U_676,U_675,U_672,U_674) = hAPP(U_676,U_675,U_672,U_673)
          | ti(U_676,U_674) != ti(U_676,U_673) )
        & ( ti(U_676,U_674) = ti(U_676,U_673)
          | hAPP(U_676,U_675,U_672,U_674) != hAPP(U_676,U_675,U_672,U_673) ) )
      | ~ hBOOL(hAPP(fun(U_676,bool),bool,hAPP(fun(U_676,U_675),fun(fun(U_676,bool),bool),inj_on(U_676,U_675),U_672),top_top(fun(U_676,bool)))) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

cnf(f_235_3,plain,
    ( ti(U_676,U_674) = ti(U_676,U_673)
    | hAPP(U_676,U_675,U_672,U_674) != hAPP(U_676,U_675,U_672,U_673)
    | ~ hBOOL(hAPP(fun(U_676,bool),bool,hAPP(fun(U_676,U_675),fun(fun(U_676,bool),bool),inj_on(U_676,U_675),U_672),top_top(fun(U_676,bool)))) ),
    inference(clausify,[status(thm)],[f_235_2]) ).

cnf(f_235_4,plain,
    ( hAPP(U_676,U_675,U_672,U_674) = hAPP(U_676,U_675,U_672,U_673)
    | ti(U_676,U_674) != ti(U_676,U_673)
    | ~ hBOOL(hAPP(fun(U_676,bool),bool,hAPP(fun(U_676,U_675),fun(fun(U_676,bool),bool),inj_on(U_676,U_675),U_672),top_top(fun(U_676,bool)))) ),
    inference(clausify,[status(thm)],[f_235_2]) ).

fof(f_236_1,plain,
    ! [X_a,X_b,X_2,Y_1,F] :
      ( ti(X_a,X_2) = ti(X_a,Y_1)
      | hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_146_injD]) ).

fof(f_236_2,plain,
    ! [U_681,U_680,U_679,U_678,U_677] :
      ( ti(U_681,U_679) = ti(U_681,U_678)
      | hAPP(U_681,U_680,U_677,U_679) != hAPP(U_681,U_680,U_677,U_678)
      | ~ hBOOL(hAPP(fun(U_681,bool),bool,hAPP(fun(U_681,U_680),fun(fun(U_681,bool),bool),inj_on(U_681,U_680),U_677),top_top(fun(U_681,bool)))) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

cnf(f_236_3,plain,
    ( ti(U_681,U_679) = ti(U_681,U_678)
    | hAPP(U_681,U_680,U_677,U_679) != hAPP(U_681,U_680,U_677,U_678)
    | ~ hBOOL(hAPP(fun(U_681,bool),bool,hAPP(fun(U_681,U_680),fun(fun(U_681,bool),bool),inj_on(U_681,U_680),U_677),top_top(fun(U_681,bool)))) ),
    inference(clausify,[status(thm)],[f_236_2]) ).

fof(f_237_1,plain,
    ! [X_a,X_b,X_2,F,A_1] :
      ( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_147_inv__into__f__f]) ).

fof(f_237_2,plain,
    ! [U_686,U_685,U_684,U_683,U_682] :
      ( hAPP(U_685,U_686,hAPP(fun(U_686,U_685),fun(U_685,U_686),hAPP(fun(U_686,bool),fun(fun(U_686,U_685),fun(U_685,U_686)),hilbert_inv_into(U_686,U_685),U_682),U_683),hAPP(U_686,U_685,U_683,U_684)) = ti(U_686,U_684)
      | ~ hBOOL(hAPP(fun(U_686,bool),bool,hAPP(U_686,fun(fun(U_686,bool),bool),member(U_686),U_684),U_682))
      | ~ hBOOL(hAPP(fun(U_686,bool),bool,hAPP(fun(U_686,U_685),fun(fun(U_686,bool),bool),inj_on(U_686,U_685),U_683),U_682)) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

cnf(f_237_3,plain,
    ( hAPP(U_685,U_686,hAPP(fun(U_686,U_685),fun(U_685,U_686),hAPP(fun(U_686,bool),fun(fun(U_686,U_685),fun(U_685,U_686)),hilbert_inv_into(U_686,U_685),U_682),U_683),hAPP(U_686,U_685,U_683,U_684)) = ti(U_686,U_684)
    | ~ hBOOL(hAPP(fun(U_686,bool),bool,hAPP(U_686,fun(fun(U_686,bool),bool),member(U_686),U_684),U_682))
    | ~ hBOOL(hAPP(fun(U_686,bool),bool,hAPP(fun(U_686,U_685),fun(fun(U_686,bool),bool),inj_on(U_686,U_685),U_683),U_682)) ),
    inference(clausify,[status(thm)],[f_237_2]) ).

fof(f_238_1,plain,
    ! [X_a,X_b,Y_1,X_2,F,A_1] :
      ( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),Y_1) = ti(X_a,X_2)
      | hAPP(X_a,X_b,F,X_2) != ti(X_b,Y_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_148_inv__into__f__eq]) ).

fof(f_238_2,plain,
    ! [U_692,U_691,U_690,U_689,U_688,U_687] :
      ( hAPP(U_691,U_692,hAPP(fun(U_692,U_691),fun(U_691,U_692),hAPP(fun(U_692,bool),fun(fun(U_692,U_691),fun(U_691,U_692)),hilbert_inv_into(U_692,U_691),U_687),U_688),U_690) = ti(U_692,U_689)
      | hAPP(U_692,U_691,U_688,U_689) != ti(U_691,U_690)
      | ~ hBOOL(hAPP(fun(U_692,bool),bool,hAPP(U_692,fun(fun(U_692,bool),bool),member(U_692),U_689),U_687))
      | ~ hBOOL(hAPP(fun(U_692,bool),bool,hAPP(fun(U_692,U_691),fun(fun(U_692,bool),bool),inj_on(U_692,U_691),U_688),U_687)) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

cnf(f_238_3,plain,
    ( hAPP(U_691,U_692,hAPP(fun(U_692,U_691),fun(U_691,U_692),hAPP(fun(U_692,bool),fun(fun(U_692,U_691),fun(U_691,U_692)),hilbert_inv_into(U_692,U_691),U_687),U_688),U_690) = ti(U_692,U_689)
    | hAPP(U_692,U_691,U_688,U_689) != ti(U_691,U_690)
    | ~ hBOOL(hAPP(fun(U_692,bool),bool,hAPP(U_692,fun(fun(U_692,bool),bool),member(U_692),U_689),U_687))
    | ~ hBOOL(hAPP(fun(U_692,bool),bool,hAPP(fun(U_692,U_691),fun(fun(U_692,bool),bool),inj_on(U_692,U_691),U_688),U_687)) ),
    inference(clausify,[status(thm)],[f_238_2]) ).

fof(f_239_1,plain,
    ! [X_b,X_a,F,B,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1)))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_149_Pi__I]) ).

fof(f_239_2,plain,
    ! [U_698,U_697,U_696,U_695,U_694] :
      ( hBOOL(hAPP(fun(fun(U_697,U_698),bool),bool,hAPP(fun(U_697,U_698),fun(fun(fun(U_697,U_698),bool),bool),member(fun(U_697,U_698)),U_696),hAPP(fun(U_697,fun(U_698,bool)),fun(fun(U_697,U_698),bool),hAPP(fun(U_697,bool),fun(fun(U_697,fun(U_698,bool)),fun(fun(U_697,U_698),bool)),pi(U_697,U_698),U_694),U_695)))
      | ? [U_693] :
          ( ~ hBOOL(hAPP(fun(U_698,bool),bool,hAPP(U_698,fun(fun(U_698,bool),bool),member(U_698),hAPP(U_697,U_698,U_696,U_693)),hAPP(U_697,fun(U_698,bool),U_695,U_693)))
          & hBOOL(hAPP(fun(U_697,bool),bool,hAPP(U_697,fun(fun(U_697,bool),bool),member(U_697),U_693),U_694)) ) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ! [U_698,U_697,U_696,U_695,U_694] :
      ( hBOOL(hAPP(fun(fun(U_697,U_698),bool),bool,hAPP(fun(U_697,U_698),fun(fun(fun(U_697,U_698),bool),bool),member(fun(U_697,U_698)),U_696),hAPP(fun(U_697,fun(U_698,bool)),fun(fun(U_697,U_698),bool),hAPP(fun(U_697,bool),fun(fun(U_697,fun(U_698,bool)),fun(fun(U_697,U_698),bool)),pi(U_697,U_698),U_694),U_695)))
      | ( ~ hBOOL(hAPP(fun(U_698,bool),bool,hAPP(U_698,fun(fun(U_698,bool),bool),member(U_698),hAPP(U_697,U_698,U_696,sK41(U_698,U_697,U_696,U_695,U_694))),hAPP(U_697,fun(U_698,bool),U_695,sK41(U_698,U_697,U_696,U_695,U_694))))
        & hBOOL(hAPP(fun(U_697,bool),bool,hAPP(U_697,fun(fun(U_697,bool),bool),member(U_697),sK41(U_698,U_697,U_696,U_695,U_694)),U_694)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_693,sK41(U_698,U_697,U_696,U_695,U_694))],[f_239_2]) ).

cnf(f_239_4,plain,
    ( hBOOL(hAPP(fun(U_697,bool),bool,hAPP(U_697,fun(fun(U_697,bool),bool),member(U_697),sK41(U_698,U_697,U_696,U_695,U_694)),U_694))
    | hBOOL(hAPP(fun(fun(U_697,U_698),bool),bool,hAPP(fun(U_697,U_698),fun(fun(fun(U_697,U_698),bool),bool),member(fun(U_697,U_698)),U_696),hAPP(fun(U_697,fun(U_698,bool)),fun(fun(U_697,U_698),bool),hAPP(fun(U_697,bool),fun(fun(U_697,fun(U_698,bool)),fun(fun(U_697,U_698),bool)),pi(U_697,U_698),U_694),U_695))) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

cnf(f_239_5,plain,
    ( ~ hBOOL(hAPP(fun(U_698,bool),bool,hAPP(U_698,fun(fun(U_698,bool),bool),member(U_698),hAPP(U_697,U_698,U_696,sK41(U_698,U_697,U_696,U_695,U_694))),hAPP(U_697,fun(U_698,bool),U_695,sK41(U_698,U_697,U_696,U_695,U_694))))
    | hBOOL(hAPP(fun(fun(U_697,U_698),bool),bool,hAPP(fun(U_697,U_698),fun(fun(fun(U_697,U_698),bool),bool),member(fun(U_697,U_698)),U_696),hAPP(fun(U_697,fun(U_698,bool)),fun(fun(U_697,U_698),bool),hAPP(fun(U_697,bool),fun(fun(U_697,fun(U_698,bool)),fun(fun(U_697,U_698),bool)),pi(U_697,U_698),U_694),U_695))) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

fof(f_240_1,plain,
    ! [X_a,X_b,G,F] :
      ( hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F) = ti(fun(X_b,X_a),G)
      | ? [X_1] : hAPP(X_a,X_b,F,hAPP(X_b,X_a,G,X_1)) != ti(X_b,X_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_150_inj__imp__inv__eq]) ).

fof(f_240_2,plain,
    ! [U_703,U_702,U_701,U_700] :
      ( hAPP(fun(U_703,U_702),fun(U_702,U_703),hAPP(fun(U_703,bool),fun(fun(U_703,U_702),fun(U_702,U_703)),hilbert_inv_into(U_703,U_702),top_top(fun(U_703,bool))),U_700) = ti(fun(U_702,U_703),U_701)
      | ? [U_699] : hAPP(U_703,U_702,U_700,hAPP(U_702,U_703,U_701,U_699)) != ti(U_702,U_699)
      | ~ hBOOL(hAPP(fun(U_703,bool),bool,hAPP(fun(U_703,U_702),fun(fun(U_703,bool),bool),inj_on(U_703,U_702),U_700),top_top(fun(U_703,bool)))) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ! [U_703,U_702,U_701,U_700] :
      ( hAPP(fun(U_703,U_702),fun(U_702,U_703),hAPP(fun(U_703,bool),fun(fun(U_703,U_702),fun(U_702,U_703)),hilbert_inv_into(U_703,U_702),top_top(fun(U_703,bool))),U_700) = ti(fun(U_702,U_703),U_701)
      | hAPP(U_703,U_702,U_700,hAPP(U_702,U_703,U_701,sK42(U_703,U_702,U_701,U_700))) != ti(U_702,sK42(U_703,U_702,U_701,U_700))
      | ~ hBOOL(hAPP(fun(U_703,bool),bool,hAPP(fun(U_703,U_702),fun(fun(U_703,bool),bool),inj_on(U_703,U_702),U_700),top_top(fun(U_703,bool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_699,sK42(U_703,U_702,U_701,U_700))],[f_240_2]) ).

cnf(f_240_4,plain,
    ( hAPP(fun(U_703,U_702),fun(U_702,U_703),hAPP(fun(U_703,bool),fun(fun(U_703,U_702),fun(U_702,U_703)),hilbert_inv_into(U_703,U_702),top_top(fun(U_703,bool))),U_700) = ti(fun(U_702,U_703),U_701)
    | hAPP(U_703,U_702,U_700,hAPP(U_702,U_703,U_701,sK42(U_703,U_702,U_701,U_700))) != ti(U_702,sK42(U_703,U_702,U_701,U_700))
    | ~ hBOOL(hAPP(fun(U_703,bool),bool,hAPP(fun(U_703,U_702),fun(fun(U_703,bool),bool),inj_on(U_703,U_702),U_700),top_top(fun(U_703,bool)))) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

fof(f_241_1,plain,
    ! [X_a] :
      ( ! [A_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),one_one(X_a))))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_151_less__add__one]) ).

fof(f_241_2,plain,
    ! [U_705] :
      ( ! [U_704] : hBOOL(hAPP(U_705,bool,hAPP(U_705,fun(U_705,bool),ord_less(U_705),U_704),hAPP(U_705,U_705,hAPP(U_705,fun(U_705,U_705),plus_plus(U_705),U_704),one_one(U_705))))
      | ~ linordered_semidom(U_705) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

cnf(f_241_3,plain,
    ( hBOOL(hAPP(U_705,bool,hAPP(U_705,fun(U_705,bool),ord_less(U_705),U_704),hAPP(U_705,U_705,hAPP(U_705,fun(U_705,U_705),plus_plus(U_705),U_704),one_one(U_705))))
    | ~ linordered_semidom(U_705) ),
    inference(clausify,[status(thm)],[f_241_2]) ).

fof(f_242_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_152_add__less__le__mono]) ).

fof(f_242_2,plain,
    ! [U_710] :
      ( ! [U_709,U_708,U_707,U_706] :
          ( hBOOL(hAPP(U_710,bool,hAPP(U_710,fun(U_710,bool),ord_less(U_710),hAPP(U_710,U_710,hAPP(U_710,fun(U_710,U_710),plus_plus(U_710),U_707),U_709)),hAPP(U_710,U_710,hAPP(U_710,fun(U_710,U_710),plus_plus(U_710),U_706),U_708)))
          | ~ hBOOL(hAPP(U_710,bool,hAPP(U_710,fun(U_710,bool),ord_less_eq(U_710),U_709),U_708))
          | ~ hBOOL(hAPP(U_710,bool,hAPP(U_710,fun(U_710,bool),ord_less(U_710),U_707),U_706)) )
      | ~ ordere223160158up_add(U_710) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

cnf(f_242_3,plain,
    ( hBOOL(hAPP(U_710,bool,hAPP(U_710,fun(U_710,bool),ord_less(U_710),hAPP(U_710,U_710,hAPP(U_710,fun(U_710,U_710),plus_plus(U_710),U_707),U_709)),hAPP(U_710,U_710,hAPP(U_710,fun(U_710,U_710),plus_plus(U_710),U_706),U_708)))
    | ~ hBOOL(hAPP(U_710,bool,hAPP(U_710,fun(U_710,bool),ord_less_eq(U_710),U_709),U_708))
    | ~ hBOOL(hAPP(U_710,bool,hAPP(U_710,fun(U_710,bool),ord_less(U_710),U_707),U_706))
    | ~ ordere223160158up_add(U_710) ),
    inference(clausify,[status(thm)],[f_242_2]) ).

fof(f_243_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_153_add__le__less__mono]) ).

fof(f_243_2,plain,
    ! [U_715] :
      ( ! [U_714,U_713,U_712,U_711] :
          ( hBOOL(hAPP(U_715,bool,hAPP(U_715,fun(U_715,bool),ord_less(U_715),hAPP(U_715,U_715,hAPP(U_715,fun(U_715,U_715),plus_plus(U_715),U_712),U_714)),hAPP(U_715,U_715,hAPP(U_715,fun(U_715,U_715),plus_plus(U_715),U_711),U_713)))
          | ~ hBOOL(hAPP(U_715,bool,hAPP(U_715,fun(U_715,bool),ord_less(U_715),U_714),U_713))
          | ~ hBOOL(hAPP(U_715,bool,hAPP(U_715,fun(U_715,bool),ord_less_eq(U_715),U_712),U_711)) )
      | ~ ordere223160158up_add(U_715) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

cnf(f_243_3,plain,
    ( hBOOL(hAPP(U_715,bool,hAPP(U_715,fun(U_715,bool),ord_less(U_715),hAPP(U_715,U_715,hAPP(U_715,fun(U_715,U_715),plus_plus(U_715),U_712),U_714)),hAPP(U_715,U_715,hAPP(U_715,fun(U_715,U_715),plus_plus(U_715),U_711),U_713)))
    | ~ hBOOL(hAPP(U_715,bool,hAPP(U_715,fun(U_715,bool),ord_less(U_715),U_714),U_713))
    | ~ hBOOL(hAPP(U_715,bool,hAPP(U_715,fun(U_715,bool),ord_less_eq(U_715),U_712),U_711))
    | ~ ordere223160158up_add(U_715) ),
    inference(clausify,[status(thm)],[f_243_2]) ).

fof(f_244_1,plain,
    ! [X_a,X_b,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
      | ? [X_1,Y_2] :
          ( ti(X_a,X_1) != ti(X_a,Y_2)
          & hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_154_injI]) ).

fof(f_244_2,plain,
    ! [U_720,U_719,U_718] :
      ( hBOOL(hAPP(fun(U_720,bool),bool,hAPP(fun(U_720,U_719),fun(fun(U_720,bool),bool),inj_on(U_720,U_719),U_718),top_top(fun(U_720,bool))))
      | ? [U_717,U_716] :
          ( ti(U_720,U_717) != ti(U_720,U_716)
          & hAPP(U_720,U_719,U_718,U_717) = hAPP(U_720,U_719,U_718,U_716) ) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ! [U_720,U_719,U_718] :
      ( hBOOL(hAPP(fun(U_720,bool),bool,hAPP(fun(U_720,U_719),fun(fun(U_720,bool),bool),inj_on(U_720,U_719),U_718),top_top(fun(U_720,bool))))
      | ? [U_716] :
          ( ti(U_720,sK43(U_720,U_719,U_718)) != ti(U_720,U_716)
          & hAPP(U_720,U_719,U_718,sK43(U_720,U_719,U_718)) = hAPP(U_720,U_719,U_718,U_716) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_717,sK43(U_720,U_719,U_718))],[f_244_2]) ).

fof(f_244_4,plain,
    ! [U_720,U_719,U_718] :
      ( hBOOL(hAPP(fun(U_720,bool),bool,hAPP(fun(U_720,U_719),fun(fun(U_720,bool),bool),inj_on(U_720,U_719),U_718),top_top(fun(U_720,bool))))
      | ( ti(U_720,sK43(U_720,U_719,U_718)) != ti(U_720,sK44(U_720,U_719,U_718))
        & hAPP(U_720,U_719,U_718,sK43(U_720,U_719,U_718)) = hAPP(U_720,U_719,U_718,sK44(U_720,U_719,U_718)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_716,sK44(U_720,U_719,U_718))],[f_244_3]) ).

cnf(f_244_5,plain,
    ( hAPP(U_720,U_719,U_718,sK43(U_720,U_719,U_718)) = hAPP(U_720,U_719,U_718,sK44(U_720,U_719,U_718))
    | hBOOL(hAPP(fun(U_720,bool),bool,hAPP(fun(U_720,U_719),fun(fun(U_720,bool),bool),inj_on(U_720,U_719),U_718),top_top(fun(U_720,bool)))) ),
    inference(clausify,[status(thm)],[f_244_4]) ).

cnf(f_244_6,plain,
    ( ti(U_720,sK43(U_720,U_719,U_718)) != ti(U_720,sK44(U_720,U_719,U_718))
    | hBOOL(hAPP(fun(U_720,bool),bool,hAPP(fun(U_720,U_719),fun(fun(U_720,bool),bool),inj_on(U_720,U_719),U_718),top_top(fun(U_720,bool)))) ),
    inference(clausify,[status(thm)],[f_244_4]) ).

fof(f_245_1,plain,
    ! [X_a] :
      ( ! [Z,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
          | ? [X_1] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) ) )
      | ~ dense_linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_155_dense__le]) ).

fof(f_245_2,plain,
    ! [U_724] :
      ( ! [U_723,U_722] :
          ( hBOOL(hAPP(U_724,bool,hAPP(U_724,fun(U_724,bool),ord_less_eq(U_724),U_722),U_723))
          | ? [U_721] :
              ( ~ hBOOL(hAPP(U_724,bool,hAPP(U_724,fun(U_724,bool),ord_less_eq(U_724),U_721),U_723))
              & hBOOL(hAPP(U_724,bool,hAPP(U_724,fun(U_724,bool),ord_less(U_724),U_721),U_722)) ) )
      | ~ dense_linorder(U_724) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ! [U_724] :
      ( ! [U_723,U_722] :
          ( hBOOL(hAPP(U_724,bool,hAPP(U_724,fun(U_724,bool),ord_less_eq(U_724),U_722),U_723))
          | ( ~ hBOOL(hAPP(U_724,bool,hAPP(U_724,fun(U_724,bool),ord_less_eq(U_724),sK45(U_724,U_723,U_722)),U_723))
            & hBOOL(hAPP(U_724,bool,hAPP(U_724,fun(U_724,bool),ord_less(U_724),sK45(U_724,U_723,U_722)),U_722)) ) )
      | ~ dense_linorder(U_724) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_721,sK45(U_724,U_723,U_722))],[f_245_2]) ).

cnf(f_245_4,plain,
    ( hBOOL(hAPP(U_724,bool,hAPP(U_724,fun(U_724,bool),ord_less(U_724),sK45(U_724,U_723,U_722)),U_722))
    | hBOOL(hAPP(U_724,bool,hAPP(U_724,fun(U_724,bool),ord_less_eq(U_724),U_722),U_723))
    | ~ dense_linorder(U_724) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

cnf(f_245_5,plain,
    ( ~ hBOOL(hAPP(U_724,bool,hAPP(U_724,fun(U_724,bool),ord_less_eq(U_724),sK45(U_724,U_723,U_722)),U_723))
    | hBOOL(hAPP(U_724,bool,hAPP(U_724,fun(U_724,bool),ord_less_eq(U_724),U_722),U_723))
    | ~ dense_linorder(U_724) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
          | ? [W_1] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_1),Z))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_1),Y))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_1)) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ dense_linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_156_dense__le__bounded]) ).

fof(f_246_2,plain,
    ! [U_729] :
      ( ! [U_728,U_727,U_726] :
          ( hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less_eq(U_729),U_726),U_728))
          | ? [U_725] :
              ( ~ hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less_eq(U_729),U_725),U_728))
              & hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),U_725),U_726))
              & hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),U_727),U_725)) )
          | ~ hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),U_727),U_726)) )
      | ~ dense_linorder(U_729) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ! [U_729] :
      ( ! [U_728,U_727,U_726] :
          ( hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less_eq(U_729),U_726),U_728))
          | ( ~ hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less_eq(U_729),sK46(U_729,U_728,U_727,U_726)),U_728))
            & hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),sK46(U_729,U_728,U_727,U_726)),U_726))
            & hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),U_727),sK46(U_729,U_728,U_727,U_726))) )
          | ~ hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),U_727),U_726)) )
      | ~ dense_linorder(U_729) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_725,sK46(U_729,U_728,U_727,U_726))],[f_246_2]) ).

cnf(f_246_4,plain,
    ( hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),U_727),sK46(U_729,U_728,U_727,U_726)))
    | hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less_eq(U_729),U_726),U_728))
    | ~ hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),U_727),U_726))
    | ~ dense_linorder(U_729) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

cnf(f_246_5,plain,
    ( hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),sK46(U_729,U_728,U_727,U_726)),U_726))
    | hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less_eq(U_729),U_726),U_728))
    | ~ hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),U_727),U_726))
    | ~ dense_linorder(U_729) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

cnf(f_246_6,plain,
    ( ~ hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less_eq(U_729),sK46(U_729,U_728,U_727,U_726)),U_728))
    | hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less_eq(U_729),U_726),U_728))
    | ~ hBOOL(hAPP(U_729,bool,hAPP(U_729,fun(U_729,bool),ord_less(U_729),U_727),U_726))
    | ~ dense_linorder(U_729) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

fof(f_247_1,plain,
    ! [X_b,X_a] :
      ( ! [Ca,F,Ba,Aa] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Aa)))
          | ? [X_1,Y_2] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_1)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),hAPP(X_a,X_b,F,Ba)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)) )
      | ~ order(X_b)
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_157_xt5]) ).

fof(f_247_2,plain,
    ! [U_737,U_736] :
      ( ! [U_735,U_734,U_733,U_732] :
          ( hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less(U_737),U_735),hAPP(U_736,U_737,U_734,U_732)))
          | ? [U_731,U_730] :
              ( ~ hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less(U_737),hAPP(U_736,U_737,U_734,U_730)),hAPP(U_736,U_737,U_734,U_731)))
              & hBOOL(hAPP(U_736,bool,hAPP(U_736,fun(U_736,bool),ord_less(U_736),U_730),U_731)) )
          | ~ hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less_eq(U_737),U_735),hAPP(U_736,U_737,U_734,U_733)))
          | ~ hBOOL(hAPP(U_736,bool,hAPP(U_736,fun(U_736,bool),ord_less(U_736),U_733),U_732)) )
      | ~ order(U_737)
      | ~ order(U_736) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ! [U_737,U_736] :
      ( ! [U_735,U_734,U_733,U_732] :
          ( hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less(U_737),U_735),hAPP(U_736,U_737,U_734,U_732)))
          | ? [U_730] :
              ( ~ hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less(U_737),hAPP(U_736,U_737,U_734,U_730)),hAPP(U_736,U_737,U_734,sK47(U_737,U_736,U_735,U_734,U_733,U_732))))
              & hBOOL(hAPP(U_736,bool,hAPP(U_736,fun(U_736,bool),ord_less(U_736),U_730),sK47(U_737,U_736,U_735,U_734,U_733,U_732))) )
          | ~ hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less_eq(U_737),U_735),hAPP(U_736,U_737,U_734,U_733)))
          | ~ hBOOL(hAPP(U_736,bool,hAPP(U_736,fun(U_736,bool),ord_less(U_736),U_733),U_732)) )
      | ~ order(U_737)
      | ~ order(U_736) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_731,sK47(U_737,U_736,U_735,U_734,U_733,U_732))],[f_247_2]) ).

fof(f_247_4,plain,
    ! [U_737,U_736] :
      ( ! [U_735,U_734,U_733,U_732] :
          ( hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less(U_737),U_735),hAPP(U_736,U_737,U_734,U_732)))
          | ( ~ hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less(U_737),hAPP(U_736,U_737,U_734,sK48(U_737,U_736,U_735,U_734,U_733,U_732))),hAPP(U_736,U_737,U_734,sK47(U_737,U_736,U_735,U_734,U_733,U_732))))
            & hBOOL(hAPP(U_736,bool,hAPP(U_736,fun(U_736,bool),ord_less(U_736),sK48(U_737,U_736,U_735,U_734,U_733,U_732)),sK47(U_737,U_736,U_735,U_734,U_733,U_732))) )
          | ~ hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less_eq(U_737),U_735),hAPP(U_736,U_737,U_734,U_733)))
          | ~ hBOOL(hAPP(U_736,bool,hAPP(U_736,fun(U_736,bool),ord_less(U_736),U_733),U_732)) )
      | ~ order(U_737)
      | ~ order(U_736) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_730,sK48(U_737,U_736,U_735,U_734,U_733,U_732))],[f_247_3]) ).

cnf(f_247_5,plain,
    ( hBOOL(hAPP(U_736,bool,hAPP(U_736,fun(U_736,bool),ord_less(U_736),sK48(U_737,U_736,U_735,U_734,U_733,U_732)),sK47(U_737,U_736,U_735,U_734,U_733,U_732)))
    | hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less(U_737),U_735),hAPP(U_736,U_737,U_734,U_732)))
    | ~ hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less_eq(U_737),U_735),hAPP(U_736,U_737,U_734,U_733)))
    | ~ hBOOL(hAPP(U_736,bool,hAPP(U_736,fun(U_736,bool),ord_less(U_736),U_733),U_732))
    | ~ order(U_737)
    | ~ order(U_736) ),
    inference(clausify,[status(thm)],[f_247_4]) ).

cnf(f_247_6,plain,
    ( ~ hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less(U_737),hAPP(U_736,U_737,U_734,sK48(U_737,U_736,U_735,U_734,U_733,U_732))),hAPP(U_736,U_737,U_734,sK47(U_737,U_736,U_735,U_734,U_733,U_732))))
    | hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less(U_737),U_735),hAPP(U_736,U_737,U_734,U_732)))
    | ~ hBOOL(hAPP(U_737,bool,hAPP(U_737,fun(U_737,bool),ord_less_eq(U_737),U_735),hAPP(U_736,U_737,U_734,U_733)))
    | ~ hBOOL(hAPP(U_736,bool,hAPP(U_736,fun(U_736,bool),ord_less(U_736),U_733),U_732))
    | ~ order(U_737)
    | ~ order(U_736) ),
    inference(clausify,[status(thm)],[f_247_4]) ).

fof(f_248_1,plain,
    ! [X_b,X_a] :
      ( ! [Ca,F,Ba,Aa] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Aa)))
          | ? [X_1,Y_2] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_1)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_1)) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_a,X_b,F,Ba)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) )
      | ~ order(X_b)
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_158_xt7]) ).

fof(f_248_2,plain,
    ! [U_745,U_744] :
      ( ! [U_743,U_742,U_741,U_740] :
          ( hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less(U_745),U_743),hAPP(U_744,U_745,U_742,U_740)))
          | ? [U_739,U_738] :
              ( ~ hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less_eq(U_745),hAPP(U_744,U_745,U_742,U_738)),hAPP(U_744,U_745,U_742,U_739)))
              & hBOOL(hAPP(U_744,bool,hAPP(U_744,fun(U_744,bool),ord_less_eq(U_744),U_738),U_739)) )
          | ~ hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less(U_745),U_743),hAPP(U_744,U_745,U_742,U_741)))
          | ~ hBOOL(hAPP(U_744,bool,hAPP(U_744,fun(U_744,bool),ord_less_eq(U_744),U_741),U_740)) )
      | ~ order(U_745)
      | ~ order(U_744) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ! [U_745,U_744] :
      ( ! [U_743,U_742,U_741,U_740] :
          ( hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less(U_745),U_743),hAPP(U_744,U_745,U_742,U_740)))
          | ? [U_738] :
              ( ~ hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less_eq(U_745),hAPP(U_744,U_745,U_742,U_738)),hAPP(U_744,U_745,U_742,sK49(U_745,U_744,U_743,U_742,U_741,U_740))))
              & hBOOL(hAPP(U_744,bool,hAPP(U_744,fun(U_744,bool),ord_less_eq(U_744),U_738),sK49(U_745,U_744,U_743,U_742,U_741,U_740))) )
          | ~ hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less(U_745),U_743),hAPP(U_744,U_745,U_742,U_741)))
          | ~ hBOOL(hAPP(U_744,bool,hAPP(U_744,fun(U_744,bool),ord_less_eq(U_744),U_741),U_740)) )
      | ~ order(U_745)
      | ~ order(U_744) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_739,sK49(U_745,U_744,U_743,U_742,U_741,U_740))],[f_248_2]) ).

fof(f_248_4,plain,
    ! [U_745,U_744] :
      ( ! [U_743,U_742,U_741,U_740] :
          ( hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less(U_745),U_743),hAPP(U_744,U_745,U_742,U_740)))
          | ( ~ hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less_eq(U_745),hAPP(U_744,U_745,U_742,sK50(U_745,U_744,U_743,U_742,U_741,U_740))),hAPP(U_744,U_745,U_742,sK49(U_745,U_744,U_743,U_742,U_741,U_740))))
            & hBOOL(hAPP(U_744,bool,hAPP(U_744,fun(U_744,bool),ord_less_eq(U_744),sK50(U_745,U_744,U_743,U_742,U_741,U_740)),sK49(U_745,U_744,U_743,U_742,U_741,U_740))) )
          | ~ hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less(U_745),U_743),hAPP(U_744,U_745,U_742,U_741)))
          | ~ hBOOL(hAPP(U_744,bool,hAPP(U_744,fun(U_744,bool),ord_less_eq(U_744),U_741),U_740)) )
      | ~ order(U_745)
      | ~ order(U_744) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_738,sK50(U_745,U_744,U_743,U_742,U_741,U_740))],[f_248_3]) ).

cnf(f_248_5,plain,
    ( hBOOL(hAPP(U_744,bool,hAPP(U_744,fun(U_744,bool),ord_less_eq(U_744),sK50(U_745,U_744,U_743,U_742,U_741,U_740)),sK49(U_745,U_744,U_743,U_742,U_741,U_740)))
    | hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less(U_745),U_743),hAPP(U_744,U_745,U_742,U_740)))
    | ~ hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less(U_745),U_743),hAPP(U_744,U_745,U_742,U_741)))
    | ~ hBOOL(hAPP(U_744,bool,hAPP(U_744,fun(U_744,bool),ord_less_eq(U_744),U_741),U_740))
    | ~ order(U_745)
    | ~ order(U_744) ),
    inference(clausify,[status(thm)],[f_248_4]) ).

cnf(f_248_6,plain,
    ( ~ hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less_eq(U_745),hAPP(U_744,U_745,U_742,sK50(U_745,U_744,U_743,U_742,U_741,U_740))),hAPP(U_744,U_745,U_742,sK49(U_745,U_744,U_743,U_742,U_741,U_740))))
    | hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less(U_745),U_743),hAPP(U_744,U_745,U_742,U_740)))
    | ~ hBOOL(hAPP(U_745,bool,hAPP(U_745,fun(U_745,bool),ord_less(U_745),U_743),hAPP(U_744,U_745,U_742,U_741)))
    | ~ hBOOL(hAPP(U_744,bool,hAPP(U_744,fun(U_744,bool),ord_less_eq(U_744),U_741),U_740))
    | ~ order(U_745)
    | ~ order(U_744) ),
    inference(clausify,[status(thm)],[f_248_4]) ).

fof(f_249_1,plain,
    ! [X_a,X_b] :
      ( ! [F,G] :
          ( ( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G))
            | hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F))
            | ~ hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) )
          & ( ( ~ hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F))
              & hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) )
            | ~ hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)) ) )
      | ~ ord(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_159_less__fun__def]) ).

fof(f_249_2,plain,
    ! [U_749,U_748] :
      ( ! [U_747,U_746] :
          ( ( hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less(fun(U_749,U_748)),U_747),U_746))
            | hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_746),U_747))
            | ~ hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_747),U_746)) )
          & ( ( ~ hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_746),U_747))
              & hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_747),U_746)) )
            | ~ hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less(fun(U_749,U_748)),U_747),U_746)) ) )
      | ~ ord(U_748) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ! [U_749,U_748] :
      ( ( ! [U_753,U_751] :
            ( hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less(fun(U_749,U_748)),U_753),U_751))
            | hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_751),U_753))
            | ~ hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_753),U_751)) )
        & ! [U_752,U_750] :
            ( ( ~ hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_750),U_752))
              & hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_752),U_750)) )
            | ~ hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less(fun(U_749,U_748)),U_752),U_750)) ) )
      | ~ ord(U_748) ),
    inference(miniscope,[status(thm)],[f_249_2]) ).

cnf(f_249_4,plain,
    ( hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_752),U_750))
    | ~ hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less(fun(U_749,U_748)),U_752),U_750))
    | ~ ord(U_748) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

cnf(f_249_5,plain,
    ( ~ hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_750),U_752))
    | ~ hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less(fun(U_749,U_748)),U_752),U_750))
    | ~ ord(U_748) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

cnf(f_249_6,plain,
    ( hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less(fun(U_749,U_748)),U_753),U_751))
    | hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_751),U_753))
    | ~ hBOOL(hAPP(fun(U_749,U_748),bool,hAPP(fun(U_749,U_748),fun(fun(U_749,U_748),bool),ord_less_eq(fun(U_749,U_748)),U_753),U_751))
    | ~ ord(U_748) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

fof(f_250_1,plain,
    ! [X_b,X_a,B,A_3,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(fun(X_a,X_b),bool),fun(fun(fun(X_a,X_b),bool),bool),ord_less_eq(fun(fun(X_a,X_b),bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_3),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_160_Pi__anti__mono]) ).

fof(f_250_2,plain,
    ! [U_758,U_757,U_756,U_755,U_754] :
      ( hBOOL(hAPP(fun(fun(U_757,U_758),bool),bool,hAPP(fun(fun(U_757,U_758),bool),fun(fun(fun(U_757,U_758),bool),bool),ord_less_eq(fun(fun(U_757,U_758),bool)),hAPP(fun(U_757,fun(U_758,bool)),fun(fun(U_757,U_758),bool),hAPP(fun(U_757,bool),fun(fun(U_757,fun(U_758,bool)),fun(fun(U_757,U_758),bool)),pi(U_757,U_758),U_754),U_756)),hAPP(fun(U_757,fun(U_758,bool)),fun(fun(U_757,U_758),bool),hAPP(fun(U_757,bool),fun(fun(U_757,fun(U_758,bool)),fun(fun(U_757,U_758),bool)),pi(U_757,U_758),U_755),U_756)))
      | ~ hBOOL(hAPP(fun(U_757,bool),bool,hAPP(fun(U_757,bool),fun(fun(U_757,bool),bool),ord_less_eq(fun(U_757,bool)),U_755),U_754)) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

cnf(f_250_3,plain,
    ( hBOOL(hAPP(fun(fun(U_757,U_758),bool),bool,hAPP(fun(fun(U_757,U_758),bool),fun(fun(fun(U_757,U_758),bool),bool),ord_less_eq(fun(fun(U_757,U_758),bool)),hAPP(fun(U_757,fun(U_758,bool)),fun(fun(U_757,U_758),bool),hAPP(fun(U_757,bool),fun(fun(U_757,fun(U_758,bool)),fun(fun(U_757,U_758),bool)),pi(U_757,U_758),U_754),U_756)),hAPP(fun(U_757,fun(U_758,bool)),fun(fun(U_757,U_758),bool),hAPP(fun(U_757,bool),fun(fun(U_757,fun(U_758,bool)),fun(fun(U_757,U_758),bool)),pi(U_757,U_758),U_755),U_756)))
    | ~ hBOOL(hAPP(fun(U_757,bool),bool,hAPP(fun(U_757,bool),fun(fun(U_757,bool),bool),ord_less_eq(fun(U_757,bool)),U_755),U_754)) ),
    inference(clausify,[status(thm)],[f_250_2]) ).

fof(f_251_1,plain,
    ! [X_a,X_b,R_2,S] :
      ( ( hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_2)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S)))
        | ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),bool),ord_less_eq(fun(product_prod(X_a,X_b),bool)),R_2),S)) )
      & ( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),bool),ord_less_eq(fun(product_prod(X_a,X_b),bool)),R_2),S))
        | ~ hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_2)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S))) ) ),
    inference(fof_nnf,[status(thm)],[fact_161_pred__subset__eq2]) ).

fof(f_251_2,plain,
    ! [U_762,U_761,U_760,U_759] :
      ( ( hBOOL(hAPP(fun(U_762,fun(U_761,bool)),bool,hAPP(fun(U_762,fun(U_761,bool)),fun(fun(U_762,fun(U_761,bool)),bool),ord_less_eq(fun(U_762,fun(U_761,bool))),hAPP(fun(product_prod(U_762,U_761),bool),fun(U_762,fun(U_761,bool)),hAPP(fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),fun(fun(product_prod(U_762,U_761),bool),fun(U_762,fun(U_761,bool))),combc(U_762,fun(product_prod(U_762,U_761),bool),fun(U_761,bool)),hAPP(fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),hAPP(fun(fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),fun(fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool)))),combb(fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool)),U_762),combc(U_761,fun(product_prod(U_762,U_761),bool),bool)),hAPP(fun(U_762,fun(U_761,product_prod(U_762,U_761))),fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),hAPP(fun(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(fun(U_762,fun(U_761,product_prod(U_762,U_761))),fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)))),combb(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),U_762),hAPP(fun(product_prod(U_762,U_761),fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),combb(product_prod(U_762,U_761),fun(fun(product_prod(U_762,U_761),bool),bool),U_761),member(product_prod(U_762,U_761)))),product_Pair(U_762,U_761)))),U_760)),hAPP(fun(product_prod(U_762,U_761),bool),fun(U_762,fun(U_761,bool)),hAPP(fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),fun(fun(product_prod(U_762,U_761),bool),fun(U_762,fun(U_761,bool))),combc(U_762,fun(product_prod(U_762,U_761),bool),fun(U_761,bool)),hAPP(fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),hAPP(fun(fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),fun(fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool)))),combb(fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool)),U_762),combc(U_761,fun(product_prod(U_762,U_761),bool),bool)),hAPP(fun(U_762,fun(U_761,product_prod(U_762,U_761))),fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),hAPP(fun(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(fun(U_762,fun(U_761,product_prod(U_762,U_761))),fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)))),combb(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),U_762),hAPP(fun(product_prod(U_762,U_761),fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),combb(product_prod(U_762,U_761),fun(fun(product_prod(U_762,U_761),bool),bool),U_761),member(product_prod(U_762,U_761)))),product_Pair(U_762,U_761)))),U_759)))
        | ~ hBOOL(hAPP(fun(product_prod(U_762,U_761),bool),bool,hAPP(fun(product_prod(U_762,U_761),bool),fun(fun(product_prod(U_762,U_761),bool),bool),ord_less_eq(fun(product_prod(U_762,U_761),bool)),U_760),U_759)) )
      & ( hBOOL(hAPP(fun(product_prod(U_762,U_761),bool),bool,hAPP(fun(product_prod(U_762,U_761),bool),fun(fun(product_prod(U_762,U_761),bool),bool),ord_less_eq(fun(product_prod(U_762,U_761),bool)),U_760),U_759))
        | ~ hBOOL(hAPP(fun(U_762,fun(U_761,bool)),bool,hAPP(fun(U_762,fun(U_761,bool)),fun(fun(U_762,fun(U_761,bool)),bool),ord_less_eq(fun(U_762,fun(U_761,bool))),hAPP(fun(product_prod(U_762,U_761),bool),fun(U_762,fun(U_761,bool)),hAPP(fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),fun(fun(product_prod(U_762,U_761),bool),fun(U_762,fun(U_761,bool))),combc(U_762,fun(product_prod(U_762,U_761),bool),fun(U_761,bool)),hAPP(fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),hAPP(fun(fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),fun(fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool)))),combb(fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool)),U_762),combc(U_761,fun(product_prod(U_762,U_761),bool),bool)),hAPP(fun(U_762,fun(U_761,product_prod(U_762,U_761))),fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),hAPP(fun(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(fun(U_762,fun(U_761,product_prod(U_762,U_761))),fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)))),combb(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),U_762),hAPP(fun(product_prod(U_762,U_761),fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),combb(product_prod(U_762,U_761),fun(fun(product_prod(U_762,U_761),bool),bool),U_761),member(product_prod(U_762,U_761)))),product_Pair(U_762,U_761)))),U_760)),hAPP(fun(product_prod(U_762,U_761),bool),fun(U_762,fun(U_761,bool)),hAPP(fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),fun(fun(product_prod(U_762,U_761),bool),fun(U_762,fun(U_761,bool))),combc(U_762,fun(product_prod(U_762,U_761),bool),fun(U_761,bool)),hAPP(fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),hAPP(fun(fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool))),fun(fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(U_762,fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool)))),combb(fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(product_prod(U_762,U_761),bool),fun(U_761,bool)),U_762),combc(U_761,fun(product_prod(U_762,U_761),bool),bool)),hAPP(fun(U_762,fun(U_761,product_prod(U_762,U_761))),fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),hAPP(fun(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),fun(fun(U_762,fun(U_761,product_prod(U_762,U_761))),fun(U_762,fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)))),combb(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool)),U_762),hAPP(fun(product_prod(U_762,U_761),fun(fun(product_prod(U_762,U_761),bool),bool)),fun(fun(U_761,product_prod(U_762,U_761)),fun(U_761,fun(fun(product_prod(U_762,U_761),bool),bool))),combb(product_prod(U_762,U_761),fun(fun(product_prod(U_762,U_761),bool),bool),U_761),member(product_prod(U_762,U_761)))),product_Pair(U_762,U_761)))),U_759))) ) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ( ! [U_770,U_768,U_766,U_764] :
        ( hBOOL(hAPP(fun(U_770,fun(U_768,bool)),bool,hAPP(fun(U_770,fun(U_768,bool)),fun(fun(U_770,fun(U_768,bool)),bool),ord_less_eq(fun(U_770,fun(U_768,bool))),hAPP(fun(product_prod(U_770,U_768),bool),fun(U_770,fun(U_768,bool)),hAPP(fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),fun(fun(product_prod(U_770,U_768),bool),fun(U_770,fun(U_768,bool))),combc(U_770,fun(product_prod(U_770,U_768),bool),fun(U_768,bool)),hAPP(fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),hAPP(fun(fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),fun(fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool)))),combb(fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool)),U_770),combc(U_768,fun(product_prod(U_770,U_768),bool),bool)),hAPP(fun(U_770,fun(U_768,product_prod(U_770,U_768))),fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),hAPP(fun(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(fun(U_770,fun(U_768,product_prod(U_770,U_768))),fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)))),combb(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),U_770),hAPP(fun(product_prod(U_770,U_768),fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),combb(product_prod(U_770,U_768),fun(fun(product_prod(U_770,U_768),bool),bool),U_768),member(product_prod(U_770,U_768)))),product_Pair(U_770,U_768)))),U_766)),hAPP(fun(product_prod(U_770,U_768),bool),fun(U_770,fun(U_768,bool)),hAPP(fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),fun(fun(product_prod(U_770,U_768),bool),fun(U_770,fun(U_768,bool))),combc(U_770,fun(product_prod(U_770,U_768),bool),fun(U_768,bool)),hAPP(fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),hAPP(fun(fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),fun(fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool)))),combb(fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool)),U_770),combc(U_768,fun(product_prod(U_770,U_768),bool),bool)),hAPP(fun(U_770,fun(U_768,product_prod(U_770,U_768))),fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),hAPP(fun(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(fun(U_770,fun(U_768,product_prod(U_770,U_768))),fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)))),combb(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),U_770),hAPP(fun(product_prod(U_770,U_768),fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),combb(product_prod(U_770,U_768),fun(fun(product_prod(U_770,U_768),bool),bool),U_768),member(product_prod(U_770,U_768)))),product_Pair(U_770,U_768)))),U_764)))
        | ~ hBOOL(hAPP(fun(product_prod(U_770,U_768),bool),bool,hAPP(fun(product_prod(U_770,U_768),bool),fun(fun(product_prod(U_770,U_768),bool),bool),ord_less_eq(fun(product_prod(U_770,U_768),bool)),U_766),U_764)) )
    & ! [U_769,U_767,U_765,U_763] :
        ( hBOOL(hAPP(fun(product_prod(U_769,U_767),bool),bool,hAPP(fun(product_prod(U_769,U_767),bool),fun(fun(product_prod(U_769,U_767),bool),bool),ord_less_eq(fun(product_prod(U_769,U_767),bool)),U_765),U_763))
        | ~ hBOOL(hAPP(fun(U_769,fun(U_767,bool)),bool,hAPP(fun(U_769,fun(U_767,bool)),fun(fun(U_769,fun(U_767,bool)),bool),ord_less_eq(fun(U_769,fun(U_767,bool))),hAPP(fun(product_prod(U_769,U_767),bool),fun(U_769,fun(U_767,bool)),hAPP(fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),fun(fun(product_prod(U_769,U_767),bool),fun(U_769,fun(U_767,bool))),combc(U_769,fun(product_prod(U_769,U_767),bool),fun(U_767,bool)),hAPP(fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),hAPP(fun(fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),fun(fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool)))),combb(fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool)),U_769),combc(U_767,fun(product_prod(U_769,U_767),bool),bool)),hAPP(fun(U_769,fun(U_767,product_prod(U_769,U_767))),fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),hAPP(fun(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(fun(U_769,fun(U_767,product_prod(U_769,U_767))),fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)))),combb(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),U_769),hAPP(fun(product_prod(U_769,U_767),fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),combb(product_prod(U_769,U_767),fun(fun(product_prod(U_769,U_767),bool),bool),U_767),member(product_prod(U_769,U_767)))),product_Pair(U_769,U_767)))),U_765)),hAPP(fun(product_prod(U_769,U_767),bool),fun(U_769,fun(U_767,bool)),hAPP(fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),fun(fun(product_prod(U_769,U_767),bool),fun(U_769,fun(U_767,bool))),combc(U_769,fun(product_prod(U_769,U_767),bool),fun(U_767,bool)),hAPP(fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),hAPP(fun(fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),fun(fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool)))),combb(fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool)),U_769),combc(U_767,fun(product_prod(U_769,U_767),bool),bool)),hAPP(fun(U_769,fun(U_767,product_prod(U_769,U_767))),fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),hAPP(fun(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(fun(U_769,fun(U_767,product_prod(U_769,U_767))),fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)))),combb(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),U_769),hAPP(fun(product_prod(U_769,U_767),fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),combb(product_prod(U_769,U_767),fun(fun(product_prod(U_769,U_767),bool),bool),U_767),member(product_prod(U_769,U_767)))),product_Pair(U_769,U_767)))),U_763))) ) ),
    inference(miniscope,[status(thm)],[f_251_2]) ).

cnf(f_251_4,plain,
    ( hBOOL(hAPP(fun(product_prod(U_769,U_767),bool),bool,hAPP(fun(product_prod(U_769,U_767),bool),fun(fun(product_prod(U_769,U_767),bool),bool),ord_less_eq(fun(product_prod(U_769,U_767),bool)),U_765),U_763))
    | ~ hBOOL(hAPP(fun(U_769,fun(U_767,bool)),bool,hAPP(fun(U_769,fun(U_767,bool)),fun(fun(U_769,fun(U_767,bool)),bool),ord_less_eq(fun(U_769,fun(U_767,bool))),hAPP(fun(product_prod(U_769,U_767),bool),fun(U_769,fun(U_767,bool)),hAPP(fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),fun(fun(product_prod(U_769,U_767),bool),fun(U_769,fun(U_767,bool))),combc(U_769,fun(product_prod(U_769,U_767),bool),fun(U_767,bool)),hAPP(fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),hAPP(fun(fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),fun(fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool)))),combb(fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool)),U_769),combc(U_767,fun(product_prod(U_769,U_767),bool),bool)),hAPP(fun(U_769,fun(U_767,product_prod(U_769,U_767))),fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),hAPP(fun(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(fun(U_769,fun(U_767,product_prod(U_769,U_767))),fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)))),combb(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),U_769),hAPP(fun(product_prod(U_769,U_767),fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),combb(product_prod(U_769,U_767),fun(fun(product_prod(U_769,U_767),bool),bool),U_767),member(product_prod(U_769,U_767)))),product_Pair(U_769,U_767)))),U_765)),hAPP(fun(product_prod(U_769,U_767),bool),fun(U_769,fun(U_767,bool)),hAPP(fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),fun(fun(product_prod(U_769,U_767),bool),fun(U_769,fun(U_767,bool))),combc(U_769,fun(product_prod(U_769,U_767),bool),fun(U_767,bool)),hAPP(fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),hAPP(fun(fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool))),fun(fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(U_769,fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool)))),combb(fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(product_prod(U_769,U_767),bool),fun(U_767,bool)),U_769),combc(U_767,fun(product_prod(U_769,U_767),bool),bool)),hAPP(fun(U_769,fun(U_767,product_prod(U_769,U_767))),fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),hAPP(fun(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),fun(fun(U_769,fun(U_767,product_prod(U_769,U_767))),fun(U_769,fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)))),combb(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool)),U_769),hAPP(fun(product_prod(U_769,U_767),fun(fun(product_prod(U_769,U_767),bool),bool)),fun(fun(U_767,product_prod(U_769,U_767)),fun(U_767,fun(fun(product_prod(U_769,U_767),bool),bool))),combb(product_prod(U_769,U_767),fun(fun(product_prod(U_769,U_767),bool),bool),U_767),member(product_prod(U_769,U_767)))),product_Pair(U_769,U_767)))),U_763))) ),
    inference(clausify,[status(thm)],[f_251_3]) ).

cnf(f_251_5,plain,
    ( hBOOL(hAPP(fun(U_770,fun(U_768,bool)),bool,hAPP(fun(U_770,fun(U_768,bool)),fun(fun(U_770,fun(U_768,bool)),bool),ord_less_eq(fun(U_770,fun(U_768,bool))),hAPP(fun(product_prod(U_770,U_768),bool),fun(U_770,fun(U_768,bool)),hAPP(fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),fun(fun(product_prod(U_770,U_768),bool),fun(U_770,fun(U_768,bool))),combc(U_770,fun(product_prod(U_770,U_768),bool),fun(U_768,bool)),hAPP(fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),hAPP(fun(fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),fun(fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool)))),combb(fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool)),U_770),combc(U_768,fun(product_prod(U_770,U_768),bool),bool)),hAPP(fun(U_770,fun(U_768,product_prod(U_770,U_768))),fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),hAPP(fun(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(fun(U_770,fun(U_768,product_prod(U_770,U_768))),fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)))),combb(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),U_770),hAPP(fun(product_prod(U_770,U_768),fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),combb(product_prod(U_770,U_768),fun(fun(product_prod(U_770,U_768),bool),bool),U_768),member(product_prod(U_770,U_768)))),product_Pair(U_770,U_768)))),U_766)),hAPP(fun(product_prod(U_770,U_768),bool),fun(U_770,fun(U_768,bool)),hAPP(fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),fun(fun(product_prod(U_770,U_768),bool),fun(U_770,fun(U_768,bool))),combc(U_770,fun(product_prod(U_770,U_768),bool),fun(U_768,bool)),hAPP(fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),hAPP(fun(fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool))),fun(fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(U_770,fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool)))),combb(fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(product_prod(U_770,U_768),bool),fun(U_768,bool)),U_770),combc(U_768,fun(product_prod(U_770,U_768),bool),bool)),hAPP(fun(U_770,fun(U_768,product_prod(U_770,U_768))),fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),hAPP(fun(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),fun(fun(U_770,fun(U_768,product_prod(U_770,U_768))),fun(U_770,fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)))),combb(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool)),U_770),hAPP(fun(product_prod(U_770,U_768),fun(fun(product_prod(U_770,U_768),bool),bool)),fun(fun(U_768,product_prod(U_770,U_768)),fun(U_768,fun(fun(product_prod(U_770,U_768),bool),bool))),combb(product_prod(U_770,U_768),fun(fun(product_prod(U_770,U_768),bool),bool),U_768),member(product_prod(U_770,U_768)))),product_Pair(U_770,U_768)))),U_764)))
    | ~ hBOOL(hAPP(fun(product_prod(U_770,U_768),bool),bool,hAPP(fun(product_prod(U_770,U_768),bool),fun(fun(product_prod(U_770,U_768),bool),bool),ord_less_eq(fun(product_prod(U_770,U_768),bool)),U_766),U_764)) ),
    inference(clausify,[status(thm)],[f_251_3]) ).

fof(f_252_1,plain,
    ! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),top_top(fun(X_a,bool)))),
    inference(fof_nnf,[status(thm)],[fact_162_subset__UNIV]) ).

fof(f_252_2,plain,
    ! [U_772,U_771] : hBOOL(hAPP(fun(U_772,bool),bool,hAPP(fun(U_772,bool),fun(fun(U_772,bool),bool),ord_less_eq(fun(U_772,bool)),U_771),top_top(fun(U_772,bool)))),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

cnf(f_252_3,plain,
    hBOOL(hAPP(fun(U_772,bool),bool,hAPP(fun(U_772,bool),fun(fun(U_772,bool),bool),ord_less_eq(fun(U_772,bool)),U_771),top_top(fun(U_772,bool)))),
    inference(clausify,[status(thm)],[f_252_2]) ).

fof(f_253_1,plain,
    ! [X_a,X_b,A_1,F,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B)) ),
    inference(fof_nnf,[status(thm)],[fact_163_subset__inj__on]) ).

fof(f_253_2,plain,
    ! [U_777,U_776,U_775,U_774,U_773] :
      ( hBOOL(hAPP(fun(U_777,bool),bool,hAPP(fun(U_777,U_776),fun(fun(U_777,bool),bool),inj_on(U_777,U_776),U_774),U_775))
      | ~ hBOOL(hAPP(fun(U_777,bool),bool,hAPP(fun(U_777,bool),fun(fun(U_777,bool),bool),ord_less_eq(fun(U_777,bool)),U_775),U_773))
      | ~ hBOOL(hAPP(fun(U_777,bool),bool,hAPP(fun(U_777,U_776),fun(fun(U_777,bool),bool),inj_on(U_777,U_776),U_774),U_773)) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

cnf(f_253_3,plain,
    ( hBOOL(hAPP(fun(U_777,bool),bool,hAPP(fun(U_777,U_776),fun(fun(U_777,bool),bool),inj_on(U_777,U_776),U_774),U_775))
    | ~ hBOOL(hAPP(fun(U_777,bool),bool,hAPP(fun(U_777,bool),fun(fun(U_777,bool),bool),ord_less_eq(fun(U_777,bool)),U_775),U_773))
    | ~ hBOOL(hAPP(fun(U_777,bool),bool,hAPP(fun(U_777,U_776),fun(fun(U_777,bool),bool),inj_on(U_777,U_776),U_774),U_773)) ),
    inference(clausify,[status(thm)],[f_253_2]) ).

fof(f_254_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
          | ti(X_a,X) = ti(X_a,Y) )
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_164_linorder__neqE__linordered__idom]) ).

fof(f_254_2,plain,
    ! [U_780] :
      ( ! [U_779,U_778] :
          ( hBOOL(hAPP(U_780,bool,hAPP(U_780,fun(U_780,bool),ord_less(U_780),U_778),U_779))
          | hBOOL(hAPP(U_780,bool,hAPP(U_780,fun(U_780,bool),ord_less(U_780),U_779),U_778))
          | ti(U_780,U_779) = ti(U_780,U_778) )
      | ~ linordered_idom(U_780) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

cnf(f_254_3,plain,
    ( hBOOL(hAPP(U_780,bool,hAPP(U_780,fun(U_780,bool),ord_less(U_780),U_778),U_779))
    | hBOOL(hAPP(U_780,bool,hAPP(U_780,fun(U_780,bool),ord_less(U_780),U_779),U_778))
    | ti(U_780,U_779) = ti(U_780,U_778)
    | ~ linordered_idom(U_780) ),
    inference(clausify,[status(thm)],[f_254_2]) ).

fof(f_255_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2,C_1] :
          ( ti(X_a,B_1) = ti(X_a,C_1)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2) )
      | ~ cancel_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_165_add__right__imp__eq]) ).

fof(f_255_2,plain,
    ! [U_784] :
      ( ! [U_783,U_782,U_781] :
          ( ti(U_784,U_783) = ti(U_784,U_781)
          | hAPP(U_784,U_784,hAPP(U_784,fun(U_784,U_784),plus_plus(U_784),U_783),U_782) != hAPP(U_784,U_784,hAPP(U_784,fun(U_784,U_784),plus_plus(U_784),U_781),U_782) )
      | ~ cancel_semigroup_add(U_784) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

cnf(f_255_3,plain,
    ( ti(U_784,U_783) = ti(U_784,U_781)
    | hAPP(U_784,U_784,hAPP(U_784,fun(U_784,U_784),plus_plus(U_784),U_783),U_782) != hAPP(U_784,U_784,hAPP(U_784,fun(U_784,U_784),plus_plus(U_784),U_781),U_782)
    | ~ cancel_semigroup_add(U_784) ),
    inference(clausify,[status(thm)],[f_255_2]) ).

fof(f_256_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1] :
          ( ti(X_a,B_1) = ti(X_a,C_1)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1) )
      | ~ cancel146912293up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_166_add__imp__eq]) ).

fof(f_256_2,plain,
    ! [U_788] :
      ( ! [U_787,U_786,U_785] :
          ( ti(U_788,U_786) = ti(U_788,U_785)
          | hAPP(U_788,U_788,hAPP(U_788,fun(U_788,U_788),plus_plus(U_788),U_787),U_786) != hAPP(U_788,U_788,hAPP(U_788,fun(U_788,U_788),plus_plus(U_788),U_787),U_785) )
      | ~ cancel146912293up_add(U_788) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

cnf(f_256_3,plain,
    ( ti(U_788,U_786) = ti(U_788,U_785)
    | hAPP(U_788,U_788,hAPP(U_788,fun(U_788,U_788),plus_plus(U_788),U_787),U_786) != hAPP(U_788,U_788,hAPP(U_788,fun(U_788,U_788),plus_plus(U_788),U_787),U_785)
    | ~ cancel146912293up_add(U_788) ),
    inference(clausify,[status(thm)],[f_256_2]) ).

fof(f_257_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1] :
          ( ti(X_a,B_1) = ti(X_a,C_1)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1) )
      | ~ cancel_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_167_add__left__imp__eq]) ).

fof(f_257_2,plain,
    ! [U_792] :
      ( ! [U_791,U_790,U_789] :
          ( ti(U_792,U_790) = ti(U_792,U_789)
          | hAPP(U_792,U_792,hAPP(U_792,fun(U_792,U_792),plus_plus(U_792),U_791),U_790) != hAPP(U_792,U_792,hAPP(U_792,fun(U_792,U_792),plus_plus(U_792),U_791),U_789) )
      | ~ cancel_semigroup_add(U_792) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

cnf(f_257_3,plain,
    ( ti(U_792,U_790) = ti(U_792,U_789)
    | hAPP(U_792,U_792,hAPP(U_792,fun(U_792,U_792),plus_plus(U_792),U_791),U_790) != hAPP(U_792,U_792,hAPP(U_792,fun(U_792,U_792),plus_plus(U_792),U_791),U_789)
    | ~ cancel_semigroup_add(U_792) ),
    inference(clausify,[status(thm)],[f_257_2]) ).

fof(f_258_1,plain,
    ! [X_a] :
      ( ! [Ba,Aa,Ca] :
          ( ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)
            | ti(X_a,Ba) != ti(X_a,Ca) )
          & ( ti(X_a,Ba) = ti(X_a,Ca)
            | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa) ) )
      | ~ cancel_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_168_add__right__cancel]) ).

fof(f_258_2,plain,
    ! [U_796] :
      ( ! [U_795,U_794,U_793] :
          ( ( hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_795),U_794) = hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_793),U_794)
            | ti(U_796,U_795) != ti(U_796,U_793) )
          & ( ti(U_796,U_795) = ti(U_796,U_793)
            | hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_795),U_794) != hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_793),U_794) ) )
      | ~ cancel_semigroup_add(U_796) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ! [U_796] :
      ( ( ! [U_802,U_800,U_798] :
            ( hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_802),U_800) = hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_798),U_800)
            | ti(U_796,U_802) != ti(U_796,U_798) )
        & ! [U_801,U_799,U_797] :
            ( ti(U_796,U_801) = ti(U_796,U_797)
            | hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_801),U_799) != hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_797),U_799) ) )
      | ~ cancel_semigroup_add(U_796) ),
    inference(miniscope,[status(thm)],[f_258_2]) ).

cnf(f_258_4,plain,
    ( ti(U_796,U_801) = ti(U_796,U_797)
    | hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_801),U_799) != hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_797),U_799)
    | ~ cancel_semigroup_add(U_796) ),
    inference(clausify,[status(thm)],[f_258_3]) ).

cnf(f_258_5,plain,
    ( hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_802),U_800) = hAPP(U_796,U_796,hAPP(U_796,fun(U_796,U_796),plus_plus(U_796),U_798),U_800)
    | ti(U_796,U_802) != ti(U_796,U_798)
    | ~ cancel_semigroup_add(U_796) ),
    inference(clausify,[status(thm)],[f_258_3]) ).

fof(f_259_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca] :
          ( ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)
            | ti(X_a,Ba) != ti(X_a,Ca) )
          & ( ti(X_a,Ba) = ti(X_a,Ca)
            | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca) ) )
      | ~ cancel_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_169_add__left__cancel]) ).

fof(f_259_2,plain,
    ! [U_806] :
      ( ! [U_805,U_804,U_803] :
          ( ( hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_805),U_804) = hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_805),U_803)
            | ti(U_806,U_804) != ti(U_806,U_803) )
          & ( ti(U_806,U_804) = ti(U_806,U_803)
            | hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_805),U_804) != hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_805),U_803) ) )
      | ~ cancel_semigroup_add(U_806) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ! [U_806] :
      ( ( ! [U_812,U_810,U_808] :
            ( hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_812),U_810) = hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_812),U_808)
            | ti(U_806,U_810) != ti(U_806,U_808) )
        & ! [U_811,U_809,U_807] :
            ( ti(U_806,U_809) = ti(U_806,U_807)
            | hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_811),U_809) != hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_811),U_807) ) )
      | ~ cancel_semigroup_add(U_806) ),
    inference(miniscope,[status(thm)],[f_259_2]) ).

cnf(f_259_4,plain,
    ( ti(U_806,U_809) = ti(U_806,U_807)
    | hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_811),U_809) != hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_811),U_807)
    | ~ cancel_semigroup_add(U_806) ),
    inference(clausify,[status(thm)],[f_259_3]) ).

cnf(f_259_5,plain,
    ( hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_812),U_810) = hAPP(U_806,U_806,hAPP(U_806,fun(U_806,U_806),plus_plus(U_806),U_812),U_808)
    | ti(U_806,U_810) != ti(U_806,U_808)
    | ~ cancel_semigroup_add(U_806) ),
    inference(clausify,[status(thm)],[f_259_3]) ).

fof(f_260_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))
      | ~ ab_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_170_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(f_260_2,plain,
    ! [U_816] :
      ( ! [U_815,U_814,U_813] : hAPP(U_816,U_816,hAPP(U_816,fun(U_816,U_816),plus_plus(U_816),hAPP(U_816,U_816,hAPP(U_816,fun(U_816,U_816),plus_plus(U_816),U_815),U_814)),U_813) = hAPP(U_816,U_816,hAPP(U_816,fun(U_816,U_816),plus_plus(U_816),U_815),hAPP(U_816,U_816,hAPP(U_816,fun(U_816,U_816),plus_plus(U_816),U_814),U_813))
      | ~ ab_semigroup_add(U_816) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

cnf(f_260_3,plain,
    ( hAPP(U_816,U_816,hAPP(U_816,fun(U_816,U_816),plus_plus(U_816),hAPP(U_816,U_816,hAPP(U_816,fun(U_816,U_816),plus_plus(U_816),U_815),U_814)),U_813) = hAPP(U_816,U_816,hAPP(U_816,fun(U_816,U_816),plus_plus(U_816),U_815),hAPP(U_816,U_816,hAPP(U_816,fun(U_816,U_816),plus_plus(U_816),U_814),U_813))
    | ~ ab_semigroup_add(U_816) ),
    inference(clausify,[status(thm)],[f_260_2]) ).

fof(f_261_1,plain,
    ! [X_a] :
      ( ! [X_2] :
          ( ( one_one(X_a) = ti(X_a,X_2)
            | ti(X_a,X_2) != one_one(X_a) )
          & ( ti(X_a,X_2) = one_one(X_a)
            | one_one(X_a) != ti(X_a,X_2) ) )
      | ~ one(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_171_one__reorient]) ).

fof(f_261_2,plain,
    ! [U_818] :
      ( ! [U_817] :
          ( ( one_one(U_818) = ti(U_818,U_817)
            | ti(U_818,U_817) != one_one(U_818) )
          & ( ti(U_818,U_817) = one_one(U_818)
            | one_one(U_818) != ti(U_818,U_817) ) )
      | ~ one(U_818) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ! [U_818] :
      ( ( ! [U_820] :
            ( one_one(U_818) = ti(U_818,U_820)
            | ti(U_818,U_820) != one_one(U_818) )
        & ! [U_819] :
            ( ti(U_818,U_819) = one_one(U_818)
            | one_one(U_818) != ti(U_818,U_819) ) )
      | ~ one(U_818) ),
    inference(miniscope,[status(thm)],[f_261_2]) ).

cnf(f_261_4,plain,
    ( ti(U_818,U_819) = one_one(U_818)
    | one_one(U_818) != ti(U_818,U_819)
    | ~ one(U_818) ),
    inference(clausify,[status(thm)],[f_261_3]) ).

cnf(f_261_5,plain,
    ( one_one(U_818) = ti(U_818,U_820)
    | ti(U_818,U_820) != one_one(U_818)
    | ~ one(U_818) ),
    inference(clausify,[status(thm)],[f_261_3]) ).

fof(f_262_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_172_add__le__imp__le__left]) ).

fof(f_262_2,plain,
    ! [U_824] :
      ( ! [U_823,U_822,U_821] :
          ( hBOOL(hAPP(U_824,bool,hAPP(U_824,fun(U_824,bool),ord_less_eq(U_824),U_822),U_821))
          | ~ hBOOL(hAPP(U_824,bool,hAPP(U_824,fun(U_824,bool),ord_less_eq(U_824),hAPP(U_824,U_824,hAPP(U_824,fun(U_824,U_824),plus_plus(U_824),U_823),U_822)),hAPP(U_824,U_824,hAPP(U_824,fun(U_824,U_824),plus_plus(U_824),U_823),U_821))) )
      | ~ ordere236663937imp_le(U_824) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

cnf(f_262_3,plain,
    ( hBOOL(hAPP(U_824,bool,hAPP(U_824,fun(U_824,bool),ord_less_eq(U_824),U_822),U_821))
    | ~ hBOOL(hAPP(U_824,bool,hAPP(U_824,fun(U_824,bool),ord_less_eq(U_824),hAPP(U_824,U_824,hAPP(U_824,fun(U_824,U_824),plus_plus(U_824),U_823),U_822)),hAPP(U_824,U_824,hAPP(U_824,fun(U_824,U_824),plus_plus(U_824),U_823),U_821)))
    | ~ ordere236663937imp_le(U_824) ),
    inference(clausify,[status(thm)],[f_262_2]) ).

fof(f_263_1,plain,
    ! [X_a] :
      ( ! [A_2,C_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_173_add__le__imp__le__right]) ).

fof(f_263_2,plain,
    ! [U_828] :
      ( ! [U_827,U_826,U_825] :
          ( hBOOL(hAPP(U_828,bool,hAPP(U_828,fun(U_828,bool),ord_less_eq(U_828),U_827),U_825))
          | ~ hBOOL(hAPP(U_828,bool,hAPP(U_828,fun(U_828,bool),ord_less_eq(U_828),hAPP(U_828,U_828,hAPP(U_828,fun(U_828,U_828),plus_plus(U_828),U_827),U_826)),hAPP(U_828,U_828,hAPP(U_828,fun(U_828,U_828),plus_plus(U_828),U_825),U_826))) )
      | ~ ordere236663937imp_le(U_828) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

cnf(f_263_3,plain,
    ( hBOOL(hAPP(U_828,bool,hAPP(U_828,fun(U_828,bool),ord_less_eq(U_828),U_827),U_825))
    | ~ hBOOL(hAPP(U_828,bool,hAPP(U_828,fun(U_828,bool),ord_less_eq(U_828),hAPP(U_828,U_828,hAPP(U_828,fun(U_828,U_828),plus_plus(U_828),U_827),U_826)),hAPP(U_828,U_828,hAPP(U_828,fun(U_828,U_828),plus_plus(U_828),U_825),U_826)))
    | ~ ordere236663937imp_le(U_828) ),
    inference(clausify,[status(thm)],[f_263_2]) ).

fof(f_264_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ ordere779506340up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_174_add__mono]) ).

fof(f_264_2,plain,
    ! [U_833] :
      ( ! [U_832,U_831,U_830,U_829] :
          ( hBOOL(hAPP(U_833,bool,hAPP(U_833,fun(U_833,bool),ord_less_eq(U_833),hAPP(U_833,U_833,hAPP(U_833,fun(U_833,U_833),plus_plus(U_833),U_830),U_832)),hAPP(U_833,U_833,hAPP(U_833,fun(U_833,U_833),plus_plus(U_833),U_829),U_831)))
          | ~ hBOOL(hAPP(U_833,bool,hAPP(U_833,fun(U_833,bool),ord_less_eq(U_833),U_832),U_831))
          | ~ hBOOL(hAPP(U_833,bool,hAPP(U_833,fun(U_833,bool),ord_less_eq(U_833),U_830),U_829)) )
      | ~ ordere779506340up_add(U_833) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

cnf(f_264_3,plain,
    ( hBOOL(hAPP(U_833,bool,hAPP(U_833,fun(U_833,bool),ord_less_eq(U_833),hAPP(U_833,U_833,hAPP(U_833,fun(U_833,U_833),plus_plus(U_833),U_830),U_832)),hAPP(U_833,U_833,hAPP(U_833,fun(U_833,U_833),plus_plus(U_833),U_829),U_831)))
    | ~ hBOOL(hAPP(U_833,bool,hAPP(U_833,fun(U_833,bool),ord_less_eq(U_833),U_832),U_831))
    | ~ hBOOL(hAPP(U_833,bool,hAPP(U_833,fun(U_833,bool),ord_less_eq(U_833),U_830),U_829))
    | ~ ordere779506340up_add(U_833) ),
    inference(clausify,[status(thm)],[f_264_2]) ).

fof(f_265_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ ordere779506340up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_175_add__left__mono]) ).

fof(f_265_2,plain,
    ! [U_837] :
      ( ! [U_836,U_835,U_834] :
          ( hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less_eq(U_837),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_836),U_835)),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_836),U_834)))
          | ~ hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less_eq(U_837),U_835),U_834)) )
      | ~ ordere779506340up_add(U_837) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

cnf(f_265_3,plain,
    ( hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less_eq(U_837),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_836),U_835)),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_836),U_834)))
    | ~ hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less_eq(U_837),U_835),U_834))
    | ~ ordere779506340up_add(U_837) ),
    inference(clausify,[status(thm)],[f_265_2]) ).

fof(f_266_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ ordere779506340up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_176_add__right__mono]) ).

fof(f_266_2,plain,
    ! [U_841] :
      ( ! [U_840,U_839,U_838] :
          ( hBOOL(hAPP(U_841,bool,hAPP(U_841,fun(U_841,bool),ord_less_eq(U_841),hAPP(U_841,U_841,hAPP(U_841,fun(U_841,U_841),plus_plus(U_841),U_839),U_840)),hAPP(U_841,U_841,hAPP(U_841,fun(U_841,U_841),plus_plus(U_841),U_838),U_840)))
          | ~ hBOOL(hAPP(U_841,bool,hAPP(U_841,fun(U_841,bool),ord_less_eq(U_841),U_839),U_838)) )
      | ~ ordere779506340up_add(U_841) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

cnf(f_266_3,plain,
    ( hBOOL(hAPP(U_841,bool,hAPP(U_841,fun(U_841,bool),ord_less_eq(U_841),hAPP(U_841,U_841,hAPP(U_841,fun(U_841,U_841),plus_plus(U_841),U_839),U_840)),hAPP(U_841,U_841,hAPP(U_841,fun(U_841,U_841),plus_plus(U_841),U_838),U_840)))
    | ~ hBOOL(hAPP(U_841,bool,hAPP(U_841,fun(U_841,bool),ord_less_eq(U_841),U_839),U_838))
    | ~ ordere779506340up_add(U_841) ),
    inference(clausify,[status(thm)],[f_266_2]) ).

fof(f_267_1,plain,
    ! [X_a] :
      ( ! [Ca,Aa,Ba] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Ba)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Ba))) ) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_177_add__le__cancel__left]) ).

fof(f_267_2,plain,
    ! [U_845] :
      ( ! [U_844,U_843,U_842] :
          ( ( hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_844),U_843)),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_844),U_842)))
            | ~ hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),U_843),U_842)) )
          & ( hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),U_843),U_842))
            | ~ hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_844),U_843)),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_844),U_842))) ) )
      | ~ ordere236663937imp_le(U_845) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_845] :
      ( ( ! [U_851,U_849,U_847] :
            ( hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_851),U_849)),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_851),U_847)))
            | ~ hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),U_849),U_847)) )
        & ! [U_850,U_848,U_846] :
            ( hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),U_848),U_846))
            | ~ hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_850),U_848)),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_850),U_846))) ) )
      | ~ ordere236663937imp_le(U_845) ),
    inference(miniscope,[status(thm)],[f_267_2]) ).

cnf(f_267_4,plain,
    ( hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),U_848),U_846))
    | ~ hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_850),U_848)),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_850),U_846)))
    | ~ ordere236663937imp_le(U_845) ),
    inference(clausify,[status(thm)],[f_267_3]) ).

cnf(f_267_5,plain,
    ( hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_851),U_849)),hAPP(U_845,U_845,hAPP(U_845,fun(U_845,U_845),plus_plus(U_845),U_851),U_847)))
    | ~ hBOOL(hAPP(U_845,bool,hAPP(U_845,fun(U_845,bool),ord_less_eq(U_845),U_849),U_847))
    | ~ ordere236663937imp_le(U_845) ),
    inference(clausify,[status(thm)],[f_267_3]) ).

fof(f_268_1,plain,
    ! [X_a] :
      ( ! [Aa,Ca,Ba] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Ca)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Ca))) ) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_178_add__le__cancel__right]) ).

fof(f_268_2,plain,
    ! [U_855] :
      ( ! [U_854,U_853,U_852] :
          ( ( hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_854),U_853)),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_852),U_853)))
            | ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),U_854),U_852)) )
          & ( hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),U_854),U_852))
            | ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_854),U_853)),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_852),U_853))) ) )
      | ~ ordere236663937imp_le(U_855) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ! [U_855] :
      ( ( ! [U_861,U_859,U_857] :
            ( hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_861),U_859)),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_857),U_859)))
            | ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),U_861),U_857)) )
        & ! [U_860,U_858,U_856] :
            ( hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),U_860),U_856))
            | ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_860),U_858)),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_856),U_858))) ) )
      | ~ ordere236663937imp_le(U_855) ),
    inference(miniscope,[status(thm)],[f_268_2]) ).

cnf(f_268_4,plain,
    ( hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),U_860),U_856))
    | ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_860),U_858)),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_856),U_858)))
    | ~ ordere236663937imp_le(U_855) ),
    inference(clausify,[status(thm)],[f_268_3]) ).

cnf(f_268_5,plain,
    ( hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_861),U_859)),hAPP(U_855,U_855,hAPP(U_855,fun(U_855,U_855),plus_plus(U_855),U_857),U_859)))
    | ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),U_861),U_857))
    | ~ ordere236663937imp_le(U_855) ),
    inference(clausify,[status(thm)],[f_268_3]) ).

fof(f_269_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_179_add__less__imp__less__left]) ).

fof(f_269_2,plain,
    ! [U_865] :
      ( ! [U_864,U_863,U_862] :
          ( hBOOL(hAPP(U_865,bool,hAPP(U_865,fun(U_865,bool),ord_less(U_865),U_863),U_862))
          | ~ hBOOL(hAPP(U_865,bool,hAPP(U_865,fun(U_865,bool),ord_less(U_865),hAPP(U_865,U_865,hAPP(U_865,fun(U_865,U_865),plus_plus(U_865),U_864),U_863)),hAPP(U_865,U_865,hAPP(U_865,fun(U_865,U_865),plus_plus(U_865),U_864),U_862))) )
      | ~ ordere236663937imp_le(U_865) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

cnf(f_269_3,plain,
    ( hBOOL(hAPP(U_865,bool,hAPP(U_865,fun(U_865,bool),ord_less(U_865),U_863),U_862))
    | ~ hBOOL(hAPP(U_865,bool,hAPP(U_865,fun(U_865,bool),ord_less(U_865),hAPP(U_865,U_865,hAPP(U_865,fun(U_865,U_865),plus_plus(U_865),U_864),U_863)),hAPP(U_865,U_865,hAPP(U_865,fun(U_865,U_865),plus_plus(U_865),U_864),U_862)))
    | ~ ordere236663937imp_le(U_865) ),
    inference(clausify,[status(thm)],[f_269_2]) ).

fof(f_270_1,plain,
    ! [X_a] :
      ( ! [A_2,C_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_180_add__less__imp__less__right]) ).

fof(f_270_2,plain,
    ! [U_869] :
      ( ! [U_868,U_867,U_866] :
          ( hBOOL(hAPP(U_869,bool,hAPP(U_869,fun(U_869,bool),ord_less(U_869),U_868),U_866))
          | ~ hBOOL(hAPP(U_869,bool,hAPP(U_869,fun(U_869,bool),ord_less(U_869),hAPP(U_869,U_869,hAPP(U_869,fun(U_869,U_869),plus_plus(U_869),U_868),U_867)),hAPP(U_869,U_869,hAPP(U_869,fun(U_869,U_869),plus_plus(U_869),U_866),U_867))) )
      | ~ ordere236663937imp_le(U_869) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

cnf(f_270_3,plain,
    ( hBOOL(hAPP(U_869,bool,hAPP(U_869,fun(U_869,bool),ord_less(U_869),U_868),U_866))
    | ~ hBOOL(hAPP(U_869,bool,hAPP(U_869,fun(U_869,bool),ord_less(U_869),hAPP(U_869,U_869,hAPP(U_869,fun(U_869,U_869),plus_plus(U_869),U_868),U_867)),hAPP(U_869,U_869,hAPP(U_869,fun(U_869,U_869),plus_plus(U_869),U_866),U_867)))
    | ~ ordere236663937imp_le(U_869) ),
    inference(clausify,[status(thm)],[f_270_2]) ).

fof(f_271_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_181_add__strict__mono]) ).

fof(f_271_2,plain,
    ! [U_874] :
      ( ! [U_873,U_872,U_871,U_870] :
          ( hBOOL(hAPP(U_874,bool,hAPP(U_874,fun(U_874,bool),ord_less(U_874),hAPP(U_874,U_874,hAPP(U_874,fun(U_874,U_874),plus_plus(U_874),U_871),U_873)),hAPP(U_874,U_874,hAPP(U_874,fun(U_874,U_874),plus_plus(U_874),U_870),U_872)))
          | ~ hBOOL(hAPP(U_874,bool,hAPP(U_874,fun(U_874,bool),ord_less(U_874),U_873),U_872))
          | ~ hBOOL(hAPP(U_874,bool,hAPP(U_874,fun(U_874,bool),ord_less(U_874),U_871),U_870)) )
      | ~ ordere223160158up_add(U_874) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

cnf(f_271_3,plain,
    ( hBOOL(hAPP(U_874,bool,hAPP(U_874,fun(U_874,bool),ord_less(U_874),hAPP(U_874,U_874,hAPP(U_874,fun(U_874,U_874),plus_plus(U_874),U_871),U_873)),hAPP(U_874,U_874,hAPP(U_874,fun(U_874,U_874),plus_plus(U_874),U_870),U_872)))
    | ~ hBOOL(hAPP(U_874,bool,hAPP(U_874,fun(U_874,bool),ord_less(U_874),U_873),U_872))
    | ~ hBOOL(hAPP(U_874,bool,hAPP(U_874,fun(U_874,bool),ord_less(U_874),U_871),U_870))
    | ~ ordere223160158up_add(U_874) ),
    inference(clausify,[status(thm)],[f_271_2]) ).

fof(f_272_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_182_add__strict__left__mono]) ).

fof(f_272_2,plain,
    ! [U_878] :
      ( ! [U_877,U_876,U_875] :
          ( hBOOL(hAPP(U_878,bool,hAPP(U_878,fun(U_878,bool),ord_less(U_878),hAPP(U_878,U_878,hAPP(U_878,fun(U_878,U_878),plus_plus(U_878),U_877),U_876)),hAPP(U_878,U_878,hAPP(U_878,fun(U_878,U_878),plus_plus(U_878),U_877),U_875)))
          | ~ hBOOL(hAPP(U_878,bool,hAPP(U_878,fun(U_878,bool),ord_less(U_878),U_876),U_875)) )
      | ~ ordere223160158up_add(U_878) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

cnf(f_272_3,plain,
    ( hBOOL(hAPP(U_878,bool,hAPP(U_878,fun(U_878,bool),ord_less(U_878),hAPP(U_878,U_878,hAPP(U_878,fun(U_878,U_878),plus_plus(U_878),U_877),U_876)),hAPP(U_878,U_878,hAPP(U_878,fun(U_878,U_878),plus_plus(U_878),U_877),U_875)))
    | ~ hBOOL(hAPP(U_878,bool,hAPP(U_878,fun(U_878,bool),ord_less(U_878),U_876),U_875))
    | ~ ordere223160158up_add(U_878) ),
    inference(clausify,[status(thm)],[f_272_2]) ).

fof(f_273_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_183_add__strict__right__mono]) ).

fof(f_273_2,plain,
    ! [U_882] :
      ( ! [U_881,U_880,U_879] :
          ( hBOOL(hAPP(U_882,bool,hAPP(U_882,fun(U_882,bool),ord_less(U_882),hAPP(U_882,U_882,hAPP(U_882,fun(U_882,U_882),plus_plus(U_882),U_880),U_881)),hAPP(U_882,U_882,hAPP(U_882,fun(U_882,U_882),plus_plus(U_882),U_879),U_881)))
          | ~ hBOOL(hAPP(U_882,bool,hAPP(U_882,fun(U_882,bool),ord_less(U_882),U_880),U_879)) )
      | ~ ordere223160158up_add(U_882) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

cnf(f_273_3,plain,
    ( hBOOL(hAPP(U_882,bool,hAPP(U_882,fun(U_882,bool),ord_less(U_882),hAPP(U_882,U_882,hAPP(U_882,fun(U_882,U_882),plus_plus(U_882),U_880),U_881)),hAPP(U_882,U_882,hAPP(U_882,fun(U_882,U_882),plus_plus(U_882),U_879),U_881)))
    | ~ hBOOL(hAPP(U_882,bool,hAPP(U_882,fun(U_882,bool),ord_less(U_882),U_880),U_879))
    | ~ ordere223160158up_add(U_882) ),
    inference(clausify,[status(thm)],[f_273_2]) ).

fof(f_274_1,plain,
    ! [X_a] :
      ( ! [Ca,Aa,Ba] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Ba)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ca),Ba))) ) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_184_add__less__cancel__left]) ).

fof(f_274_2,plain,
    ! [U_886] :
      ( ! [U_885,U_884,U_883] :
          ( ( hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_885),U_884)),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_885),U_883)))
            | ~ hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),U_884),U_883)) )
          & ( hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),U_884),U_883))
            | ~ hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_885),U_884)),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_885),U_883))) ) )
      | ~ ordere236663937imp_le(U_886) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ! [U_886] :
      ( ( ! [U_892,U_890,U_888] :
            ( hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_892),U_890)),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_892),U_888)))
            | ~ hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),U_890),U_888)) )
        & ! [U_891,U_889,U_887] :
            ( hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),U_889),U_887))
            | ~ hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_891),U_889)),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_891),U_887))) ) )
      | ~ ordere236663937imp_le(U_886) ),
    inference(miniscope,[status(thm)],[f_274_2]) ).

cnf(f_274_4,plain,
    ( hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),U_889),U_887))
    | ~ hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_891),U_889)),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_891),U_887)))
    | ~ ordere236663937imp_le(U_886) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

cnf(f_274_5,plain,
    ( hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_892),U_890)),hAPP(U_886,U_886,hAPP(U_886,fun(U_886,U_886),plus_plus(U_886),U_892),U_888)))
    | ~ hBOOL(hAPP(U_886,bool,hAPP(U_886,fun(U_886,bool),ord_less(U_886),U_890),U_888))
    | ~ ordere236663937imp_le(U_886) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

fof(f_275_1,plain,
    ! [X_a] :
      ( ! [Aa,Ca,Ba] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Ca)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Ca))) ) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_185_add__less__cancel__right]) ).

fof(f_275_2,plain,
    ! [U_896] :
      ( ! [U_895,U_894,U_893] :
          ( ( hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_895),U_894)),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_893),U_894)))
            | ~ hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),U_895),U_893)) )
          & ( hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),U_895),U_893))
            | ~ hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_895),U_894)),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_893),U_894))) ) )
      | ~ ordere236663937imp_le(U_896) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ! [U_896] :
      ( ( ! [U_902,U_900,U_898] :
            ( hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_902),U_900)),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_898),U_900)))
            | ~ hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),U_902),U_898)) )
        & ! [U_901,U_899,U_897] :
            ( hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),U_901),U_897))
            | ~ hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_901),U_899)),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_897),U_899))) ) )
      | ~ ordere236663937imp_le(U_896) ),
    inference(miniscope,[status(thm)],[f_275_2]) ).

cnf(f_275_4,plain,
    ( hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),U_901),U_897))
    | ~ hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_901),U_899)),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_897),U_899)))
    | ~ ordere236663937imp_le(U_896) ),
    inference(clausify,[status(thm)],[f_275_3]) ).

cnf(f_275_5,plain,
    ( hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_902),U_900)),hAPP(U_896,U_896,hAPP(U_896,fun(U_896,U_896),plus_plus(U_896),U_898),U_900)))
    | ~ hBOOL(hAPP(U_896,bool,hAPP(U_896,fun(U_896,bool),ord_less(U_896),U_902),U_898))
    | ~ ordere236663937imp_le(U_896) ),
    inference(clausify,[status(thm)],[f_275_3]) ).

fof(f_276_1,plain,
    ! [X_a,X_b] :
      ( ! [F,G] :
          ( hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G))
          | ? [X_1] : ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))) )
      | ~ ord(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_186_le__funI]) ).

fof(f_276_2,plain,
    ! [U_907,U_906] :
      ( ! [U_905,U_904] :
          ( hBOOL(hAPP(fun(U_907,U_906),bool,hAPP(fun(U_907,U_906),fun(fun(U_907,U_906),bool),ord_less_eq(fun(U_907,U_906)),U_905),U_904))
          | ? [U_903] : ~ hBOOL(hAPP(U_906,bool,hAPP(U_906,fun(U_906,bool),ord_less_eq(U_906),hAPP(U_907,U_906,U_905,U_903)),hAPP(U_907,U_906,U_904,U_903))) )
      | ~ ord(U_906) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ! [U_907,U_906] :
      ( ! [U_905,U_904] :
          ( hBOOL(hAPP(fun(U_907,U_906),bool,hAPP(fun(U_907,U_906),fun(fun(U_907,U_906),bool),ord_less_eq(fun(U_907,U_906)),U_905),U_904))
          | ~ hBOOL(hAPP(U_906,bool,hAPP(U_906,fun(U_906,bool),ord_less_eq(U_906),hAPP(U_907,U_906,U_905,sK51(U_907,U_906,U_905,U_904))),hAPP(U_907,U_906,U_904,sK51(U_907,U_906,U_905,U_904)))) )
      | ~ ord(U_906) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_903,sK51(U_907,U_906,U_905,U_904))],[f_276_2]) ).

cnf(f_276_4,plain,
    ( hBOOL(hAPP(fun(U_907,U_906),bool,hAPP(fun(U_907,U_906),fun(fun(U_907,U_906),bool),ord_less_eq(fun(U_907,U_906)),U_905),U_904))
    | ~ hBOOL(hAPP(U_906,bool,hAPP(U_906,fun(U_906,bool),ord_less_eq(U_906),hAPP(U_907,U_906,U_905,sK51(U_907,U_906,U_905,U_904))),hAPP(U_907,U_906,U_904,sK51(U_907,U_906,U_905,U_904))))
    | ~ ord(U_906) ),
    inference(clausify,[status(thm)],[f_276_3]) ).

fof(f_277_1,plain,
    ! [X_b,X_a] :
      ( ! [Ca,F,Ba,Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ca)),Aa))
          | ? [X_1,Y_2] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_1)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),Ba))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) )
      | ~ ord(X_b)
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_187_xt6]) ).

fof(f_277_2,plain,
    ! [U_915,U_914] :
      ( ! [U_913,U_912,U_911,U_910] :
          ( hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less(U_914),hAPP(U_915,U_914,U_912,U_913)),U_910))
          | ? [U_909,U_908] :
              ( ~ hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less(U_914),hAPP(U_915,U_914,U_912,U_908)),hAPP(U_915,U_914,U_912,U_909)))
              & hBOOL(hAPP(U_915,bool,hAPP(U_915,fun(U_915,bool),ord_less(U_915),U_908),U_909)) )
          | ~ hBOOL(hAPP(U_915,bool,hAPP(U_915,fun(U_915,bool),ord_less(U_915),U_913),U_911))
          | ~ hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less_eq(U_914),hAPP(U_915,U_914,U_912,U_911)),U_910)) )
      | ~ ord(U_915)
      | ~ order(U_914) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_915,U_914] :
      ( ! [U_913,U_912,U_911,U_910] :
          ( hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less(U_914),hAPP(U_915,U_914,U_912,U_913)),U_910))
          | ? [U_908] :
              ( ~ hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less(U_914),hAPP(U_915,U_914,U_912,U_908)),hAPP(U_915,U_914,U_912,sK52(U_915,U_914,U_913,U_912,U_911,U_910))))
              & hBOOL(hAPP(U_915,bool,hAPP(U_915,fun(U_915,bool),ord_less(U_915),U_908),sK52(U_915,U_914,U_913,U_912,U_911,U_910))) )
          | ~ hBOOL(hAPP(U_915,bool,hAPP(U_915,fun(U_915,bool),ord_less(U_915),U_913),U_911))
          | ~ hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less_eq(U_914),hAPP(U_915,U_914,U_912,U_911)),U_910)) )
      | ~ ord(U_915)
      | ~ order(U_914) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_909,sK52(U_915,U_914,U_913,U_912,U_911,U_910))],[f_277_2]) ).

fof(f_277_4,plain,
    ! [U_915,U_914] :
      ( ! [U_913,U_912,U_911,U_910] :
          ( hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less(U_914),hAPP(U_915,U_914,U_912,U_913)),U_910))
          | ( ~ hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less(U_914),hAPP(U_915,U_914,U_912,sK53(U_915,U_914,U_913,U_912,U_911,U_910))),hAPP(U_915,U_914,U_912,sK52(U_915,U_914,U_913,U_912,U_911,U_910))))
            & hBOOL(hAPP(U_915,bool,hAPP(U_915,fun(U_915,bool),ord_less(U_915),sK53(U_915,U_914,U_913,U_912,U_911,U_910)),sK52(U_915,U_914,U_913,U_912,U_911,U_910))) )
          | ~ hBOOL(hAPP(U_915,bool,hAPP(U_915,fun(U_915,bool),ord_less(U_915),U_913),U_911))
          | ~ hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less_eq(U_914),hAPP(U_915,U_914,U_912,U_911)),U_910)) )
      | ~ ord(U_915)
      | ~ order(U_914) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_908,sK53(U_915,U_914,U_913,U_912,U_911,U_910))],[f_277_3]) ).

cnf(f_277_5,plain,
    ( hBOOL(hAPP(U_915,bool,hAPP(U_915,fun(U_915,bool),ord_less(U_915),sK53(U_915,U_914,U_913,U_912,U_911,U_910)),sK52(U_915,U_914,U_913,U_912,U_911,U_910)))
    | hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less(U_914),hAPP(U_915,U_914,U_912,U_913)),U_910))
    | ~ hBOOL(hAPP(U_915,bool,hAPP(U_915,fun(U_915,bool),ord_less(U_915),U_913),U_911))
    | ~ hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less_eq(U_914),hAPP(U_915,U_914,U_912,U_911)),U_910))
    | ~ ord(U_915)
    | ~ order(U_914) ),
    inference(clausify,[status(thm)],[f_277_4]) ).

cnf(f_277_6,plain,
    ( ~ hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less(U_914),hAPP(U_915,U_914,U_912,sK53(U_915,U_914,U_913,U_912,U_911,U_910))),hAPP(U_915,U_914,U_912,sK52(U_915,U_914,U_913,U_912,U_911,U_910))))
    | hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less(U_914),hAPP(U_915,U_914,U_912,U_913)),U_910))
    | ~ hBOOL(hAPP(U_915,bool,hAPP(U_915,fun(U_915,bool),ord_less(U_915),U_913),U_911))
    | ~ hBOOL(hAPP(U_914,bool,hAPP(U_914,fun(U_914,bool),ord_less_eq(U_914),hAPP(U_915,U_914,U_912,U_911)),U_910))
    | ~ ord(U_915)
    | ~ order(U_914) ),
    inference(clausify,[status(thm)],[f_277_4]) ).

fof(f_278_1,plain,
    ! [X_b,X_a] :
      ( ! [Ca,F,Ba,Aa] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ca)),Aa))
          | ? [X_1,Y_2] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_1)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),Ba))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) )
      | ~ order(X_b)
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_188_xt4]) ).

fof(f_278_2,plain,
    ! [U_923,U_922] :
      ( ! [U_921,U_920,U_919,U_918] :
          ( hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less(U_922),hAPP(U_923,U_922,U_920,U_921)),U_918))
          | ? [U_917,U_916] :
              ( ~ hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less_eq(U_922),hAPP(U_923,U_922,U_920,U_916)),hAPP(U_923,U_922,U_920,U_917)))
              & hBOOL(hAPP(U_923,bool,hAPP(U_923,fun(U_923,bool),ord_less_eq(U_923),U_916),U_917)) )
          | ~ hBOOL(hAPP(U_923,bool,hAPP(U_923,fun(U_923,bool),ord_less_eq(U_923),U_921),U_919))
          | ~ hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less(U_922),hAPP(U_923,U_922,U_920,U_919)),U_918)) )
      | ~ order(U_923)
      | ~ order(U_922) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ! [U_923,U_922] :
      ( ! [U_921,U_920,U_919,U_918] :
          ( hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less(U_922),hAPP(U_923,U_922,U_920,U_921)),U_918))
          | ? [U_916] :
              ( ~ hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less_eq(U_922),hAPP(U_923,U_922,U_920,U_916)),hAPP(U_923,U_922,U_920,sK54(U_923,U_922,U_921,U_920,U_919,U_918))))
              & hBOOL(hAPP(U_923,bool,hAPP(U_923,fun(U_923,bool),ord_less_eq(U_923),U_916),sK54(U_923,U_922,U_921,U_920,U_919,U_918))) )
          | ~ hBOOL(hAPP(U_923,bool,hAPP(U_923,fun(U_923,bool),ord_less_eq(U_923),U_921),U_919))
          | ~ hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less(U_922),hAPP(U_923,U_922,U_920,U_919)),U_918)) )
      | ~ order(U_923)
      | ~ order(U_922) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_917,sK54(U_923,U_922,U_921,U_920,U_919,U_918))],[f_278_2]) ).

fof(f_278_4,plain,
    ! [U_923,U_922] :
      ( ! [U_921,U_920,U_919,U_918] :
          ( hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less(U_922),hAPP(U_923,U_922,U_920,U_921)),U_918))
          | ( ~ hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less_eq(U_922),hAPP(U_923,U_922,U_920,sK55(U_923,U_922,U_921,U_920,U_919,U_918))),hAPP(U_923,U_922,U_920,sK54(U_923,U_922,U_921,U_920,U_919,U_918))))
            & hBOOL(hAPP(U_923,bool,hAPP(U_923,fun(U_923,bool),ord_less_eq(U_923),sK55(U_923,U_922,U_921,U_920,U_919,U_918)),sK54(U_923,U_922,U_921,U_920,U_919,U_918))) )
          | ~ hBOOL(hAPP(U_923,bool,hAPP(U_923,fun(U_923,bool),ord_less_eq(U_923),U_921),U_919))
          | ~ hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less(U_922),hAPP(U_923,U_922,U_920,U_919)),U_918)) )
      | ~ order(U_923)
      | ~ order(U_922) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_916,sK55(U_923,U_922,U_921,U_920,U_919,U_918))],[f_278_3]) ).

cnf(f_278_5,plain,
    ( hBOOL(hAPP(U_923,bool,hAPP(U_923,fun(U_923,bool),ord_less_eq(U_923),sK55(U_923,U_922,U_921,U_920,U_919,U_918)),sK54(U_923,U_922,U_921,U_920,U_919,U_918)))
    | hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less(U_922),hAPP(U_923,U_922,U_920,U_921)),U_918))
    | ~ hBOOL(hAPP(U_923,bool,hAPP(U_923,fun(U_923,bool),ord_less_eq(U_923),U_921),U_919))
    | ~ hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less(U_922),hAPP(U_923,U_922,U_920,U_919)),U_918))
    | ~ order(U_923)
    | ~ order(U_922) ),
    inference(clausify,[status(thm)],[f_278_4]) ).

cnf(f_278_6,plain,
    ( ~ hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less_eq(U_922),hAPP(U_923,U_922,U_920,sK55(U_923,U_922,U_921,U_920,U_919,U_918))),hAPP(U_923,U_922,U_920,sK54(U_923,U_922,U_921,U_920,U_919,U_918))))
    | hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less(U_922),hAPP(U_923,U_922,U_920,U_921)),U_918))
    | ~ hBOOL(hAPP(U_923,bool,hAPP(U_923,fun(U_923,bool),ord_less_eq(U_923),U_921),U_919))
    | ~ hBOOL(hAPP(U_922,bool,hAPP(U_922,fun(U_922,bool),ord_less(U_922),hAPP(U_923,U_922,U_920,U_919)),U_918))
    | ~ order(U_923)
    | ~ order(U_922) ),
    inference(clausify,[status(thm)],[f_278_4]) ).

fof(f_279_1,plain,
    ! [X_a,X_b] :
      ( ! [Ca,Aa,F,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ca)))
          | ? [X_1,Y_2] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_2)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),Ca))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_b,X_a,F,Ba))) )
      | ~ order(X_a)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_189_order__le__less__subst1]) ).

fof(f_279_2,plain,
    ! [U_931,U_930] :
      ( ! [U_929,U_928,U_927,U_926] :
          ( hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less(U_931),U_928),hAPP(U_930,U_931,U_927,U_929)))
          | ? [U_925,U_924] :
              ( ~ hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less(U_931),hAPP(U_930,U_931,U_927,U_925)),hAPP(U_930,U_931,U_927,U_924)))
              & hBOOL(hAPP(U_930,bool,hAPP(U_930,fun(U_930,bool),ord_less(U_930),U_925),U_924)) )
          | ~ hBOOL(hAPP(U_930,bool,hAPP(U_930,fun(U_930,bool),ord_less(U_930),U_926),U_929))
          | ~ hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less_eq(U_931),U_928),hAPP(U_930,U_931,U_927,U_926))) )
      | ~ order(U_931)
      | ~ order(U_930) ),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ! [U_931,U_930] :
      ( ! [U_929,U_928,U_927,U_926] :
          ( hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less(U_931),U_928),hAPP(U_930,U_931,U_927,U_929)))
          | ? [U_924] :
              ( ~ hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less(U_931),hAPP(U_930,U_931,U_927,sK56(U_931,U_930,U_929,U_928,U_927,U_926))),hAPP(U_930,U_931,U_927,U_924)))
              & hBOOL(hAPP(U_930,bool,hAPP(U_930,fun(U_930,bool),ord_less(U_930),sK56(U_931,U_930,U_929,U_928,U_927,U_926)),U_924)) )
          | ~ hBOOL(hAPP(U_930,bool,hAPP(U_930,fun(U_930,bool),ord_less(U_930),U_926),U_929))
          | ~ hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less_eq(U_931),U_928),hAPP(U_930,U_931,U_927,U_926))) )
      | ~ order(U_931)
      | ~ order(U_930) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_925,sK56(U_931,U_930,U_929,U_928,U_927,U_926))],[f_279_2]) ).

fof(f_279_4,plain,
    ! [U_931,U_930] :
      ( ! [U_929,U_928,U_927,U_926] :
          ( hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less(U_931),U_928),hAPP(U_930,U_931,U_927,U_929)))
          | ( ~ hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less(U_931),hAPP(U_930,U_931,U_927,sK56(U_931,U_930,U_929,U_928,U_927,U_926))),hAPP(U_930,U_931,U_927,sK57(U_931,U_930,U_929,U_928,U_927,U_926))))
            & hBOOL(hAPP(U_930,bool,hAPP(U_930,fun(U_930,bool),ord_less(U_930),sK56(U_931,U_930,U_929,U_928,U_927,U_926)),sK57(U_931,U_930,U_929,U_928,U_927,U_926))) )
          | ~ hBOOL(hAPP(U_930,bool,hAPP(U_930,fun(U_930,bool),ord_less(U_930),U_926),U_929))
          | ~ hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less_eq(U_931),U_928),hAPP(U_930,U_931,U_927,U_926))) )
      | ~ order(U_931)
      | ~ order(U_930) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_924,sK57(U_931,U_930,U_929,U_928,U_927,U_926))],[f_279_3]) ).

cnf(f_279_5,plain,
    ( hBOOL(hAPP(U_930,bool,hAPP(U_930,fun(U_930,bool),ord_less(U_930),sK56(U_931,U_930,U_929,U_928,U_927,U_926)),sK57(U_931,U_930,U_929,U_928,U_927,U_926)))
    | hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less(U_931),U_928),hAPP(U_930,U_931,U_927,U_929)))
    | ~ hBOOL(hAPP(U_930,bool,hAPP(U_930,fun(U_930,bool),ord_less(U_930),U_926),U_929))
    | ~ hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less_eq(U_931),U_928),hAPP(U_930,U_931,U_927,U_926)))
    | ~ order(U_931)
    | ~ order(U_930) ),
    inference(clausify,[status(thm)],[f_279_4]) ).

cnf(f_279_6,plain,
    ( ~ hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less(U_931),hAPP(U_930,U_931,U_927,sK56(U_931,U_930,U_929,U_928,U_927,U_926))),hAPP(U_930,U_931,U_927,sK57(U_931,U_930,U_929,U_928,U_927,U_926))))
    | hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less(U_931),U_928),hAPP(U_930,U_931,U_927,U_929)))
    | ~ hBOOL(hAPP(U_930,bool,hAPP(U_930,fun(U_930,bool),ord_less(U_930),U_926),U_929))
    | ~ hBOOL(hAPP(U_931,bool,hAPP(U_931,fun(U_931,bool),ord_less_eq(U_931),U_928),hAPP(U_930,U_931,U_927,U_926)))
    | ~ order(U_931)
    | ~ order(U_930) ),
    inference(clausify,[status(thm)],[f_279_4]) ).

fof(f_280_1,plain,
    ! [X_a,X_b] :
      ( ! [Ca,Aa,F,Ba] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ca)))
          | ? [X_1,Y_2] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_2)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),Ca))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ba))) )
      | ~ order(X_a)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_190_order__less__le__subst1]) ).

fof(f_280_2,plain,
    ! [U_939,U_938] :
      ( ! [U_937,U_936,U_935,U_934] :
          ( hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less(U_939),U_936),hAPP(U_938,U_939,U_935,U_937)))
          | ? [U_933,U_932] :
              ( ~ hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less_eq(U_939),hAPP(U_938,U_939,U_935,U_933)),hAPP(U_938,U_939,U_935,U_932)))
              & hBOOL(hAPP(U_938,bool,hAPP(U_938,fun(U_938,bool),ord_less_eq(U_938),U_933),U_932)) )
          | ~ hBOOL(hAPP(U_938,bool,hAPP(U_938,fun(U_938,bool),ord_less_eq(U_938),U_934),U_937))
          | ~ hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less(U_939),U_936),hAPP(U_938,U_939,U_935,U_934))) )
      | ~ order(U_939)
      | ~ order(U_938) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

fof(f_280_3,plain,
    ! [U_939,U_938] :
      ( ! [U_937,U_936,U_935,U_934] :
          ( hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less(U_939),U_936),hAPP(U_938,U_939,U_935,U_937)))
          | ? [U_932] :
              ( ~ hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less_eq(U_939),hAPP(U_938,U_939,U_935,sK58(U_939,U_938,U_937,U_936,U_935,U_934))),hAPP(U_938,U_939,U_935,U_932)))
              & hBOOL(hAPP(U_938,bool,hAPP(U_938,fun(U_938,bool),ord_less_eq(U_938),sK58(U_939,U_938,U_937,U_936,U_935,U_934)),U_932)) )
          | ~ hBOOL(hAPP(U_938,bool,hAPP(U_938,fun(U_938,bool),ord_less_eq(U_938),U_934),U_937))
          | ~ hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less(U_939),U_936),hAPP(U_938,U_939,U_935,U_934))) )
      | ~ order(U_939)
      | ~ order(U_938) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_933,sK58(U_939,U_938,U_937,U_936,U_935,U_934))],[f_280_2]) ).

fof(f_280_4,plain,
    ! [U_939,U_938] :
      ( ! [U_937,U_936,U_935,U_934] :
          ( hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less(U_939),U_936),hAPP(U_938,U_939,U_935,U_937)))
          | ( ~ hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less_eq(U_939),hAPP(U_938,U_939,U_935,sK58(U_939,U_938,U_937,U_936,U_935,U_934))),hAPP(U_938,U_939,U_935,sK59(U_939,U_938,U_937,U_936,U_935,U_934))))
            & hBOOL(hAPP(U_938,bool,hAPP(U_938,fun(U_938,bool),ord_less_eq(U_938),sK58(U_939,U_938,U_937,U_936,U_935,U_934)),sK59(U_939,U_938,U_937,U_936,U_935,U_934))) )
          | ~ hBOOL(hAPP(U_938,bool,hAPP(U_938,fun(U_938,bool),ord_less_eq(U_938),U_934),U_937))
          | ~ hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less(U_939),U_936),hAPP(U_938,U_939,U_935,U_934))) )
      | ~ order(U_939)
      | ~ order(U_938) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_932,sK59(U_939,U_938,U_937,U_936,U_935,U_934))],[f_280_3]) ).

cnf(f_280_5,plain,
    ( hBOOL(hAPP(U_938,bool,hAPP(U_938,fun(U_938,bool),ord_less_eq(U_938),sK58(U_939,U_938,U_937,U_936,U_935,U_934)),sK59(U_939,U_938,U_937,U_936,U_935,U_934)))
    | hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less(U_939),U_936),hAPP(U_938,U_939,U_935,U_937)))
    | ~ hBOOL(hAPP(U_938,bool,hAPP(U_938,fun(U_938,bool),ord_less_eq(U_938),U_934),U_937))
    | ~ hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less(U_939),U_936),hAPP(U_938,U_939,U_935,U_934)))
    | ~ order(U_939)
    | ~ order(U_938) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_6,plain,
    ( ~ hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less_eq(U_939),hAPP(U_938,U_939,U_935,sK58(U_939,U_938,U_937,U_936,U_935,U_934))),hAPP(U_938,U_939,U_935,sK59(U_939,U_938,U_937,U_936,U_935,U_934))))
    | hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less(U_939),U_936),hAPP(U_938,U_939,U_935,U_937)))
    | ~ hBOOL(hAPP(U_938,bool,hAPP(U_938,fun(U_938,bool),ord_less_eq(U_938),U_934),U_937))
    | ~ hBOOL(hAPP(U_939,bool,hAPP(U_939,fun(U_939,bool),ord_less(U_939),U_936),hAPP(U_938,U_939,U_935,U_934)))
    | ~ order(U_939)
    | ~ order(U_938) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

fof(f_281_1,plain,
    ! [X_a,X_b] :
      ( ! [F,Ca,Aa,Ba] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),Ca))
          | ? [X_1,Y_2] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_2)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2)) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),Ca))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) )
      | ~ order(X_a)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_191_order__le__less__subst2]) ).

fof(f_281_2,plain,
    ! [U_947,U_946] :
      ( ! [U_945,U_944,U_943,U_942] :
          ( hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less(U_946),hAPP(U_947,U_946,U_945,U_943)),U_944))
          | ? [U_941,U_940] :
              ( ~ hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less_eq(U_946),hAPP(U_947,U_946,U_945,U_941)),hAPP(U_947,U_946,U_945,U_940)))
              & hBOOL(hAPP(U_947,bool,hAPP(U_947,fun(U_947,bool),ord_less_eq(U_947),U_941),U_940)) )
          | ~ hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less(U_946),hAPP(U_947,U_946,U_945,U_942)),U_944))
          | ~ hBOOL(hAPP(U_947,bool,hAPP(U_947,fun(U_947,bool),ord_less_eq(U_947),U_943),U_942)) )
      | ~ order(U_947)
      | ~ order(U_946) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ! [U_947,U_946] :
      ( ! [U_945,U_944,U_943,U_942] :
          ( hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less(U_946),hAPP(U_947,U_946,U_945,U_943)),U_944))
          | ? [U_940] :
              ( ~ hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less_eq(U_946),hAPP(U_947,U_946,U_945,sK60(U_947,U_946,U_945,U_944,U_943,U_942))),hAPP(U_947,U_946,U_945,U_940)))
              & hBOOL(hAPP(U_947,bool,hAPP(U_947,fun(U_947,bool),ord_less_eq(U_947),sK60(U_947,U_946,U_945,U_944,U_943,U_942)),U_940)) )
          | ~ hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less(U_946),hAPP(U_947,U_946,U_945,U_942)),U_944))
          | ~ hBOOL(hAPP(U_947,bool,hAPP(U_947,fun(U_947,bool),ord_less_eq(U_947),U_943),U_942)) )
      | ~ order(U_947)
      | ~ order(U_946) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_941,sK60(U_947,U_946,U_945,U_944,U_943,U_942))],[f_281_2]) ).

fof(f_281_4,plain,
    ! [U_947,U_946] :
      ( ! [U_945,U_944,U_943,U_942] :
          ( hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less(U_946),hAPP(U_947,U_946,U_945,U_943)),U_944))
          | ( ~ hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less_eq(U_946),hAPP(U_947,U_946,U_945,sK60(U_947,U_946,U_945,U_944,U_943,U_942))),hAPP(U_947,U_946,U_945,sK61(U_947,U_946,U_945,U_944,U_943,U_942))))
            & hBOOL(hAPP(U_947,bool,hAPP(U_947,fun(U_947,bool),ord_less_eq(U_947),sK60(U_947,U_946,U_945,U_944,U_943,U_942)),sK61(U_947,U_946,U_945,U_944,U_943,U_942))) )
          | ~ hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less(U_946),hAPP(U_947,U_946,U_945,U_942)),U_944))
          | ~ hBOOL(hAPP(U_947,bool,hAPP(U_947,fun(U_947,bool),ord_less_eq(U_947),U_943),U_942)) )
      | ~ order(U_947)
      | ~ order(U_946) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_940,sK61(U_947,U_946,U_945,U_944,U_943,U_942))],[f_281_3]) ).

cnf(f_281_5,plain,
    ( hBOOL(hAPP(U_947,bool,hAPP(U_947,fun(U_947,bool),ord_less_eq(U_947),sK60(U_947,U_946,U_945,U_944,U_943,U_942)),sK61(U_947,U_946,U_945,U_944,U_943,U_942)))
    | hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less(U_946),hAPP(U_947,U_946,U_945,U_943)),U_944))
    | ~ hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less(U_946),hAPP(U_947,U_946,U_945,U_942)),U_944))
    | ~ hBOOL(hAPP(U_947,bool,hAPP(U_947,fun(U_947,bool),ord_less_eq(U_947),U_943),U_942))
    | ~ order(U_947)
    | ~ order(U_946) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

cnf(f_281_6,plain,
    ( ~ hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less_eq(U_946),hAPP(U_947,U_946,U_945,sK60(U_947,U_946,U_945,U_944,U_943,U_942))),hAPP(U_947,U_946,U_945,sK61(U_947,U_946,U_945,U_944,U_943,U_942))))
    | hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less(U_946),hAPP(U_947,U_946,U_945,U_943)),U_944))
    | ~ hBOOL(hAPP(U_946,bool,hAPP(U_946,fun(U_946,bool),ord_less(U_946),hAPP(U_947,U_946,U_945,U_942)),U_944))
    | ~ hBOOL(hAPP(U_947,bool,hAPP(U_947,fun(U_947,bool),ord_less_eq(U_947),U_943),U_942))
    | ~ order(U_947)
    | ~ order(U_946) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

fof(f_282_1,plain,
    ! [X_a,X_b] :
      ( ! [F,Ca,Aa,Ba] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),Ca))
          | ? [X_1,Y_2] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_2)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Ba)),Ca))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) )
      | ~ order(X_a)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_192_order__less__le__subst2]) ).

fof(f_282_2,plain,
    ! [U_955,U_954] :
      ( ! [U_953,U_952,U_951,U_950] :
          ( hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less(U_954),hAPP(U_955,U_954,U_953,U_951)),U_952))
          | ? [U_949,U_948] :
              ( ~ hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less(U_954),hAPP(U_955,U_954,U_953,U_949)),hAPP(U_955,U_954,U_953,U_948)))
              & hBOOL(hAPP(U_955,bool,hAPP(U_955,fun(U_955,bool),ord_less(U_955),U_949),U_948)) )
          | ~ hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less_eq(U_954),hAPP(U_955,U_954,U_953,U_950)),U_952))
          | ~ hBOOL(hAPP(U_955,bool,hAPP(U_955,fun(U_955,bool),ord_less(U_955),U_951),U_950)) )
      | ~ order(U_955)
      | ~ order(U_954) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ! [U_955,U_954] :
      ( ! [U_953,U_952,U_951,U_950] :
          ( hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less(U_954),hAPP(U_955,U_954,U_953,U_951)),U_952))
          | ? [U_948] :
              ( ~ hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less(U_954),hAPP(U_955,U_954,U_953,sK62(U_955,U_954,U_953,U_952,U_951,U_950))),hAPP(U_955,U_954,U_953,U_948)))
              & hBOOL(hAPP(U_955,bool,hAPP(U_955,fun(U_955,bool),ord_less(U_955),sK62(U_955,U_954,U_953,U_952,U_951,U_950)),U_948)) )
          | ~ hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less_eq(U_954),hAPP(U_955,U_954,U_953,U_950)),U_952))
          | ~ hBOOL(hAPP(U_955,bool,hAPP(U_955,fun(U_955,bool),ord_less(U_955),U_951),U_950)) )
      | ~ order(U_955)
      | ~ order(U_954) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_949,sK62(U_955,U_954,U_953,U_952,U_951,U_950))],[f_282_2]) ).

fof(f_282_4,plain,
    ! [U_955,U_954] :
      ( ! [U_953,U_952,U_951,U_950] :
          ( hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less(U_954),hAPP(U_955,U_954,U_953,U_951)),U_952))
          | ( ~ hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less(U_954),hAPP(U_955,U_954,U_953,sK62(U_955,U_954,U_953,U_952,U_951,U_950))),hAPP(U_955,U_954,U_953,sK63(U_955,U_954,U_953,U_952,U_951,U_950))))
            & hBOOL(hAPP(U_955,bool,hAPP(U_955,fun(U_955,bool),ord_less(U_955),sK62(U_955,U_954,U_953,U_952,U_951,U_950)),sK63(U_955,U_954,U_953,U_952,U_951,U_950))) )
          | ~ hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less_eq(U_954),hAPP(U_955,U_954,U_953,U_950)),U_952))
          | ~ hBOOL(hAPP(U_955,bool,hAPP(U_955,fun(U_955,bool),ord_less(U_955),U_951),U_950)) )
      | ~ order(U_955)
      | ~ order(U_954) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_948,sK63(U_955,U_954,U_953,U_952,U_951,U_950))],[f_282_3]) ).

cnf(f_282_5,plain,
    ( hBOOL(hAPP(U_955,bool,hAPP(U_955,fun(U_955,bool),ord_less(U_955),sK62(U_955,U_954,U_953,U_952,U_951,U_950)),sK63(U_955,U_954,U_953,U_952,U_951,U_950)))
    | hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less(U_954),hAPP(U_955,U_954,U_953,U_951)),U_952))
    | ~ hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less_eq(U_954),hAPP(U_955,U_954,U_953,U_950)),U_952))
    | ~ hBOOL(hAPP(U_955,bool,hAPP(U_955,fun(U_955,bool),ord_less(U_955),U_951),U_950))
    | ~ order(U_955)
    | ~ order(U_954) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_6,plain,
    ( ~ hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less(U_954),hAPP(U_955,U_954,U_953,sK62(U_955,U_954,U_953,U_952,U_951,U_950))),hAPP(U_955,U_954,U_953,sK63(U_955,U_954,U_953,U_952,U_951,U_950))))
    | hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less(U_954),hAPP(U_955,U_954,U_953,U_951)),U_952))
    | ~ hBOOL(hAPP(U_954,bool,hAPP(U_954,fun(U_954,bool),ord_less_eq(U_954),hAPP(U_955,U_954,U_953,U_950)),U_952))
    | ~ hBOOL(hAPP(U_955,bool,hAPP(U_955,fun(U_955,bool),ord_less(U_955),U_951),U_950))
    | ~ order(U_955)
    | ~ order(U_954) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

fof(f_283_1,plain,
    ! [M_3,K_2,N] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_2)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_193_add__leE]) ).

fof(f_283_2,plain,
    ! [U_958,U_957,U_956] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_957),U_956))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_958),U_956)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_958),U_957)),U_956)) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

cnf(f_283_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_958),U_956))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_958),U_957)),U_956)) ),
    inference(clausify,[status(thm)],[f_283_2]) ).

cnf(f_283_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_957),U_956))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_958),U_957)),U_956)) ),
    inference(clausify,[status(thm)],[f_283_2]) ).

fof(f_284_1,plain,
    ! [X_a,A_1,B] :
      ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_194_equalityI]) ).

fof(f_284_2,plain,
    ! [U_961,U_960,U_959] :
      ( ti(fun(U_961,bool),U_960) = ti(fun(U_961,bool),U_959)
      | ~ hBOOL(hAPP(fun(U_961,bool),bool,hAPP(fun(U_961,bool),fun(fun(U_961,bool),bool),ord_less_eq(fun(U_961,bool)),U_959),U_960))
      | ~ hBOOL(hAPP(fun(U_961,bool),bool,hAPP(fun(U_961,bool),fun(fun(U_961,bool),bool),ord_less_eq(fun(U_961,bool)),U_960),U_959)) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

cnf(f_284_3,plain,
    ( ti(fun(U_961,bool),U_960) = ti(fun(U_961,bool),U_959)
    | ~ hBOOL(hAPP(fun(U_961,bool),bool,hAPP(fun(U_961,bool),fun(fun(U_961,bool),bool),ord_less_eq(fun(U_961,bool)),U_959),U_960))
    | ~ hBOOL(hAPP(fun(U_961,bool),bool,hAPP(fun(U_961,bool),fun(fun(U_961,bool),bool),ord_less_eq(fun(U_961,bool)),U_960),U_959)) ),
    inference(clausify,[status(thm)],[f_284_2]) ).

fof(f_285_1,plain,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_195_subsetD]) ).

fof(f_285_2,plain,
    ! [U_965,U_964,U_963,U_962] :
      ( hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),U_962))
      | ~ hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),U_963))
      | ~ hBOOL(hAPP(fun(U_965,bool),bool,hAPP(fun(U_965,bool),fun(fun(U_965,bool),bool),ord_less_eq(fun(U_965,bool)),U_963),U_962)) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

cnf(f_285_3,plain,
    ( hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),U_962))
    | ~ hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),U_963))
    | ~ hBOOL(hAPP(fun(U_965,bool),bool,hAPP(fun(U_965,bool),fun(fun(U_965,bool),bool),ord_less_eq(fun(U_965,bool)),U_963),U_962)) ),
    inference(clausify,[status(thm)],[f_285_2]) ).

fof(f_286_1,plain,
    ! [X_a,A_1,B] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
        | ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) )
      & ( ( ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B)
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) )
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_196_psubset__eq]) ).

fof(f_286_2,plain,
    ! [U_968,U_967,U_966] :
      ( ( hBOOL(hAPP(fun(U_968,bool),bool,hAPP(fun(U_968,bool),fun(fun(U_968,bool),bool),ord_less(fun(U_968,bool)),U_967),U_966))
        | ti(fun(U_968,bool),U_967) = ti(fun(U_968,bool),U_966)
        | ~ hBOOL(hAPP(fun(U_968,bool),bool,hAPP(fun(U_968,bool),fun(fun(U_968,bool),bool),ord_less_eq(fun(U_968,bool)),U_967),U_966)) )
      & ( ( ti(fun(U_968,bool),U_967) != ti(fun(U_968,bool),U_966)
          & hBOOL(hAPP(fun(U_968,bool),bool,hAPP(fun(U_968,bool),fun(fun(U_968,bool),bool),ord_less_eq(fun(U_968,bool)),U_967),U_966)) )
        | ~ hBOOL(hAPP(fun(U_968,bool),bool,hAPP(fun(U_968,bool),fun(fun(U_968,bool),bool),ord_less(fun(U_968,bool)),U_967),U_966)) ) ),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ( ! [U_974,U_972,U_970] :
        ( hBOOL(hAPP(fun(U_974,bool),bool,hAPP(fun(U_974,bool),fun(fun(U_974,bool),bool),ord_less(fun(U_974,bool)),U_972),U_970))
        | ti(fun(U_974,bool),U_972) = ti(fun(U_974,bool),U_970)
        | ~ hBOOL(hAPP(fun(U_974,bool),bool,hAPP(fun(U_974,bool),fun(fun(U_974,bool),bool),ord_less_eq(fun(U_974,bool)),U_972),U_970)) )
    & ! [U_973,U_971,U_969] :
        ( ( ti(fun(U_973,bool),U_971) != ti(fun(U_973,bool),U_969)
          & hBOOL(hAPP(fun(U_973,bool),bool,hAPP(fun(U_973,bool),fun(fun(U_973,bool),bool),ord_less_eq(fun(U_973,bool)),U_971),U_969)) )
        | ~ hBOOL(hAPP(fun(U_973,bool),bool,hAPP(fun(U_973,bool),fun(fun(U_973,bool),bool),ord_less(fun(U_973,bool)),U_971),U_969)) ) ),
    inference(miniscope,[status(thm)],[f_286_2]) ).

cnf(f_286_4,plain,
    ( hBOOL(hAPP(fun(U_973,bool),bool,hAPP(fun(U_973,bool),fun(fun(U_973,bool),bool),ord_less_eq(fun(U_973,bool)),U_971),U_969))
    | ~ hBOOL(hAPP(fun(U_973,bool),bool,hAPP(fun(U_973,bool),fun(fun(U_973,bool),bool),ord_less(fun(U_973,bool)),U_971),U_969)) ),
    inference(clausify,[status(thm)],[f_286_3]) ).

cnf(f_286_5,plain,
    ( ti(fun(U_973,bool),U_971) != ti(fun(U_973,bool),U_969)
    | ~ hBOOL(hAPP(fun(U_973,bool),bool,hAPP(fun(U_973,bool),fun(fun(U_973,bool),bool),ord_less(fun(U_973,bool)),U_971),U_969)) ),
    inference(clausify,[status(thm)],[f_286_3]) ).

cnf(f_286_6,plain,
    ( hBOOL(hAPP(fun(U_974,bool),bool,hAPP(fun(U_974,bool),fun(fun(U_974,bool),bool),ord_less(fun(U_974,bool)),U_972),U_970))
    | ti(fun(U_974,bool),U_972) = ti(fun(U_974,bool),U_970)
    | ~ hBOOL(hAPP(fun(U_974,bool),bool,hAPP(fun(U_974,bool),fun(fun(U_974,bool),bool),ord_less_eq(fun(U_974,bool)),U_972),U_970)) ),
    inference(clausify,[status(thm)],[f_286_3]) ).

fof(f_287_1,plain,
    ! [X_a,A_1,B] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
        | ( ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B)
          & ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) ) )
      & ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
        | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_197_subset__iff__psubset__eq]) ).

fof(f_287_2,plain,
    ! [U_977,U_976,U_975] :
      ( ( hBOOL(hAPP(fun(U_977,bool),bool,hAPP(fun(U_977,bool),fun(fun(U_977,bool),bool),ord_less_eq(fun(U_977,bool)),U_976),U_975))
        | ( ti(fun(U_977,bool),U_976) != ti(fun(U_977,bool),U_975)
          & ~ hBOOL(hAPP(fun(U_977,bool),bool,hAPP(fun(U_977,bool),fun(fun(U_977,bool),bool),ord_less(fun(U_977,bool)),U_976),U_975)) ) )
      & ( ti(fun(U_977,bool),U_976) = ti(fun(U_977,bool),U_975)
        | hBOOL(hAPP(fun(U_977,bool),bool,hAPP(fun(U_977,bool),fun(fun(U_977,bool),bool),ord_less(fun(U_977,bool)),U_976),U_975))
        | ~ hBOOL(hAPP(fun(U_977,bool),bool,hAPP(fun(U_977,bool),fun(fun(U_977,bool),bool),ord_less_eq(fun(U_977,bool)),U_976),U_975)) ) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ( ! [U_983,U_981,U_979] :
        ( hBOOL(hAPP(fun(U_983,bool),bool,hAPP(fun(U_983,bool),fun(fun(U_983,bool),bool),ord_less_eq(fun(U_983,bool)),U_981),U_979))
        | ( ti(fun(U_983,bool),U_981) != ti(fun(U_983,bool),U_979)
          & ~ hBOOL(hAPP(fun(U_983,bool),bool,hAPP(fun(U_983,bool),fun(fun(U_983,bool),bool),ord_less(fun(U_983,bool)),U_981),U_979)) ) )
    & ! [U_982,U_980,U_978] :
        ( ti(fun(U_982,bool),U_980) = ti(fun(U_982,bool),U_978)
        | hBOOL(hAPP(fun(U_982,bool),bool,hAPP(fun(U_982,bool),fun(fun(U_982,bool),bool),ord_less(fun(U_982,bool)),U_980),U_978))
        | ~ hBOOL(hAPP(fun(U_982,bool),bool,hAPP(fun(U_982,bool),fun(fun(U_982,bool),bool),ord_less_eq(fun(U_982,bool)),U_980),U_978)) ) ),
    inference(miniscope,[status(thm)],[f_287_2]) ).

cnf(f_287_4,plain,
    ( ti(fun(U_982,bool),U_980) = ti(fun(U_982,bool),U_978)
    | hBOOL(hAPP(fun(U_982,bool),bool,hAPP(fun(U_982,bool),fun(fun(U_982,bool),bool),ord_less(fun(U_982,bool)),U_980),U_978))
    | ~ hBOOL(hAPP(fun(U_982,bool),bool,hAPP(fun(U_982,bool),fun(fun(U_982,bool),bool),ord_less_eq(fun(U_982,bool)),U_980),U_978)) ),
    inference(clausify,[status(thm)],[f_287_3]) ).

cnf(f_287_5,plain,
    ( ~ hBOOL(hAPP(fun(U_983,bool),bool,hAPP(fun(U_983,bool),fun(fun(U_983,bool),bool),ord_less(fun(U_983,bool)),U_981),U_979))
    | hBOOL(hAPP(fun(U_983,bool),bool,hAPP(fun(U_983,bool),fun(fun(U_983,bool),bool),ord_less_eq(fun(U_983,bool)),U_981),U_979)) ),
    inference(clausify,[status(thm)],[f_287_3]) ).

cnf(f_287_6,plain,
    ( ti(fun(U_983,bool),U_981) != ti(fun(U_983,bool),U_979)
    | hBOOL(hAPP(fun(U_983,bool),bool,hAPP(fun(U_983,bool),fun(fun(U_983,bool),bool),ord_less_eq(fun(U_983,bool)),U_981),U_979)) ),
    inference(clausify,[status(thm)],[f_287_3]) ).

fof(f_288_1,plain,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_198_psubset__imp__subset]) ).

fof(f_288_2,plain,
    ! [U_986,U_985,U_984] :
      ( hBOOL(hAPP(fun(U_986,bool),bool,hAPP(fun(U_986,bool),fun(fun(U_986,bool),bool),ord_less_eq(fun(U_986,bool)),U_985),U_984))
      | ~ hBOOL(hAPP(fun(U_986,bool),bool,hAPP(fun(U_986,bool),fun(fun(U_986,bool),bool),ord_less(fun(U_986,bool)),U_985),U_984)) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

cnf(f_288_3,plain,
    ( hBOOL(hAPP(fun(U_986,bool),bool,hAPP(fun(U_986,bool),fun(fun(U_986,bool),bool),ord_less_eq(fun(U_986,bool)),U_985),U_984))
    | ~ hBOOL(hAPP(fun(U_986,bool),bool,hAPP(fun(U_986,bool),fun(fun(U_986,bool),bool),ord_less(fun(U_986,bool)),U_985),U_984)) ),
    inference(clausify,[status(thm)],[f_288_2]) ).

fof(f_289_1,plain,
    ! [X_a,C,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_199_psubset__subset__trans]) ).

fof(f_289_2,plain,
    ! [U_990,U_989,U_988,U_987] :
      ( hBOOL(hAPP(fun(U_990,bool),bool,hAPP(fun(U_990,bool),fun(fun(U_990,bool),bool),ord_less(fun(U_990,bool)),U_988),U_989))
      | ~ hBOOL(hAPP(fun(U_990,bool),bool,hAPP(fun(U_990,bool),fun(fun(U_990,bool),bool),ord_less_eq(fun(U_990,bool)),U_987),U_989))
      | ~ hBOOL(hAPP(fun(U_990,bool),bool,hAPP(fun(U_990,bool),fun(fun(U_990,bool),bool),ord_less(fun(U_990,bool)),U_988),U_987)) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

cnf(f_289_3,plain,
    ( hBOOL(hAPP(fun(U_990,bool),bool,hAPP(fun(U_990,bool),fun(fun(U_990,bool),bool),ord_less(fun(U_990,bool)),U_988),U_989))
    | ~ hBOOL(hAPP(fun(U_990,bool),bool,hAPP(fun(U_990,bool),fun(fun(U_990,bool),bool),ord_less_eq(fun(U_990,bool)),U_987),U_989))
    | ~ hBOOL(hAPP(fun(U_990,bool),bool,hAPP(fun(U_990,bool),fun(fun(U_990,bool),bool),ord_less(fun(U_990,bool)),U_988),U_987)) ),
    inference(clausify,[status(thm)],[f_289_2]) ).

fof(f_290_1,plain,
    ! [X_a,C,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_200_subset__psubset__trans]) ).

fof(f_290_2,plain,
    ! [U_994,U_993,U_992,U_991] :
      ( hBOOL(hAPP(fun(U_994,bool),bool,hAPP(fun(U_994,bool),fun(fun(U_994,bool),bool),ord_less(fun(U_994,bool)),U_992),U_993))
      | ~ hBOOL(hAPP(fun(U_994,bool),bool,hAPP(fun(U_994,bool),fun(fun(U_994,bool),bool),ord_less(fun(U_994,bool)),U_991),U_993))
      | ~ hBOOL(hAPP(fun(U_994,bool),bool,hAPP(fun(U_994,bool),fun(fun(U_994,bool),bool),ord_less_eq(fun(U_994,bool)),U_992),U_991)) ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

cnf(f_290_3,plain,
    ( hBOOL(hAPP(fun(U_994,bool),bool,hAPP(fun(U_994,bool),fun(fun(U_994,bool),bool),ord_less(fun(U_994,bool)),U_992),U_993))
    | ~ hBOOL(hAPP(fun(U_994,bool),bool,hAPP(fun(U_994,bool),fun(fun(U_994,bool),bool),ord_less(fun(U_994,bool)),U_991),U_993))
    | ~ hBOOL(hAPP(fun(U_994,bool),bool,hAPP(fun(U_994,bool),fun(fun(U_994,bool),bool),ord_less_eq(fun(U_994,bool)),U_992),U_991)) ),
    inference(clausify,[status(thm)],[f_290_2]) ).

fof(f_291_1,plain,
    ! [X_b,X_a,Q_1,Pa,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_1))
      | ~ hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1))
      | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_2),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_201_rev__predicate2D]) ).

fof(f_291_2,plain,
    ! [U_1000,U_999,U_998,U_997,U_996,U_995] :
      ( hBOOL(hAPP(U_1000,bool,hAPP(U_999,fun(U_1000,bool),U_998,U_996),U_995))
      | ~ hBOOL(hAPP(fun(U_999,fun(U_1000,bool)),bool,hAPP(fun(U_999,fun(U_1000,bool)),fun(fun(U_999,fun(U_1000,bool)),bool),ord_less_eq(fun(U_999,fun(U_1000,bool))),U_997),U_998))
      | ~ hBOOL(hAPP(U_1000,bool,hAPP(U_999,fun(U_1000,bool),U_997,U_996),U_995)) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

cnf(f_291_3,plain,
    ( hBOOL(hAPP(U_1000,bool,hAPP(U_999,fun(U_1000,bool),U_998,U_996),U_995))
    | ~ hBOOL(hAPP(fun(U_999,fun(U_1000,bool)),bool,hAPP(fun(U_999,fun(U_1000,bool)),fun(fun(U_999,fun(U_1000,bool)),bool),ord_less_eq(fun(U_999,fun(U_1000,bool))),U_997),U_998))
    | ~ hBOOL(hAPP(U_1000,bool,hAPP(U_999,fun(U_1000,bool),U_997,U_996),U_995)) ),
    inference(clausify,[status(thm)],[f_291_2]) ).

fof(f_292_1,plain,
    ! [X_a,A_1,B] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
        & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) )
      | ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) ),
    inference(fof_nnf,[status(thm)],[fact_202_equalityE]) ).

fof(f_292_2,plain,
    ! [U_1003,U_1002,U_1001] :
      ( ( hBOOL(hAPP(fun(U_1003,bool),bool,hAPP(fun(U_1003,bool),fun(fun(U_1003,bool),bool),ord_less_eq(fun(U_1003,bool)),U_1001),U_1002))
        & hBOOL(hAPP(fun(U_1003,bool),bool,hAPP(fun(U_1003,bool),fun(fun(U_1003,bool),bool),ord_less_eq(fun(U_1003,bool)),U_1002),U_1001)) )
      | ti(fun(U_1003,bool),U_1002) != ti(fun(U_1003,bool),U_1001) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

cnf(f_292_3,plain,
    ( hBOOL(hAPP(fun(U_1003,bool),bool,hAPP(fun(U_1003,bool),fun(fun(U_1003,bool),bool),ord_less_eq(fun(U_1003,bool)),U_1002),U_1001))
    | ti(fun(U_1003,bool),U_1002) != ti(fun(U_1003,bool),U_1001) ),
    inference(clausify,[status(thm)],[f_292_2]) ).

cnf(f_292_4,plain,
    ( hBOOL(hAPP(fun(U_1003,bool),bool,hAPP(fun(U_1003,bool),fun(fun(U_1003,bool),bool),ord_less_eq(fun(U_1003,bool)),U_1001),U_1002))
    | ti(fun(U_1003,bool),U_1002) != ti(fun(U_1003,bool),U_1001) ),
    inference(clausify,[status(thm)],[f_292_2]) ).

fof(f_293_1,plain,
    ! [X_a,X_b,X_2,Y_1,Pa,Q_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_1))
      | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_2),Y_1))
      | ~ hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1)) ),
    inference(fof_nnf,[status(thm)],[fact_203_predicate2D]) ).

fof(f_293_2,plain,
    ! [U_1009,U_1008,U_1007,U_1006,U_1005,U_1004] :
      ( hBOOL(hAPP(U_1008,bool,hAPP(U_1009,fun(U_1008,bool),U_1004,U_1007),U_1006))
      | ~ hBOOL(hAPP(U_1008,bool,hAPP(U_1009,fun(U_1008,bool),U_1005,U_1007),U_1006))
      | ~ hBOOL(hAPP(fun(U_1009,fun(U_1008,bool)),bool,hAPP(fun(U_1009,fun(U_1008,bool)),fun(fun(U_1009,fun(U_1008,bool)),bool),ord_less_eq(fun(U_1009,fun(U_1008,bool))),U_1005),U_1004)) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

cnf(f_293_3,plain,
    ( hBOOL(hAPP(U_1008,bool,hAPP(U_1009,fun(U_1008,bool),U_1004,U_1007),U_1006))
    | ~ hBOOL(hAPP(U_1008,bool,hAPP(U_1009,fun(U_1008,bool),U_1005,U_1007),U_1006))
    | ~ hBOOL(hAPP(fun(U_1009,fun(U_1008,bool)),bool,hAPP(fun(U_1009,fun(U_1008,bool)),fun(fun(U_1009,fun(U_1008,bool)),bool),ord_less_eq(fun(U_1009,fun(U_1008,bool))),U_1005),U_1004)) ),
    inference(clausify,[status(thm)],[f_293_2]) ).

fof(f_294_1,plain,
    ! [X_a,C,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_204_subset__trans]) ).

fof(f_294_2,plain,
    ! [U_1013,U_1012,U_1011,U_1010] :
      ( hBOOL(hAPP(fun(U_1013,bool),bool,hAPP(fun(U_1013,bool),fun(fun(U_1013,bool),bool),ord_less_eq(fun(U_1013,bool)),U_1011),U_1012))
      | ~ hBOOL(hAPP(fun(U_1013,bool),bool,hAPP(fun(U_1013,bool),fun(fun(U_1013,bool),bool),ord_less_eq(fun(U_1013,bool)),U_1010),U_1012))
      | ~ hBOOL(hAPP(fun(U_1013,bool),bool,hAPP(fun(U_1013,bool),fun(fun(U_1013,bool),bool),ord_less_eq(fun(U_1013,bool)),U_1011),U_1010)) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

cnf(f_294_3,plain,
    ( hBOOL(hAPP(fun(U_1013,bool),bool,hAPP(fun(U_1013,bool),fun(fun(U_1013,bool),bool),ord_less_eq(fun(U_1013,bool)),U_1011),U_1012))
    | ~ hBOOL(hAPP(fun(U_1013,bool),bool,hAPP(fun(U_1013,bool),fun(fun(U_1013,bool),bool),ord_less_eq(fun(U_1013,bool)),U_1010),U_1012))
    | ~ hBOOL(hAPP(fun(U_1013,bool),bool,hAPP(fun(U_1013,bool),fun(fun(U_1013,bool),bool),ord_less_eq(fun(U_1013,bool)),U_1011),U_1010)) ),
    inference(clausify,[status(thm)],[f_294_2]) ).

fof(f_295_1,plain,
    ! [X_a,X_2,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_205_set__mp]) ).

fof(f_295_2,plain,
    ! [U_1017,U_1016,U_1015,U_1014] :
      ( hBOOL(hAPP(fun(U_1017,bool),bool,hAPP(U_1017,fun(fun(U_1017,bool),bool),member(U_1017),U_1016),U_1014))
      | ~ hBOOL(hAPP(fun(U_1017,bool),bool,hAPP(U_1017,fun(fun(U_1017,bool),bool),member(U_1017),U_1016),U_1015))
      | ~ hBOOL(hAPP(fun(U_1017,bool),bool,hAPP(fun(U_1017,bool),fun(fun(U_1017,bool),bool),ord_less_eq(fun(U_1017,bool)),U_1015),U_1014)) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

cnf(f_295_3,plain,
    ( hBOOL(hAPP(fun(U_1017,bool),bool,hAPP(U_1017,fun(fun(U_1017,bool),bool),member(U_1017),U_1016),U_1014))
    | ~ hBOOL(hAPP(fun(U_1017,bool),bool,hAPP(U_1017,fun(fun(U_1017,bool),bool),member(U_1017),U_1016),U_1015))
    | ~ hBOOL(hAPP(fun(U_1017,bool),bool,hAPP(fun(U_1017,bool),fun(fun(U_1017,bool),bool),ord_less_eq(fun(U_1017,bool)),U_1015),U_1014)) ),
    inference(clausify,[status(thm)],[f_295_2]) ).

fof(f_296_1,plain,
    ! [X_a,B,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_206_set__rev__mp]) ).

fof(f_296_2,plain,
    ! [U_1021,U_1020,U_1019,U_1018] :
      ( hBOOL(hAPP(fun(U_1021,bool),bool,hAPP(U_1021,fun(fun(U_1021,bool),bool),member(U_1021),U_1019),U_1020))
      | ~ hBOOL(hAPP(fun(U_1021,bool),bool,hAPP(fun(U_1021,bool),fun(fun(U_1021,bool),bool),ord_less_eq(fun(U_1021,bool)),U_1018),U_1020))
      | ~ hBOOL(hAPP(fun(U_1021,bool),bool,hAPP(U_1021,fun(fun(U_1021,bool),bool),member(U_1021),U_1019),U_1018)) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

cnf(f_296_3,plain,
    ( hBOOL(hAPP(fun(U_1021,bool),bool,hAPP(U_1021,fun(fun(U_1021,bool),bool),member(U_1021),U_1019),U_1020))
    | ~ hBOOL(hAPP(fun(U_1021,bool),bool,hAPP(fun(U_1021,bool),fun(fun(U_1021,bool),bool),ord_less_eq(fun(U_1021,bool)),U_1018),U_1020))
    | ~ hBOOL(hAPP(fun(U_1021,bool),bool,hAPP(U_1021,fun(fun(U_1021,bool),bool),member(U_1021),U_1019),U_1018)) ),
    inference(clausify,[status(thm)],[f_296_2]) ).

fof(f_297_1,plain,
    ! [X_a,X_2,Pa,Q_1] :
      ( hBOOL(hAPP(X_a,bool,Q_1,X_2))
      | ~ hBOOL(hAPP(X_a,bool,Pa,X_2))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1)) ),
    inference(fof_nnf,[status(thm)],[fact_207_predicate1D]) ).

fof(f_297_2,plain,
    ! [U_1025,U_1024,U_1023,U_1022] :
      ( hBOOL(hAPP(U_1025,bool,U_1022,U_1024))
      | ~ hBOOL(hAPP(U_1025,bool,U_1023,U_1024))
      | ~ hBOOL(hAPP(fun(U_1025,bool),bool,hAPP(fun(U_1025,bool),fun(fun(U_1025,bool),bool),ord_less_eq(fun(U_1025,bool)),U_1023),U_1022)) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

cnf(f_297_3,plain,
    ( hBOOL(hAPP(U_1025,bool,U_1022,U_1024))
    | ~ hBOOL(hAPP(U_1025,bool,U_1023,U_1024))
    | ~ hBOOL(hAPP(fun(U_1025,bool),bool,hAPP(fun(U_1025,bool),fun(fun(U_1025,bool),bool),ord_less_eq(fun(U_1025,bool)),U_1023),U_1022)) ),
    inference(clausify,[status(thm)],[f_297_2]) ).

fof(f_298_1,plain,
    ! [X_a,X_2,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_208_in__mono]) ).

fof(f_298_2,plain,
    ! [U_1029,U_1028,U_1027,U_1026] :
      ( hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(U_1029,fun(fun(U_1029,bool),bool),member(U_1029),U_1028),U_1026))
      | ~ hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(U_1029,fun(fun(U_1029,bool),bool),member(U_1029),U_1028),U_1027))
      | ~ hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(fun(U_1029,bool),fun(fun(U_1029,bool),bool),ord_less_eq(fun(U_1029,bool)),U_1027),U_1026)) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

cnf(f_298_3,plain,
    ( hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(U_1029,fun(fun(U_1029,bool),bool),member(U_1029),U_1028),U_1026))
    | ~ hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(U_1029,fun(fun(U_1029,bool),bool),member(U_1029),U_1028),U_1027))
    | ~ hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(fun(U_1029,bool),fun(fun(U_1029,bool),bool),ord_less_eq(fun(U_1029,bool)),U_1027),U_1026)) ),
    inference(clausify,[status(thm)],[f_298_2]) ).

fof(f_299_1,plain,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
      | ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) ),
    inference(fof_nnf,[status(thm)],[fact_209_equalityD2]) ).

fof(f_299_2,plain,
    ! [U_1032,U_1031,U_1030] :
      ( hBOOL(hAPP(fun(U_1032,bool),bool,hAPP(fun(U_1032,bool),fun(fun(U_1032,bool),bool),ord_less_eq(fun(U_1032,bool)),U_1030),U_1031))
      | ti(fun(U_1032,bool),U_1031) != ti(fun(U_1032,bool),U_1030) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

cnf(f_299_3,plain,
    ( hBOOL(hAPP(fun(U_1032,bool),bool,hAPP(fun(U_1032,bool),fun(fun(U_1032,bool),bool),ord_less_eq(fun(U_1032,bool)),U_1030),U_1031))
    | ti(fun(U_1032,bool),U_1031) != ti(fun(U_1032,bool),U_1030) ),
    inference(clausify,[status(thm)],[f_299_2]) ).

fof(f_300_1,plain,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) ),
    inference(fof_nnf,[status(thm)],[fact_210_equalityD1]) ).

fof(f_300_2,plain,
    ! [U_1035,U_1034,U_1033] :
      ( hBOOL(hAPP(fun(U_1035,bool),bool,hAPP(fun(U_1035,bool),fun(fun(U_1035,bool),bool),ord_less_eq(fun(U_1035,bool)),U_1034),U_1033))
      | ti(fun(U_1035,bool),U_1034) != ti(fun(U_1035,bool),U_1033) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

cnf(f_300_3,plain,
    ( hBOOL(hAPP(fun(U_1035,bool),bool,hAPP(fun(U_1035,bool),fun(fun(U_1035,bool),bool),ord_less_eq(fun(U_1035,bool)),U_1034),U_1033))
    | ti(fun(U_1035,bool),U_1034) != ti(fun(U_1035,bool),U_1033) ),
    inference(clausify,[status(thm)],[f_300_2]) ).

fof(f_301_1,plain,
    ! [X_a,Q_1,Pa,X_2] :
      ( hBOOL(hAPP(X_a,bool,Q_1,X_2))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1))
      | ~ hBOOL(hAPP(X_a,bool,Pa,X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_211_rev__predicate1D]) ).

fof(f_301_2,plain,
    ! [U_1039,U_1038,U_1037,U_1036] :
      ( hBOOL(hAPP(U_1039,bool,U_1038,U_1036))
      | ~ hBOOL(hAPP(fun(U_1039,bool),bool,hAPP(fun(U_1039,bool),fun(fun(U_1039,bool),bool),ord_less_eq(fun(U_1039,bool)),U_1037),U_1038))
      | ~ hBOOL(hAPP(U_1039,bool,U_1037,U_1036)) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

cnf(f_301_3,plain,
    ( hBOOL(hAPP(U_1039,bool,U_1038,U_1036))
    | ~ hBOOL(hAPP(fun(U_1039,bool),bool,hAPP(fun(U_1039,bool),fun(fun(U_1039,bool),bool),ord_less_eq(fun(U_1039,bool)),U_1037),U_1038))
    | ~ hBOOL(hAPP(U_1039,bool,U_1037,U_1036)) ),
    inference(clausify,[status(thm)],[f_301_2]) ).

fof(f_302_1,plain,
    ! [X_a,A_1,B] :
      ( ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) )
      & ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) )
        | ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) ) ),
    inference(fof_nnf,[status(thm)],[fact_212_set__eq__subset]) ).

fof(f_302_2,plain,
    ! [U_1042,U_1041,U_1040] :
      ( ( ti(fun(U_1042,bool),U_1041) = ti(fun(U_1042,bool),U_1040)
        | ~ hBOOL(hAPP(fun(U_1042,bool),bool,hAPP(fun(U_1042,bool),fun(fun(U_1042,bool),bool),ord_less_eq(fun(U_1042,bool)),U_1040),U_1041))
        | ~ hBOOL(hAPP(fun(U_1042,bool),bool,hAPP(fun(U_1042,bool),fun(fun(U_1042,bool),bool),ord_less_eq(fun(U_1042,bool)),U_1041),U_1040)) )
      & ( ( hBOOL(hAPP(fun(U_1042,bool),bool,hAPP(fun(U_1042,bool),fun(fun(U_1042,bool),bool),ord_less_eq(fun(U_1042,bool)),U_1040),U_1041))
          & hBOOL(hAPP(fun(U_1042,bool),bool,hAPP(fun(U_1042,bool),fun(fun(U_1042,bool),bool),ord_less_eq(fun(U_1042,bool)),U_1041),U_1040)) )
        | ti(fun(U_1042,bool),U_1041) != ti(fun(U_1042,bool),U_1040) ) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ( ! [U_1048,U_1046,U_1044] :
        ( ti(fun(U_1048,bool),U_1046) = ti(fun(U_1048,bool),U_1044)
        | ~ hBOOL(hAPP(fun(U_1048,bool),bool,hAPP(fun(U_1048,bool),fun(fun(U_1048,bool),bool),ord_less_eq(fun(U_1048,bool)),U_1044),U_1046))
        | ~ hBOOL(hAPP(fun(U_1048,bool),bool,hAPP(fun(U_1048,bool),fun(fun(U_1048,bool),bool),ord_less_eq(fun(U_1048,bool)),U_1046),U_1044)) )
    & ! [U_1047,U_1045,U_1043] :
        ( ( hBOOL(hAPP(fun(U_1047,bool),bool,hAPP(fun(U_1047,bool),fun(fun(U_1047,bool),bool),ord_less_eq(fun(U_1047,bool)),U_1043),U_1045))
          & hBOOL(hAPP(fun(U_1047,bool),bool,hAPP(fun(U_1047,bool),fun(fun(U_1047,bool),bool),ord_less_eq(fun(U_1047,bool)),U_1045),U_1043)) )
        | ti(fun(U_1047,bool),U_1045) != ti(fun(U_1047,bool),U_1043) ) ),
    inference(miniscope,[status(thm)],[f_302_2]) ).

cnf(f_302_4,plain,
    ( hBOOL(hAPP(fun(U_1047,bool),bool,hAPP(fun(U_1047,bool),fun(fun(U_1047,bool),bool),ord_less_eq(fun(U_1047,bool)),U_1045),U_1043))
    | ti(fun(U_1047,bool),U_1045) != ti(fun(U_1047,bool),U_1043) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

cnf(f_302_5,plain,
    ( hBOOL(hAPP(fun(U_1047,bool),bool,hAPP(fun(U_1047,bool),fun(fun(U_1047,bool),bool),ord_less_eq(fun(U_1047,bool)),U_1043),U_1045))
    | ti(fun(U_1047,bool),U_1045) != ti(fun(U_1047,bool),U_1043) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

cnf(f_302_6,plain,
    ( ti(fun(U_1048,bool),U_1046) = ti(fun(U_1048,bool),U_1044)
    | ~ hBOOL(hAPP(fun(U_1048,bool),bool,hAPP(fun(U_1048,bool),fun(fun(U_1048,bool),bool),ord_less_eq(fun(U_1048,bool)),U_1044),U_1046))
    | ~ hBOOL(hAPP(fun(U_1048,bool),bool,hAPP(fun(U_1048,bool),fun(fun(U_1048,bool),bool),ord_less_eq(fun(U_1048,bool)),U_1046),U_1044)) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_1,plain,
    ! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),A_1)),
    inference(fof_nnf,[status(thm)],[fact_213_subset__refl]) ).

fof(f_303_2,plain,
    ! [U_1050,U_1049] : hBOOL(hAPP(fun(U_1050,bool),bool,hAPP(fun(U_1050,bool),fun(fun(U_1050,bool),bool),ord_less_eq(fun(U_1050,bool)),U_1049),U_1049)),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

cnf(f_303_3,plain,
    hBOOL(hAPP(fun(U_1050,bool),bool,hAPP(fun(U_1050,bool),fun(fun(U_1050,bool),bool),ord_less_eq(fun(U_1050,bool)),U_1049),U_1049)),
    inference(clausify,[status(thm)],[f_303_2]) ).

fof(f_304_1,plain,
    ! [X_a,R_2,S] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_2),S)) )
      & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_2),S))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))) ) ),
    inference(fof_nnf,[status(thm)],[fact_214_pred__subset__eq]) ).

fof(f_304_2,plain,
    ! [U_1053,U_1052,U_1051] :
      ( ( hBOOL(hAPP(fun(U_1053,bool),bool,hAPP(fun(U_1053,bool),fun(fun(U_1053,bool),bool),ord_less_eq(fun(U_1053,bool)),hAPP(fun(U_1053,bool),fun(U_1053,bool),hAPP(fun(U_1053,fun(fun(U_1053,bool),bool)),fun(fun(U_1053,bool),fun(U_1053,bool)),combc(U_1053,fun(U_1053,bool),bool),member(U_1053)),U_1052)),hAPP(fun(U_1053,bool),fun(U_1053,bool),hAPP(fun(U_1053,fun(fun(U_1053,bool),bool)),fun(fun(U_1053,bool),fun(U_1053,bool)),combc(U_1053,fun(U_1053,bool),bool),member(U_1053)),U_1051)))
        | ~ hBOOL(hAPP(fun(U_1053,bool),bool,hAPP(fun(U_1053,bool),fun(fun(U_1053,bool),bool),ord_less_eq(fun(U_1053,bool)),U_1052),U_1051)) )
      & ( hBOOL(hAPP(fun(U_1053,bool),bool,hAPP(fun(U_1053,bool),fun(fun(U_1053,bool),bool),ord_less_eq(fun(U_1053,bool)),U_1052),U_1051))
        | ~ hBOOL(hAPP(fun(U_1053,bool),bool,hAPP(fun(U_1053,bool),fun(fun(U_1053,bool),bool),ord_less_eq(fun(U_1053,bool)),hAPP(fun(U_1053,bool),fun(U_1053,bool),hAPP(fun(U_1053,fun(fun(U_1053,bool),bool)),fun(fun(U_1053,bool),fun(U_1053,bool)),combc(U_1053,fun(U_1053,bool),bool),member(U_1053)),U_1052)),hAPP(fun(U_1053,bool),fun(U_1053,bool),hAPP(fun(U_1053,fun(fun(U_1053,bool),bool)),fun(fun(U_1053,bool),fun(U_1053,bool)),combc(U_1053,fun(U_1053,bool),bool),member(U_1053)),U_1051))) ) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ( ! [U_1059,U_1057,U_1055] :
        ( hBOOL(hAPP(fun(U_1059,bool),bool,hAPP(fun(U_1059,bool),fun(fun(U_1059,bool),bool),ord_less_eq(fun(U_1059,bool)),hAPP(fun(U_1059,bool),fun(U_1059,bool),hAPP(fun(U_1059,fun(fun(U_1059,bool),bool)),fun(fun(U_1059,bool),fun(U_1059,bool)),combc(U_1059,fun(U_1059,bool),bool),member(U_1059)),U_1057)),hAPP(fun(U_1059,bool),fun(U_1059,bool),hAPP(fun(U_1059,fun(fun(U_1059,bool),bool)),fun(fun(U_1059,bool),fun(U_1059,bool)),combc(U_1059,fun(U_1059,bool),bool),member(U_1059)),U_1055)))
        | ~ hBOOL(hAPP(fun(U_1059,bool),bool,hAPP(fun(U_1059,bool),fun(fun(U_1059,bool),bool),ord_less_eq(fun(U_1059,bool)),U_1057),U_1055)) )
    & ! [U_1058,U_1056,U_1054] :
        ( hBOOL(hAPP(fun(U_1058,bool),bool,hAPP(fun(U_1058,bool),fun(fun(U_1058,bool),bool),ord_less_eq(fun(U_1058,bool)),U_1056),U_1054))
        | ~ hBOOL(hAPP(fun(U_1058,bool),bool,hAPP(fun(U_1058,bool),fun(fun(U_1058,bool),bool),ord_less_eq(fun(U_1058,bool)),hAPP(fun(U_1058,bool),fun(U_1058,bool),hAPP(fun(U_1058,fun(fun(U_1058,bool),bool)),fun(fun(U_1058,bool),fun(U_1058,bool)),combc(U_1058,fun(U_1058,bool),bool),member(U_1058)),U_1056)),hAPP(fun(U_1058,bool),fun(U_1058,bool),hAPP(fun(U_1058,fun(fun(U_1058,bool),bool)),fun(fun(U_1058,bool),fun(U_1058,bool)),combc(U_1058,fun(U_1058,bool),bool),member(U_1058)),U_1054))) ) ),
    inference(miniscope,[status(thm)],[f_304_2]) ).

cnf(f_304_4,plain,
    ( hBOOL(hAPP(fun(U_1058,bool),bool,hAPP(fun(U_1058,bool),fun(fun(U_1058,bool),bool),ord_less_eq(fun(U_1058,bool)),U_1056),U_1054))
    | ~ hBOOL(hAPP(fun(U_1058,bool),bool,hAPP(fun(U_1058,bool),fun(fun(U_1058,bool),bool),ord_less_eq(fun(U_1058,bool)),hAPP(fun(U_1058,bool),fun(U_1058,bool),hAPP(fun(U_1058,fun(fun(U_1058,bool),bool)),fun(fun(U_1058,bool),fun(U_1058,bool)),combc(U_1058,fun(U_1058,bool),bool),member(U_1058)),U_1056)),hAPP(fun(U_1058,bool),fun(U_1058,bool),hAPP(fun(U_1058,fun(fun(U_1058,bool),bool)),fun(fun(U_1058,bool),fun(U_1058,bool)),combc(U_1058,fun(U_1058,bool),bool),member(U_1058)),U_1054))) ),
    inference(clausify,[status(thm)],[f_304_3]) ).

cnf(f_304_5,plain,
    ( hBOOL(hAPP(fun(U_1059,bool),bool,hAPP(fun(U_1059,bool),fun(fun(U_1059,bool),bool),ord_less_eq(fun(U_1059,bool)),hAPP(fun(U_1059,bool),fun(U_1059,bool),hAPP(fun(U_1059,fun(fun(U_1059,bool),bool)),fun(fun(U_1059,bool),fun(U_1059,bool)),combc(U_1059,fun(U_1059,bool),bool),member(U_1059)),U_1057)),hAPP(fun(U_1059,bool),fun(U_1059,bool),hAPP(fun(U_1059,fun(fun(U_1059,bool),bool)),fun(fun(U_1059,bool),fun(U_1059,bool)),combc(U_1059,fun(U_1059,bool),bool),member(U_1059)),U_1055)))
    | ~ hBOOL(hAPP(fun(U_1059,bool),bool,hAPP(fun(U_1059,bool),fun(fun(U_1059,bool),bool),ord_less_eq(fun(U_1059,bool)),U_1057),U_1055)) ),
    inference(clausify,[status(thm)],[f_304_3]) ).

fof(f_305_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    inference(fof_nnf,[status(thm)],[fact_215_less__not__refl]) ).

fof(f_305_2,plain,
    ! [U_1060] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1060),U_1060)),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

cnf(f_305_3,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1060),U_1060)),
    inference(clausify,[status(thm)],[f_305_2]) ).

fof(f_306_1,plain,
    ! [M,Na] :
      ( ( M != Na
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | M = Na ) ),
    inference(fof_nnf,[status(thm)],[fact_216_nat__neq__iff]) ).

fof(f_306_2,plain,
    ! [U_1062,U_1061] :
      ( ( U_1062 != U_1061
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1061),U_1062))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1062),U_1061)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1061),U_1062))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1062),U_1061))
        | U_1062 = U_1061 ) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ( ! [U_1066,U_1064] :
        ( U_1066 != U_1064
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1064),U_1066))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1066),U_1064)) ) )
    & ! [U_1065,U_1063] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1063),U_1065))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1065),U_1063))
        | U_1065 = U_1063 ) ),
    inference(miniscope,[status(thm)],[f_306_2]) ).

cnf(f_306_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1063),U_1065))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1065),U_1063))
    | U_1065 = U_1063 ),
    inference(clausify,[status(thm)],[f_306_3]) ).

cnf(f_306_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1066),U_1064))
    | U_1066 != U_1064 ),
    inference(clausify,[status(thm)],[f_306_3]) ).

cnf(f_306_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1064),U_1066))
    | U_1066 != U_1064 ),
    inference(clausify,[status(thm)],[f_306_3]) ).

fof(f_307_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
      | X = Y ),
    inference(fof_nnf,[status(thm)],[fact_217_linorder__neqE__nat]) ).

fof(f_307_2,plain,
    ! [U_1068,U_1067] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1067),U_1068))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1068),U_1067))
      | U_1068 = U_1067 ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

cnf(f_307_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1067),U_1068))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1068),U_1067))
    | U_1068 = U_1067 ),
    inference(clausify,[status(thm)],[f_307_2]) ).

fof(f_308_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    inference(fof_nnf,[status(thm)],[fact_218_less__irrefl__nat]) ).

fof(f_308_2,plain,
    ! [U_1069] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1069),U_1069)),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

cnf(f_308_3,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1069),U_1069)),
    inference(clausify,[status(thm)],[f_308_2]) ).

fof(f_309_1,plain,
    ! [N,M_3] :
      ( M_3 != N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_219_less__not__refl2]) ).

fof(f_309_2,plain,
    ! [U_1071,U_1070] :
      ( U_1070 != U_1071
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1071),U_1070)) ),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

cnf(f_309_3,plain,
    ( U_1070 != U_1071
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1071),U_1070)) ),
    inference(clausify,[status(thm)],[f_309_2]) ).

fof(f_310_1,plain,
    ! [S_1,T_4] :
      ( S_1 != T_4
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_4)) ),
    inference(fof_nnf,[status(thm)],[fact_220_less__not__refl3]) ).

fof(f_310_2,plain,
    ! [U_1073,U_1072] :
      ( U_1073 != U_1072
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1073),U_1072)) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

cnf(f_310_3,plain,
    ( U_1073 != U_1072
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1073),U_1072)) ),
    inference(clausify,[status(thm)],[f_310_2]) ).

fof(f_311_1,plain,
    ! [Pa,M,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))
        & M = Na )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_221_nat__less__cases]) ).

fof(f_311_2,plain,
    ! [U_1076,U_1075,U_1074] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1074),U_1075)) )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
        & U_1075 = U_1074 )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1075),U_1074)) ) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

cnf(f_311_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1074),U_1075))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | U_1075 = U_1074
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1075),U_1074)) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_4,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | U_1075 = U_1074
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1075),U_1074)) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1074),U_1075))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1075),U_1074)) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1075),U_1074)) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1074),U_1075))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | U_1075 = U_1074
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075)) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | U_1075 = U_1074
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075)) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_9,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1074),U_1075))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075)) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_10,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1076,U_1074),U_1075)) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

fof(f_312_1,plain,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_3),
    inference(fof_nnf,[status(thm)],[fact_222_nat__add__commute]) ).

fof(f_312_2,plain,
    ! [U_1078,U_1077] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1078),U_1077) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1077),U_1078),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

cnf(f_312_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1078),U_1077) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1077),U_1078),
    inference(clausify,[status(thm)],[f_312_2]) ).

fof(f_313_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_223_nat__add__left__commute]) ).

fof(f_313_2,plain,
    ! [U_1081,U_1080,U_1079] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1081),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1080),U_1079)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1080),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1081),U_1079)),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

cnf(f_313_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1081),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1080),U_1079)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1080),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1081),U_1079)),
    inference(clausify,[status(thm)],[f_313_2]) ).

fof(f_314_1,plain,
    ! [M_3,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_3),N)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_2)),
    inference(fof_nnf,[status(thm)],[fact_224_nat__add__assoc]) ).

fof(f_314_2,plain,
    ! [U_1084,U_1083,U_1082] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1084),U_1083)),U_1082) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1084),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1083),U_1082)),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

cnf(f_314_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_1084),U_1083)),U_1082) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1084),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1083),U_1082)),
    inference(clausify,[status(thm)],[f_314_2]) ).

fof(f_315_1,plain,
    ! [K,M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)
        | M != Na )
      & ( M = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_225_nat__add__left__cancel]) ).

fof(f_315_2,plain,
    ! [U_1087,U_1086,U_1085] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1087),U_1086) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1087),U_1085)
        | U_1086 != U_1085 )
      & ( U_1086 = U_1085
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1087),U_1086) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1087),U_1085) ) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

fof(f_315_3,plain,
    ( ! [U_1093,U_1091,U_1089] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1093),U_1091) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1093),U_1089)
        | U_1091 != U_1089 )
    & ! [U_1092,U_1090,U_1088] :
        ( U_1090 = U_1088
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1092),U_1090) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1092),U_1088) ) ),
    inference(miniscope,[status(thm)],[f_315_2]) ).

cnf(f_315_4,plain,
    ( U_1090 = U_1088
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1092),U_1090) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1092),U_1088) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

cnf(f_315_5,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1093),U_1091) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1093),U_1089)
    | U_1091 != U_1089 ),
    inference(clausify,[status(thm)],[f_315_3]) ).

fof(f_316_1,plain,
    ! [M,K,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K)
        | M != Na )
      & ( M = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K) ) ),
    inference(fof_nnf,[status(thm)],[fact_226_nat__add__right__cancel]) ).

fof(f_316_2,plain,
    ! [U_1096,U_1095,U_1094] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1096),U_1095) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1094),U_1095)
        | U_1096 != U_1094 )
      & ( U_1096 = U_1094
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1096),U_1095) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1094),U_1095) ) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ( ! [U_1102,U_1100,U_1098] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1102),U_1100) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1098),U_1100)
        | U_1102 != U_1098 )
    & ! [U_1101,U_1099,U_1097] :
        ( U_1101 = U_1097
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1101),U_1099) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1097),U_1099) ) ),
    inference(miniscope,[status(thm)],[f_316_2]) ).

cnf(f_316_4,plain,
    ( U_1101 = U_1097
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1101),U_1099) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1097),U_1099) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

cnf(f_316_5,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1102),U_1100) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1098),U_1100)
    | U_1102 != U_1098 ),
    inference(clausify,[status(thm)],[f_316_3]) ).

fof(f_317_1,plain,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N)),
    inference(fof_nnf,[status(thm)],[fact_227_le__refl]) ).

fof(f_317_2,plain,
    ! [U_1103] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1103),U_1103)),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

cnf(f_317_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1103),U_1103)),
    inference(clausify,[status(thm)],[f_317_2]) ).

fof(f_318_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_3))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_228_nat__le__linear]) ).

fof(f_318_2,plain,
    ! [U_1105,U_1104] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1104),U_1105))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1105),U_1104)) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

cnf(f_318_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1104),U_1105))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1105),U_1104)) ),
    inference(clausify,[status(thm)],[f_318_2]) ).

fof(f_319_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
      | M_3 != N ),
    inference(fof_nnf,[status(thm)],[fact_229_eq__imp__le]) ).

fof(f_319_2,plain,
    ! [U_1107,U_1106] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1107),U_1106))
      | U_1107 != U_1106 ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

cnf(f_319_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1107),U_1106))
    | U_1107 != U_1106 ),
    inference(clausify,[status(thm)],[f_319_2]) ).

fof(f_320_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),K_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_230_le__trans]) ).

fof(f_320_2,plain,
    ! [U_1110,U_1109,U_1108] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1109),U_1110))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1108),U_1110))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1109),U_1108)) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

cnf(f_320_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1109),U_1110))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1108),U_1110))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1109),U_1108)) ),
    inference(clausify,[status(thm)],[f_320_2]) ).

fof(f_321_1,plain,
    ! [M_3,N] :
      ( M_3 = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_3))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_231_le__antisym]) ).

fof(f_321_2,plain,
    ! [U_1112,U_1111] :
      ( U_1112 = U_1111
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1111),U_1112))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1112),U_1111)) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

cnf(f_321_3,plain,
    ( U_1112 = U_1111
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1111),U_1112))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1112),U_1111)) ),
    inference(clausify,[status(thm)],[f_321_2]) ).

fof(f_322_1,plain,
    ! [K,N_1] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),N_1)),
    inference(fof_nnf,[status(thm)],[fact_232_inj__on__add__nat]) ).

fof(f_322_2,plain,
    ! [U_1114,U_1113] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),U_1114)),U_1113)),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

cnf(f_322_3,plain,
    hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),U_1114)),U_1113)),
    inference(clausify,[status(thm)],[f_322_2]) ).

fof(f_323_1,plain,
    ! [I_2,J_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_233_not__add__less1]) ).

fof(f_323_2,plain,
    ! [U_1116,U_1115] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1116),U_1115)),U_1116)),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

cnf(f_323_3,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1116),U_1115)),U_1116)),
    inference(clausify,[status(thm)],[f_323_2]) ).

fof(f_324_1,plain,
    ! [J_1,I_2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_234_not__add__less2]) ).

fof(f_324_2,plain,
    ! [U_1118,U_1117] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1118),U_1117)),U_1117)),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

cnf(f_324_3,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1118),U_1117)),U_1117)),
    inference(clausify,[status(thm)],[f_324_2]) ).

fof(f_325_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_235_nat__add__left__cancel__less]) ).

fof(f_325_2,plain,
    ! [U_1121,U_1120,U_1119] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),U_1120)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),U_1119)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1120),U_1119)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1120),U_1119))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),U_1120)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),U_1119))) ) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

fof(f_325_3,plain,
    ( ! [U_1127,U_1125,U_1123] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1127),U_1125)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1127),U_1123)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1125),U_1123)) )
    & ! [U_1126,U_1124,U_1122] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1124),U_1122))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1126),U_1124)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1126),U_1122))) ) ),
    inference(miniscope,[status(thm)],[f_325_2]) ).

cnf(f_325_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1124),U_1122))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1126),U_1124)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1126),U_1122))) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

cnf(f_325_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1127),U_1125)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1127),U_1123)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1125),U_1123)) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

fof(f_326_1,plain,
    ! [M_3,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),M_3)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_236_trans__less__add1]) ).

fof(f_326_2,plain,
    ! [U_1130,U_1129,U_1128] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1129),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1128),U_1130)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1129),U_1128)) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

cnf(f_326_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1129),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1128),U_1130)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1129),U_1128)) ),
    inference(clausify,[status(thm)],[f_326_2]) ).

fof(f_327_1,plain,
    ! [M_3,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),J_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_237_trans__less__add2]) ).

fof(f_327_2,plain,
    ! [U_1133,U_1132,U_1131] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1132),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1133),U_1131)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1132),U_1131)) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

cnf(f_327_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1132),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1133),U_1131)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1132),U_1131)) ),
    inference(clausify,[status(thm)],[f_327_2]) ).

fof(f_328_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_238_add__less__mono1]) ).

fof(f_328_2,plain,
    ! [U_1136,U_1135,U_1134] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1135),U_1136)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1134),U_1136)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1135),U_1134)) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

cnf(f_328_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1135),U_1136)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1134),U_1136)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1135),U_1134)) ),
    inference(clausify,[status(thm)],[f_328_2]) ).

fof(f_329_1,plain,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),K_2),L_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_239_add__less__mono]) ).

fof(f_329_2,plain,
    ! [U_1140,U_1139,U_1138,U_1137] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1138),U_1140)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1137),U_1139)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1140),U_1139))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1138),U_1137)) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

cnf(f_329_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1138),U_1140)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1137),U_1139)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1140),U_1139))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1138),U_1137)) ),
    inference(clausify,[status(thm)],[f_329_2]) ).

fof(f_330_1,plain,
    ! [M_3,N,K_2,L_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),L_1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),N)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),L_1)) ),
    inference(fof_nnf,[status(thm)],[fact_240_less__add__eq__less]) ).

fof(f_330_2,plain,
    ! [U_1144,U_1143,U_1142,U_1141] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1144),U_1143))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1144),U_1141) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1142),U_1143)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1142),U_1141)) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

cnf(f_330_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1144),U_1143))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1144),U_1141) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1142),U_1143)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1142),U_1141)) ),
    inference(clausify,[status(thm)],[f_330_2]) ).

fof(f_331_1,plain,
    ! [I_2,J_1,K_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_241_add__lessD1]) ).

fof(f_331_2,plain,
    ! [U_1147,U_1146,U_1145] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1147),U_1145))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1147),U_1146)),U_1145)) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

cnf(f_331_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1147),U_1145))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1147),U_1146)),U_1145)) ),
    inference(clausify,[status(thm)],[f_331_2]) ).

fof(f_332_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | M = Na
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      & ( ( M != Na
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_242_nat__less__le]) ).

fof(f_332_2,plain,
    ! [U_1149,U_1148] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1149),U_1148))
        | U_1149 = U_1148
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1149),U_1148)) )
      & ( ( U_1149 != U_1148
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1149),U_1148)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1149),U_1148)) ) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ( ! [U_1153,U_1151] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1153),U_1151))
        | U_1153 = U_1151
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1153),U_1151)) )
    & ! [U_1152,U_1150] :
        ( ( U_1152 != U_1150
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1152),U_1150)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1152),U_1150)) ) ),
    inference(miniscope,[status(thm)],[f_332_2]) ).

cnf(f_332_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1152),U_1150))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1152),U_1150)) ),
    inference(clausify,[status(thm)],[f_332_3]) ).

cnf(f_332_5,plain,
    ( U_1152 != U_1150
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1152),U_1150)) ),
    inference(clausify,[status(thm)],[f_332_3]) ).

cnf(f_332_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1153),U_1151))
    | U_1153 = U_1151
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1153),U_1151)) ),
    inference(clausify,[status(thm)],[f_332_3]) ).

fof(f_333_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ( M != Na
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) )
      & ( M = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_243_le__eq__less__or__eq]) ).

fof(f_333_2,plain,
    ! [U_1155,U_1154] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1155),U_1154))
        | ( U_1155 != U_1154
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1155),U_1154)) ) )
      & ( U_1155 = U_1154
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1155),U_1154))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1155),U_1154)) ) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ( ! [U_1159,U_1157] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1159),U_1157))
        | ( U_1159 != U_1157
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1159),U_1157)) ) )
    & ! [U_1158,U_1156] :
        ( U_1158 = U_1156
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1158),U_1156))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1158),U_1156)) ) ),
    inference(miniscope,[status(thm)],[f_333_2]) ).

cnf(f_333_4,plain,
    ( U_1158 = U_1156
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1158),U_1156))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1158),U_1156)) ),
    inference(clausify,[status(thm)],[f_333_3]) ).

cnf(f_333_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1159),U_1157))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1159),U_1157)) ),
    inference(clausify,[status(thm)],[f_333_3]) ).

cnf(f_333_6,plain,
    ( U_1159 != U_1157
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1159),U_1157)) ),
    inference(clausify,[status(thm)],[f_333_3]) ).

fof(f_334_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_244_less__imp__le__nat]) ).

fof(f_334_2,plain,
    ! [U_1161,U_1160] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1161),U_1160))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1161),U_1160)) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

cnf(f_334_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1161),U_1160))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1161),U_1160)) ),
    inference(clausify,[status(thm)],[f_334_2]) ).

fof(f_335_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
      | M_3 = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_245_le__neq__implies__less]) ).

fof(f_335_2,plain,
    ! [U_1163,U_1162] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1163),U_1162))
      | U_1163 = U_1162
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1163),U_1162)) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

cnf(f_335_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1163),U_1162))
    | U_1163 = U_1162
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1163),U_1162)) ),
    inference(clausify,[status(thm)],[f_335_2]) ).

fof(f_336_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
      | ( M_3 != N
        & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ) ),
    inference(fof_nnf,[status(thm)],[fact_246_less__or__eq__imp__le]) ).

fof(f_336_2,plain,
    ! [U_1165,U_1164] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1165),U_1164))
      | ( U_1165 != U_1164
        & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1165),U_1164)) ) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

cnf(f_336_3,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1165),U_1164))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1165),U_1164)) ),
    inference(clausify,[status(thm)],[f_336_2]) ).

cnf(f_336_4,plain,
    ( U_1165 != U_1164
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1165),U_1164)) ),
    inference(clausify,[status(thm)],[f_336_2]) ).

fof(f_337_1,plain,
    ! [N,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N))),
    inference(fof_nnf,[status(thm)],[fact_247_le__add2]) ).

fof(f_337_2,plain,
    ! [U_1167,U_1166] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1167),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1166),U_1167))),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

cnf(f_337_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1167),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1166),U_1167))),
    inference(clausify,[status(thm)],[f_337_2]) ).

fof(f_338_1,plain,
    ! [N,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_3))),
    inference(fof_nnf,[status(thm)],[fact_248_le__add1]) ).

fof(f_338_2,plain,
    ! [U_1169,U_1168] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1169),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1169),U_1168))),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

cnf(f_338_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1169),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1169),U_1168))),
    inference(clausify,[status(thm)],[f_338_2]) ).

fof(f_339_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ! [K_1] : Na != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1) )
      & ( ? [K_1] : Na = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_249_le__iff__add]) ).

fof(f_339_2,plain,
    ! [U_1173,U_1172] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1173),U_1172))
        | ! [U_1171] : U_1172 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1173),U_1171) )
      & ( ? [U_1170] : U_1172 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1173),U_1170)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1173),U_1172)) ) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

fof(f_339_3,plain,
    ( ! [U_1177,U_1175] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1177),U_1175))
        | ! [U_1171] : U_1175 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1177),U_1171) )
    & ! [U_1176,U_1174] :
        ( ? [U_1170] : U_1174 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1176),U_1170)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1176),U_1174)) ) ),
    inference(miniscope,[status(thm)],[f_339_2]) ).

fof(f_339_4,plain,
    ( ! [U_1177,U_1175] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1177),U_1175))
        | ! [U_1171] : U_1175 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1177),U_1171) )
    & ! [U_1176,U_1174] :
        ( U_1174 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1176),sK64(U_1176,U_1174))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1176),U_1174)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_1170,sK64(U_1176,U_1174))],[f_339_3]) ).

cnf(f_339_5,plain,
    ( U_1174 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1176),sK64(U_1176,U_1174))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1176),U_1174)) ),
    inference(clausify,[status(thm)],[f_339_4]) ).

cnf(f_339_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1177),U_1175))
    | U_1175 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1177),U_1171) ),
    inference(clausify,[status(thm)],[f_339_4]) ).

fof(f_340_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_250_nat__add__left__cancel__le]) ).

fof(f_340_2,plain,
    ! [U_1180,U_1179,U_1178] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1180),U_1179)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1180),U_1178)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1179),U_1178)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1179),U_1178))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1180),U_1179)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1180),U_1178))) ) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

fof(f_340_3,plain,
    ( ! [U_1186,U_1184,U_1182] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1186),U_1184)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1186),U_1182)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1184),U_1182)) )
    & ! [U_1185,U_1183,U_1181] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1183),U_1181))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1185),U_1183)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1185),U_1181))) ) ),
    inference(miniscope,[status(thm)],[f_340_2]) ).

cnf(f_340_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1183),U_1181))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1185),U_1183)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1185),U_1181))) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

cnf(f_340_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1186),U_1184)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1186),U_1182)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1184),U_1182)) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

fof(f_341_1,plain,
    ! [M_3,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),M_3)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_251_trans__le__add1]) ).

fof(f_341_2,plain,
    ! [U_1189,U_1188,U_1187] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1188),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1187),U_1189)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1188),U_1187)) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

cnf(f_341_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1188),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1187),U_1189)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1188),U_1187)) ),
    inference(clausify,[status(thm)],[f_341_2]) ).

fof(f_342_1,plain,
    ! [M_3,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),J_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_252_trans__le__add2]) ).

fof(f_342_2,plain,
    ! [U_1192,U_1191,U_1190] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1191),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1192),U_1190)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1191),U_1190)) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

cnf(f_342_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1191),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1192),U_1190)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1191),U_1190)) ),
    inference(clausify,[status(thm)],[f_342_2]) ).

fof(f_343_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_253_add__le__mono1]) ).

fof(f_343_2,plain,
    ! [U_1195,U_1194,U_1193] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1194),U_1195)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1193),U_1195)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1194),U_1193)) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

cnf(f_343_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1194),U_1195)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1193),U_1195)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1194),U_1193)) ),
    inference(clausify,[status(thm)],[f_343_2]) ).

fof(f_344_1,plain,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),K_2),L_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_254_add__le__mono]) ).

fof(f_344_2,plain,
    ! [U_1199,U_1198,U_1197,U_1196] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1197),U_1199)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1196),U_1198)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1199),U_1198))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1197),U_1196)) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

cnf(f_344_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1197),U_1199)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1196),U_1198)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1199),U_1198))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1197),U_1196)) ),
    inference(clausify,[status(thm)],[f_344_2]) ).

fof(f_345_1,plain,
    ! [M_3,K_2,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_2)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_255_add__leD2]) ).

fof(f_345_2,plain,
    ! [U_1202,U_1201,U_1200] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1201),U_1200))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1202),U_1201)),U_1200)) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

cnf(f_345_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1201),U_1200))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1202),U_1201)),U_1200)) ),
    inference(clausify,[status(thm)],[f_345_2]) ).

fof(f_346_1,plain,
    ! [M_3,K_2,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_2)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_256_add__leD1]) ).

fof(f_346_2,plain,
    ! [U_1205,U_1204,U_1203] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1205),U_1203))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1205),U_1204)),U_1203)) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

cnf(f_346_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1205),U_1203))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1205),U_1204)),U_1203)) ),
    inference(clausify,[status(thm)],[f_346_2]) ).

fof(f_347_1,plain,
    ! [X_b,X_a,Q_1,Pa] :
      ( hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1))
      | ? [X_1,Y_2] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_2))
          & hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_257_predicate2I]) ).

fof(f_347_2,plain,
    ! [U_1211,U_1210,U_1209,U_1208] :
      ( hBOOL(hAPP(fun(U_1210,fun(U_1211,bool)),bool,hAPP(fun(U_1210,fun(U_1211,bool)),fun(fun(U_1210,fun(U_1211,bool)),bool),ord_less_eq(fun(U_1210,fun(U_1211,bool))),U_1208),U_1209))
      | ? [U_1207,U_1206] :
          ( ~ hBOOL(hAPP(U_1211,bool,hAPP(U_1210,fun(U_1211,bool),U_1209,U_1207),U_1206))
          & hBOOL(hAPP(U_1211,bool,hAPP(U_1210,fun(U_1211,bool),U_1208,U_1207),U_1206)) ) ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ! [U_1211,U_1210,U_1209,U_1208] :
      ( hBOOL(hAPP(fun(U_1210,fun(U_1211,bool)),bool,hAPP(fun(U_1210,fun(U_1211,bool)),fun(fun(U_1210,fun(U_1211,bool)),bool),ord_less_eq(fun(U_1210,fun(U_1211,bool))),U_1208),U_1209))
      | ? [U_1206] :
          ( ~ hBOOL(hAPP(U_1211,bool,hAPP(U_1210,fun(U_1211,bool),U_1209,sK65(U_1211,U_1210,U_1209,U_1208)),U_1206))
          & hBOOL(hAPP(U_1211,bool,hAPP(U_1210,fun(U_1211,bool),U_1208,sK65(U_1211,U_1210,U_1209,U_1208)),U_1206)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_1207,sK65(U_1211,U_1210,U_1209,U_1208))],[f_347_2]) ).

fof(f_347_4,plain,
    ! [U_1211,U_1210,U_1209,U_1208] :
      ( hBOOL(hAPP(fun(U_1210,fun(U_1211,bool)),bool,hAPP(fun(U_1210,fun(U_1211,bool)),fun(fun(U_1210,fun(U_1211,bool)),bool),ord_less_eq(fun(U_1210,fun(U_1211,bool))),U_1208),U_1209))
      | ( ~ hBOOL(hAPP(U_1211,bool,hAPP(U_1210,fun(U_1211,bool),U_1209,sK65(U_1211,U_1210,U_1209,U_1208)),sK66(U_1211,U_1210,U_1209,U_1208)))
        & hBOOL(hAPP(U_1211,bool,hAPP(U_1210,fun(U_1211,bool),U_1208,sK65(U_1211,U_1210,U_1209,U_1208)),sK66(U_1211,U_1210,U_1209,U_1208))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_1206,sK66(U_1211,U_1210,U_1209,U_1208))],[f_347_3]) ).

cnf(f_347_5,plain,
    ( hBOOL(hAPP(U_1211,bool,hAPP(U_1210,fun(U_1211,bool),U_1208,sK65(U_1211,U_1210,U_1209,U_1208)),sK66(U_1211,U_1210,U_1209,U_1208)))
    | hBOOL(hAPP(fun(U_1210,fun(U_1211,bool)),bool,hAPP(fun(U_1210,fun(U_1211,bool)),fun(fun(U_1210,fun(U_1211,bool)),bool),ord_less_eq(fun(U_1210,fun(U_1211,bool))),U_1208),U_1209)) ),
    inference(clausify,[status(thm)],[f_347_4]) ).

cnf(f_347_6,plain,
    ( ~ hBOOL(hAPP(U_1211,bool,hAPP(U_1210,fun(U_1211,bool),U_1209,sK65(U_1211,U_1210,U_1209,U_1208)),sK66(U_1211,U_1210,U_1209,U_1208)))
    | hBOOL(hAPP(fun(U_1210,fun(U_1211,bool)),bool,hAPP(fun(U_1210,fun(U_1211,bool)),fun(fun(U_1210,fun(U_1211,bool)),bool),ord_less_eq(fun(U_1210,fun(U_1211,bool))),U_1208),U_1209)) ),
    inference(clausify,[status(thm)],[f_347_4]) ).

fof(f_348_1,plain,
    ! [X_b,X_a,B,C,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(fun(X_a,X_b),bool),fun(fun(fun(X_a,X_b),bool),bool),ord_less_eq(fun(fun(X_a,X_b),bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),C)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_a,fun(X_b,bool),B,X_1)),hAPP(X_a,fun(X_b,bool),C,X_1)))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_258_Pi__mono]) ).

fof(f_348_2,plain,
    ! [U_1217,U_1216,U_1215,U_1214,U_1213] :
      ( hBOOL(hAPP(fun(fun(U_1216,U_1217),bool),bool,hAPP(fun(fun(U_1216,U_1217),bool),fun(fun(fun(U_1216,U_1217),bool),bool),ord_less_eq(fun(fun(U_1216,U_1217),bool)),hAPP(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool),hAPP(fun(U_1216,bool),fun(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool)),pi(U_1216,U_1217),U_1213),U_1215)),hAPP(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool),hAPP(fun(U_1216,bool),fun(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool)),pi(U_1216,U_1217),U_1213),U_1214)))
      | ? [U_1212] :
          ( ~ hBOOL(hAPP(fun(U_1217,bool),bool,hAPP(fun(U_1217,bool),fun(fun(U_1217,bool),bool),ord_less_eq(fun(U_1217,bool)),hAPP(U_1216,fun(U_1217,bool),U_1215,U_1212)),hAPP(U_1216,fun(U_1217,bool),U_1214,U_1212)))
          & hBOOL(hAPP(fun(U_1216,bool),bool,hAPP(U_1216,fun(fun(U_1216,bool),bool),member(U_1216),U_1212),U_1213)) ) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ! [U_1217,U_1216,U_1215,U_1214,U_1213] :
      ( hBOOL(hAPP(fun(fun(U_1216,U_1217),bool),bool,hAPP(fun(fun(U_1216,U_1217),bool),fun(fun(fun(U_1216,U_1217),bool),bool),ord_less_eq(fun(fun(U_1216,U_1217),bool)),hAPP(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool),hAPP(fun(U_1216,bool),fun(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool)),pi(U_1216,U_1217),U_1213),U_1215)),hAPP(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool),hAPP(fun(U_1216,bool),fun(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool)),pi(U_1216,U_1217),U_1213),U_1214)))
      | ( ~ hBOOL(hAPP(fun(U_1217,bool),bool,hAPP(fun(U_1217,bool),fun(fun(U_1217,bool),bool),ord_less_eq(fun(U_1217,bool)),hAPP(U_1216,fun(U_1217,bool),U_1215,sK67(U_1217,U_1216,U_1215,U_1214,U_1213))),hAPP(U_1216,fun(U_1217,bool),U_1214,sK67(U_1217,U_1216,U_1215,U_1214,U_1213))))
        & hBOOL(hAPP(fun(U_1216,bool),bool,hAPP(U_1216,fun(fun(U_1216,bool),bool),member(U_1216),sK67(U_1217,U_1216,U_1215,U_1214,U_1213)),U_1213)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_1212,sK67(U_1217,U_1216,U_1215,U_1214,U_1213))],[f_348_2]) ).

cnf(f_348_4,plain,
    ( hBOOL(hAPP(fun(U_1216,bool),bool,hAPP(U_1216,fun(fun(U_1216,bool),bool),member(U_1216),sK67(U_1217,U_1216,U_1215,U_1214,U_1213)),U_1213))
    | hBOOL(hAPP(fun(fun(U_1216,U_1217),bool),bool,hAPP(fun(fun(U_1216,U_1217),bool),fun(fun(fun(U_1216,U_1217),bool),bool),ord_less_eq(fun(fun(U_1216,U_1217),bool)),hAPP(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool),hAPP(fun(U_1216,bool),fun(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool)),pi(U_1216,U_1217),U_1213),U_1215)),hAPP(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool),hAPP(fun(U_1216,bool),fun(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool)),pi(U_1216,U_1217),U_1213),U_1214))) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

cnf(f_348_5,plain,
    ( ~ hBOOL(hAPP(fun(U_1217,bool),bool,hAPP(fun(U_1217,bool),fun(fun(U_1217,bool),bool),ord_less_eq(fun(U_1217,bool)),hAPP(U_1216,fun(U_1217,bool),U_1215,sK67(U_1217,U_1216,U_1215,U_1214,U_1213))),hAPP(U_1216,fun(U_1217,bool),U_1214,sK67(U_1217,U_1216,U_1215,U_1214,U_1213))))
    | hBOOL(hAPP(fun(fun(U_1216,U_1217),bool),bool,hAPP(fun(fun(U_1216,U_1217),bool),fun(fun(fun(U_1216,U_1217),bool),bool),ord_less_eq(fun(fun(U_1216,U_1217),bool)),hAPP(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool),hAPP(fun(U_1216,bool),fun(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool)),pi(U_1216,U_1217),U_1213),U_1215)),hAPP(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool),hAPP(fun(U_1216,bool),fun(fun(U_1216,fun(U_1217,bool)),fun(fun(U_1216,U_1217),bool)),pi(U_1216,U_1217),U_1213),U_1214))) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

fof(f_349_1,plain,
    ! [X_a,B,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_259_subsetI]) ).

fof(f_349_2,plain,
    ! [U_1221,U_1220,U_1219] :
      ( hBOOL(hAPP(fun(U_1221,bool),bool,hAPP(fun(U_1221,bool),fun(fun(U_1221,bool),bool),ord_less_eq(fun(U_1221,bool)),U_1219),U_1220))
      | ? [U_1218] :
          ( ~ hBOOL(hAPP(fun(U_1221,bool),bool,hAPP(U_1221,fun(fun(U_1221,bool),bool),member(U_1221),U_1218),U_1220))
          & hBOOL(hAPP(fun(U_1221,bool),bool,hAPP(U_1221,fun(fun(U_1221,bool),bool),member(U_1221),U_1218),U_1219)) ) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ! [U_1221,U_1220,U_1219] :
      ( hBOOL(hAPP(fun(U_1221,bool),bool,hAPP(fun(U_1221,bool),fun(fun(U_1221,bool),bool),ord_less_eq(fun(U_1221,bool)),U_1219),U_1220))
      | ( ~ hBOOL(hAPP(fun(U_1221,bool),bool,hAPP(U_1221,fun(fun(U_1221,bool),bool),member(U_1221),sK68(U_1221,U_1220,U_1219)),U_1220))
        & hBOOL(hAPP(fun(U_1221,bool),bool,hAPP(U_1221,fun(fun(U_1221,bool),bool),member(U_1221),sK68(U_1221,U_1220,U_1219)),U_1219)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_1218,sK68(U_1221,U_1220,U_1219))],[f_349_2]) ).

cnf(f_349_4,plain,
    ( hBOOL(hAPP(fun(U_1221,bool),bool,hAPP(U_1221,fun(fun(U_1221,bool),bool),member(U_1221),sK68(U_1221,U_1220,U_1219)),U_1219))
    | hBOOL(hAPP(fun(U_1221,bool),bool,hAPP(fun(U_1221,bool),fun(fun(U_1221,bool),bool),ord_less_eq(fun(U_1221,bool)),U_1219),U_1220)) ),
    inference(clausify,[status(thm)],[f_349_3]) ).

cnf(f_349_5,plain,
    ( ~ hBOOL(hAPP(fun(U_1221,bool),bool,hAPP(U_1221,fun(fun(U_1221,bool),bool),member(U_1221),sK68(U_1221,U_1220,U_1219)),U_1220))
    | hBOOL(hAPP(fun(U_1221,bool),bool,hAPP(fun(U_1221,bool),fun(fun(U_1221,bool),bool),ord_less_eq(fun(U_1221,bool)),U_1219),U_1220)) ),
    inference(clausify,[status(thm)],[f_349_3]) ).

fof(f_350_1,plain,
    ! [M,K,F] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K))))
      | ? [M_1,N_2] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_1)),hAPP(nat,nat,F,N_2)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_260_mono__nat__linear__lb]) ).

fof(f_350_2,plain,
    ! [U_1226,U_1225,U_1224] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,U_1224,U_1226)),U_1225)),hAPP(nat,nat,U_1224,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1226),U_1225))))
      | ? [U_1223,U_1222] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1224,U_1223)),hAPP(nat,nat,U_1224,U_1222)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1223),U_1222)) ) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ! [U_1226,U_1225,U_1224] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,U_1224,U_1226)),U_1225)),hAPP(nat,nat,U_1224,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1226),U_1225))))
      | ? [U_1222] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1224,sK69(U_1226,U_1225,U_1224))),hAPP(nat,nat,U_1224,U_1222)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK69(U_1226,U_1225,U_1224)),U_1222)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_1223,sK69(U_1226,U_1225,U_1224))],[f_350_2]) ).

fof(f_350_4,plain,
    ! [U_1226,U_1225,U_1224] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,U_1224,U_1226)),U_1225)),hAPP(nat,nat,U_1224,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1226),U_1225))))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1224,sK69(U_1226,U_1225,U_1224))),hAPP(nat,nat,U_1224,sK70(U_1226,U_1225,U_1224))))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK69(U_1226,U_1225,U_1224)),sK70(U_1226,U_1225,U_1224))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_1222,sK70(U_1226,U_1225,U_1224))],[f_350_3]) ).

cnf(f_350_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK69(U_1226,U_1225,U_1224)),sK70(U_1226,U_1225,U_1224)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,U_1224,U_1226)),U_1225)),hAPP(nat,nat,U_1224,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1226),U_1225)))) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

cnf(f_350_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1224,sK69(U_1226,U_1225,U_1224))),hAPP(nat,nat,U_1224,sK70(U_1226,U_1225,U_1224))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,U_1224,U_1226)),U_1225)),hAPP(nat,nat,U_1224,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1226),U_1225)))) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

fof(f_351_1,plain,
    ! [I,J,F] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J))
      | ? [I_1,J_2] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_2)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_261_less__mono__imp__le__mono]) ).

fof(f_351_2,plain,
    ! [U_1231,U_1230,U_1229] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1229,U_1231)),hAPP(nat,nat,U_1229,U_1230)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1230))
      | ? [U_1228,U_1227] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1229,U_1228)),hAPP(nat,nat,U_1229,U_1227)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1228),U_1227)) ) ),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

fof(f_351_3,plain,
    ! [U_1231,U_1230,U_1229] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1229,U_1231)),hAPP(nat,nat,U_1229,U_1230)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1230))
      | ? [U_1227] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1229,sK71(U_1231,U_1230,U_1229))),hAPP(nat,nat,U_1229,U_1227)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK71(U_1231,U_1230,U_1229)),U_1227)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_1228,sK71(U_1231,U_1230,U_1229))],[f_351_2]) ).

fof(f_351_4,plain,
    ! [U_1231,U_1230,U_1229] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1229,U_1231)),hAPP(nat,nat,U_1229,U_1230)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1230))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1229,sK71(U_1231,U_1230,U_1229))),hAPP(nat,nat,U_1229,sK72(U_1231,U_1230,U_1229))))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK71(U_1231,U_1230,U_1229)),sK72(U_1231,U_1230,U_1229))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_1227,sK72(U_1231,U_1230,U_1229))],[f_351_3]) ).

cnf(f_351_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK71(U_1231,U_1230,U_1229)),sK72(U_1231,U_1230,U_1229)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1229,U_1231)),hAPP(nat,nat,U_1229,U_1230)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1230)) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

cnf(f_351_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1229,sK71(U_1231,U_1230,U_1229))),hAPP(nat,nat,U_1229,sK72(U_1231,U_1230,U_1229))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1229,U_1231)),hAPP(nat,nat,U_1229,U_1230)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1230)) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

fof(f_352_1,plain,
    ! [Z,X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_262_termination__basic__simps_I3_J]) ).

fof(f_352_2,plain,
    ! [U_1234,U_1233,U_1232] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1233),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1232),U_1234)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1233),U_1232)) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

cnf(f_352_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1233),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1232),U_1234)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1233),U_1232)) ),
    inference(clausify,[status(thm)],[f_352_2]) ).

fof(f_353_1,plain,
    ! [Y,X,Z] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_263_termination__basic__simps_I4_J]) ).

fof(f_353_2,plain,
    ! [U_1237,U_1236,U_1235] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1236),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1237),U_1235)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1236),U_1235)) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

cnf(f_353_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1236),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1237),U_1235)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1236),U_1235)) ),
    inference(clausify,[status(thm)],[f_353_2]) ).

fof(f_354_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_264_termination__basic__simps_I5_J]) ).

fof(f_354_2,plain,
    ! [U_1239,U_1238] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1239),U_1238))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1239),U_1238)) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

cnf(f_354_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1239),U_1238))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1239),U_1238)) ),
    inference(clausify,[status(thm)],[f_354_2]) ).

fof(f_355_1,plain,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_265_psubsetD]) ).

fof(f_355_2,plain,
    ! [U_1243,U_1242,U_1241,U_1240] :
      ( hBOOL(hAPP(fun(U_1243,bool),bool,hAPP(U_1243,fun(fun(U_1243,bool),bool),member(U_1243),U_1242),U_1240))
      | ~ hBOOL(hAPP(fun(U_1243,bool),bool,hAPP(U_1243,fun(fun(U_1243,bool),bool),member(U_1243),U_1242),U_1241))
      | ~ hBOOL(hAPP(fun(U_1243,bool),bool,hAPP(fun(U_1243,bool),fun(fun(U_1243,bool),bool),ord_less(fun(U_1243,bool)),U_1241),U_1240)) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

cnf(f_355_3,plain,
    ( hBOOL(hAPP(fun(U_1243,bool),bool,hAPP(U_1243,fun(fun(U_1243,bool),bool),member(U_1243),U_1242),U_1240))
    | ~ hBOOL(hAPP(fun(U_1243,bool),bool,hAPP(U_1243,fun(fun(U_1243,bool),bool),member(U_1243),U_1242),U_1241))
    | ~ hBOOL(hAPP(fun(U_1243,bool),bool,hAPP(fun(U_1243,bool),fun(fun(U_1243,bool),bool),ord_less(fun(U_1243,bool)),U_1241),U_1240)) ),
    inference(clausify,[status(thm)],[f_355_2]) ).

fof(f_356_1,plain,
    ! [X_a,C,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_266_psubset__trans]) ).

fof(f_356_2,plain,
    ! [U_1247,U_1246,U_1245,U_1244] :
      ( hBOOL(hAPP(fun(U_1247,bool),bool,hAPP(fun(U_1247,bool),fun(fun(U_1247,bool),bool),ord_less(fun(U_1247,bool)),U_1245),U_1246))
      | ~ hBOOL(hAPP(fun(U_1247,bool),bool,hAPP(fun(U_1247,bool),fun(fun(U_1247,bool),bool),ord_less(fun(U_1247,bool)),U_1244),U_1246))
      | ~ hBOOL(hAPP(fun(U_1247,bool),bool,hAPP(fun(U_1247,bool),fun(fun(U_1247,bool),bool),ord_less(fun(U_1247,bool)),U_1245),U_1244)) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

cnf(f_356_3,plain,
    ( hBOOL(hAPP(fun(U_1247,bool),bool,hAPP(fun(U_1247,bool),fun(fun(U_1247,bool),bool),ord_less(fun(U_1247,bool)),U_1245),U_1246))
    | ~ hBOOL(hAPP(fun(U_1247,bool),bool,hAPP(fun(U_1247,bool),fun(fun(U_1247,bool),bool),ord_less(fun(U_1247,bool)),U_1244),U_1246))
    | ~ hBOOL(hAPP(fun(U_1247,bool),bool,hAPP(fun(U_1247,bool),fun(fun(U_1247,bool),bool),ord_less(fun(U_1247,bool)),U_1245),U_1244)) ),
    inference(clausify,[status(thm)],[f_356_2]) ).

fof(f_357_1,plain,
    ! [Y,X,Z] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_267_termination__basic__simps_I2_J]) ).

fof(f_357_2,plain,
    ! [U_1250,U_1249,U_1248] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1249),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1250),U_1248)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1249),U_1248)) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

cnf(f_357_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1249),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1250),U_1248)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1249),U_1248)) ),
    inference(clausify,[status(thm)],[f_357_2]) ).

fof(f_358_1,plain,
    ! [Z,X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_268_termination__basic__simps_I1_J]) ).

fof(f_358_2,plain,
    ! [U_1253,U_1252,U_1251] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1252),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1251),U_1253)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1252),U_1251)) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

cnf(f_358_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1252),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1251),U_1253)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1252),U_1251)) ),
    inference(clausify,[status(thm)],[f_358_2]) ).

fof(f_359_1,plain,
    ! [X_b,X_a,R_2,X_2,Y_1] :
      ( ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_2),X_2),Y_1))
        | ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_1)),R_2)) )
      & ( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_1)),R_2))
        | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_2),X_2),Y_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_269_in__rel__def]) ).

fof(f_359_2,plain,
    ! [U_1258,U_1257,U_1256,U_1255,U_1254] :
      ( ( hBOOL(hAPP(U_1258,bool,hAPP(U_1257,fun(U_1258,bool),hAPP(fun(product_prod(U_1257,U_1258),bool),fun(U_1257,fun(U_1258,bool)),in_rel(U_1257,U_1258),U_1256),U_1255),U_1254))
        | ~ hBOOL(hAPP(fun(product_prod(U_1257,U_1258),bool),bool,hAPP(product_prod(U_1257,U_1258),fun(fun(product_prod(U_1257,U_1258),bool),bool),member(product_prod(U_1257,U_1258)),hAPP(U_1258,product_prod(U_1257,U_1258),hAPP(U_1257,fun(U_1258,product_prod(U_1257,U_1258)),product_Pair(U_1257,U_1258),U_1255),U_1254)),U_1256)) )
      & ( hBOOL(hAPP(fun(product_prod(U_1257,U_1258),bool),bool,hAPP(product_prod(U_1257,U_1258),fun(fun(product_prod(U_1257,U_1258),bool),bool),member(product_prod(U_1257,U_1258)),hAPP(U_1258,product_prod(U_1257,U_1258),hAPP(U_1257,fun(U_1258,product_prod(U_1257,U_1258)),product_Pair(U_1257,U_1258),U_1255),U_1254)),U_1256))
        | ~ hBOOL(hAPP(U_1258,bool,hAPP(U_1257,fun(U_1258,bool),hAPP(fun(product_prod(U_1257,U_1258),bool),fun(U_1257,fun(U_1258,bool)),in_rel(U_1257,U_1258),U_1256),U_1255),U_1254)) ) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ( ! [U_1268,U_1266,U_1264,U_1262,U_1260] :
        ( hBOOL(hAPP(U_1268,bool,hAPP(U_1266,fun(U_1268,bool),hAPP(fun(product_prod(U_1266,U_1268),bool),fun(U_1266,fun(U_1268,bool)),in_rel(U_1266,U_1268),U_1264),U_1262),U_1260))
        | ~ hBOOL(hAPP(fun(product_prod(U_1266,U_1268),bool),bool,hAPP(product_prod(U_1266,U_1268),fun(fun(product_prod(U_1266,U_1268),bool),bool),member(product_prod(U_1266,U_1268)),hAPP(U_1268,product_prod(U_1266,U_1268),hAPP(U_1266,fun(U_1268,product_prod(U_1266,U_1268)),product_Pair(U_1266,U_1268),U_1262),U_1260)),U_1264)) )
    & ! [U_1267,U_1265,U_1263,U_1261,U_1259] :
        ( hBOOL(hAPP(fun(product_prod(U_1265,U_1267),bool),bool,hAPP(product_prod(U_1265,U_1267),fun(fun(product_prod(U_1265,U_1267),bool),bool),member(product_prod(U_1265,U_1267)),hAPP(U_1267,product_prod(U_1265,U_1267),hAPP(U_1265,fun(U_1267,product_prod(U_1265,U_1267)),product_Pair(U_1265,U_1267),U_1261),U_1259)),U_1263))
        | ~ hBOOL(hAPP(U_1267,bool,hAPP(U_1265,fun(U_1267,bool),hAPP(fun(product_prod(U_1265,U_1267),bool),fun(U_1265,fun(U_1267,bool)),in_rel(U_1265,U_1267),U_1263),U_1261),U_1259)) ) ),
    inference(miniscope,[status(thm)],[f_359_2]) ).

cnf(f_359_4,plain,
    ( hBOOL(hAPP(fun(product_prod(U_1265,U_1267),bool),bool,hAPP(product_prod(U_1265,U_1267),fun(fun(product_prod(U_1265,U_1267),bool),bool),member(product_prod(U_1265,U_1267)),hAPP(U_1267,product_prod(U_1265,U_1267),hAPP(U_1265,fun(U_1267,product_prod(U_1265,U_1267)),product_Pair(U_1265,U_1267),U_1261),U_1259)),U_1263))
    | ~ hBOOL(hAPP(U_1267,bool,hAPP(U_1265,fun(U_1267,bool),hAPP(fun(product_prod(U_1265,U_1267),bool),fun(U_1265,fun(U_1267,bool)),in_rel(U_1265,U_1267),U_1263),U_1261),U_1259)) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

cnf(f_359_5,plain,
    ( hBOOL(hAPP(U_1268,bool,hAPP(U_1266,fun(U_1268,bool),hAPP(fun(product_prod(U_1266,U_1268),bool),fun(U_1266,fun(U_1268,bool)),in_rel(U_1266,U_1268),U_1264),U_1262),U_1260))
    | ~ hBOOL(hAPP(fun(product_prod(U_1266,U_1268),bool),bool,hAPP(product_prod(U_1266,U_1268),fun(fun(product_prod(U_1266,U_1268),bool),bool),member(product_prod(U_1266,U_1268)),hAPP(U_1268,product_prod(U_1266,U_1268),hAPP(U_1266,fun(U_1268,product_prod(U_1266,U_1268)),product_Pair(U_1266,U_1268),U_1262),U_1260)),U_1264)) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

fof(f_360_1,plain,
    ! [X_b,X_a,F,B,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_270_funcsetI]) ).

fof(f_360_2,plain,
    ! [U_1274,U_1273,U_1272,U_1271,U_1270] :
      ( hBOOL(hAPP(fun(fun(U_1273,U_1274),bool),bool,hAPP(fun(U_1273,U_1274),fun(fun(fun(U_1273,U_1274),bool),bool),member(fun(U_1273,U_1274)),U_1272),hAPP(fun(U_1273,fun(U_1274,bool)),fun(fun(U_1273,U_1274),bool),hAPP(fun(U_1273,bool),fun(fun(U_1273,fun(U_1274,bool)),fun(fun(U_1273,U_1274),bool)),pi(U_1273,U_1274),U_1270),hAPP(fun(U_1274,bool),fun(U_1273,fun(U_1274,bool)),combk(fun(U_1274,bool),U_1273),U_1271))))
      | ? [U_1269] :
          ( ~ hBOOL(hAPP(fun(U_1274,bool),bool,hAPP(U_1274,fun(fun(U_1274,bool),bool),member(U_1274),hAPP(U_1273,U_1274,U_1272,U_1269)),U_1271))
          & hBOOL(hAPP(fun(U_1273,bool),bool,hAPP(U_1273,fun(fun(U_1273,bool),bool),member(U_1273),U_1269),U_1270)) ) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

fof(f_360_3,plain,
    ! [U_1274,U_1273,U_1272,U_1271,U_1270] :
      ( hBOOL(hAPP(fun(fun(U_1273,U_1274),bool),bool,hAPP(fun(U_1273,U_1274),fun(fun(fun(U_1273,U_1274),bool),bool),member(fun(U_1273,U_1274)),U_1272),hAPP(fun(U_1273,fun(U_1274,bool)),fun(fun(U_1273,U_1274),bool),hAPP(fun(U_1273,bool),fun(fun(U_1273,fun(U_1274,bool)),fun(fun(U_1273,U_1274),bool)),pi(U_1273,U_1274),U_1270),hAPP(fun(U_1274,bool),fun(U_1273,fun(U_1274,bool)),combk(fun(U_1274,bool),U_1273),U_1271))))
      | ( ~ hBOOL(hAPP(fun(U_1274,bool),bool,hAPP(U_1274,fun(fun(U_1274,bool),bool),member(U_1274),hAPP(U_1273,U_1274,U_1272,sK73(U_1274,U_1273,U_1272,U_1271,U_1270))),U_1271))
        & hBOOL(hAPP(fun(U_1273,bool),bool,hAPP(U_1273,fun(fun(U_1273,bool),bool),member(U_1273),sK73(U_1274,U_1273,U_1272,U_1271,U_1270)),U_1270)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_1269,sK73(U_1274,U_1273,U_1272,U_1271,U_1270))],[f_360_2]) ).

cnf(f_360_4,plain,
    ( hBOOL(hAPP(fun(U_1273,bool),bool,hAPP(U_1273,fun(fun(U_1273,bool),bool),member(U_1273),sK73(U_1274,U_1273,U_1272,U_1271,U_1270)),U_1270))
    | hBOOL(hAPP(fun(fun(U_1273,U_1274),bool),bool,hAPP(fun(U_1273,U_1274),fun(fun(fun(U_1273,U_1274),bool),bool),member(fun(U_1273,U_1274)),U_1272),hAPP(fun(U_1273,fun(U_1274,bool)),fun(fun(U_1273,U_1274),bool),hAPP(fun(U_1273,bool),fun(fun(U_1273,fun(U_1274,bool)),fun(fun(U_1273,U_1274),bool)),pi(U_1273,U_1274),U_1270),hAPP(fun(U_1274,bool),fun(U_1273,fun(U_1274,bool)),combk(fun(U_1274,bool),U_1273),U_1271)))) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

cnf(f_360_5,plain,
    ( ~ hBOOL(hAPP(fun(U_1274,bool),bool,hAPP(U_1274,fun(fun(U_1274,bool),bool),member(U_1274),hAPP(U_1273,U_1274,U_1272,sK73(U_1274,U_1273,U_1272,U_1271,U_1270))),U_1271))
    | hBOOL(hAPP(fun(fun(U_1273,U_1274),bool),bool,hAPP(fun(U_1273,U_1274),fun(fun(fun(U_1273,U_1274),bool),bool),member(fun(U_1273,U_1274)),U_1272),hAPP(fun(U_1273,fun(U_1274,bool)),fun(fun(U_1273,U_1274),bool),hAPP(fun(U_1273,bool),fun(fun(U_1273,fun(U_1274,bool)),fun(fun(U_1273,U_1274),bool)),pi(U_1273,U_1274),U_1270),hAPP(fun(U_1274,bool),fun(U_1273,fun(U_1274,bool)),combk(fun(U_1274,bool),U_1273),U_1271)))) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

fof(f_361_1,plain,
    ? [L_2] : hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),L_2),arrow_1568854078le_Lin)),
    inference(fof_nnf,[status(thm)],[fact_271_linear__alt]) ).

fof(f_361_2,plain,
    ? [U_1275] : hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),U_1275),arrow_1568854078le_Lin)),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sK74),arrow_1568854078le_Lin)),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_1275,sK74)],[f_361_2]) ).

cnf(f_361_4,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),sK74),arrow_1568854078le_Lin)),
    inference(clausify,[status(thm)],[f_361_3]) ).

fof(f_362_1,plain,
    ! [X_b,X_a,B,F,G,A_1] :
      ( ( ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
          | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) )
        & ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
          | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ) )
      | ? [W_1] :
          ( hAPP(X_a,X_b,F,W_1) != hAPP(X_a,X_b,G,W_1)
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_272_Pi__cong]) ).

fof(f_362_2,plain,
    ! [U_1282,U_1281,U_1280,U_1279,U_1278,U_1277] :
      ( ( ( hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1279),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
          | ~ hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1278),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280))) )
        & ( hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1278),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
          | ~ hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1279),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280))) ) )
      | ? [U_1276] :
          ( hAPP(U_1281,U_1282,U_1279,U_1276) != hAPP(U_1281,U_1282,U_1278,U_1276)
          & hBOOL(hAPP(fun(U_1281,bool),bool,hAPP(U_1281,fun(fun(U_1281,bool),bool),member(U_1281),U_1276),U_1277)) ) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

fof(f_362_3,plain,
    ! [U_1282,U_1281,U_1280,U_1279,U_1278,U_1277] :
      ( ( ( hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1279),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
          | ~ hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1278),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280))) )
        & ( hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1278),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
          | ~ hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1279),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280))) ) )
      | ( hAPP(U_1281,U_1282,U_1279,sK75(U_1282,U_1281,U_1280,U_1279,U_1278,U_1277)) != hAPP(U_1281,U_1282,U_1278,sK75(U_1282,U_1281,U_1280,U_1279,U_1278,U_1277))
        & hBOOL(hAPP(fun(U_1281,bool),bool,hAPP(U_1281,fun(fun(U_1281,bool),bool),member(U_1281),sK75(U_1282,U_1281,U_1280,U_1279,U_1278,U_1277)),U_1277)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_1276,sK75(U_1282,U_1281,U_1280,U_1279,U_1278,U_1277))],[f_362_2]) ).

cnf(f_362_4,plain,
    ( hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1278),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
    | ~ hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1279),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
    | hBOOL(hAPP(fun(U_1281,bool),bool,hAPP(U_1281,fun(fun(U_1281,bool),bool),member(U_1281),sK75(U_1282,U_1281,U_1280,U_1279,U_1278,U_1277)),U_1277)) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

cnf(f_362_5,plain,
    ( hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1279),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
    | ~ hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1278),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
    | hBOOL(hAPP(fun(U_1281,bool),bool,hAPP(U_1281,fun(fun(U_1281,bool),bool),member(U_1281),sK75(U_1282,U_1281,U_1280,U_1279,U_1278,U_1277)),U_1277)) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

cnf(f_362_6,plain,
    ( hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1278),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
    | ~ hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1279),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
    | hAPP(U_1281,U_1282,U_1279,sK75(U_1282,U_1281,U_1280,U_1279,U_1278,U_1277)) != hAPP(U_1281,U_1282,U_1278,sK75(U_1282,U_1281,U_1280,U_1279,U_1278,U_1277)) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

cnf(f_362_7,plain,
    ( hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1279),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
    | ~ hBOOL(hAPP(fun(fun(U_1281,U_1282),bool),bool,hAPP(fun(U_1281,U_1282),fun(fun(fun(U_1281,U_1282),bool),bool),member(fun(U_1281,U_1282)),U_1278),hAPP(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool),hAPP(fun(U_1281,bool),fun(fun(U_1281,fun(U_1282,bool)),fun(fun(U_1281,U_1282),bool)),pi(U_1281,U_1282),U_1277),U_1280)))
    | hAPP(U_1281,U_1282,U_1279,sK75(U_1282,U_1281,U_1280,U_1279,U_1278,U_1277)) != hAPP(U_1281,U_1282,U_1278,sK75(U_1282,U_1281,U_1280,U_1279,U_1278,U_1277)) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

fof(f_363_1,plain,
    ! [X_b,X_a,F,B,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1)))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_273_Pi__I_H]) ).

fof(f_363_2,plain,
    ! [U_1288,U_1287,U_1286,U_1285,U_1284] :
      ( hBOOL(hAPP(fun(fun(U_1287,U_1288),bool),bool,hAPP(fun(U_1287,U_1288),fun(fun(fun(U_1287,U_1288),bool),bool),member(fun(U_1287,U_1288)),U_1286),hAPP(fun(U_1287,fun(U_1288,bool)),fun(fun(U_1287,U_1288),bool),hAPP(fun(U_1287,bool),fun(fun(U_1287,fun(U_1288,bool)),fun(fun(U_1287,U_1288),bool)),pi(U_1287,U_1288),U_1284),U_1285)))
      | ? [U_1283] :
          ( ~ hBOOL(hAPP(fun(U_1288,bool),bool,hAPP(U_1288,fun(fun(U_1288,bool),bool),member(U_1288),hAPP(U_1287,U_1288,U_1286,U_1283)),hAPP(U_1287,fun(U_1288,bool),U_1285,U_1283)))
          & hBOOL(hAPP(fun(U_1287,bool),bool,hAPP(U_1287,fun(fun(U_1287,bool),bool),member(U_1287),U_1283),U_1284)) ) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ! [U_1288,U_1287,U_1286,U_1285,U_1284] :
      ( hBOOL(hAPP(fun(fun(U_1287,U_1288),bool),bool,hAPP(fun(U_1287,U_1288),fun(fun(fun(U_1287,U_1288),bool),bool),member(fun(U_1287,U_1288)),U_1286),hAPP(fun(U_1287,fun(U_1288,bool)),fun(fun(U_1287,U_1288),bool),hAPP(fun(U_1287,bool),fun(fun(U_1287,fun(U_1288,bool)),fun(fun(U_1287,U_1288),bool)),pi(U_1287,U_1288),U_1284),U_1285)))
      | ( ~ hBOOL(hAPP(fun(U_1288,bool),bool,hAPP(U_1288,fun(fun(U_1288,bool),bool),member(U_1288),hAPP(U_1287,U_1288,U_1286,sK76(U_1288,U_1287,U_1286,U_1285,U_1284))),hAPP(U_1287,fun(U_1288,bool),U_1285,sK76(U_1288,U_1287,U_1286,U_1285,U_1284))))
        & hBOOL(hAPP(fun(U_1287,bool),bool,hAPP(U_1287,fun(fun(U_1287,bool),bool),member(U_1287),sK76(U_1288,U_1287,U_1286,U_1285,U_1284)),U_1284)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_1283,sK76(U_1288,U_1287,U_1286,U_1285,U_1284))],[f_363_2]) ).

cnf(f_363_4,plain,
    ( hBOOL(hAPP(fun(U_1287,bool),bool,hAPP(U_1287,fun(fun(U_1287,bool),bool),member(U_1287),sK76(U_1288,U_1287,U_1286,U_1285,U_1284)),U_1284))
    | hBOOL(hAPP(fun(fun(U_1287,U_1288),bool),bool,hAPP(fun(U_1287,U_1288),fun(fun(fun(U_1287,U_1288),bool),bool),member(fun(U_1287,U_1288)),U_1286),hAPP(fun(U_1287,fun(U_1288,bool)),fun(fun(U_1287,U_1288),bool),hAPP(fun(U_1287,bool),fun(fun(U_1287,fun(U_1288,bool)),fun(fun(U_1287,U_1288),bool)),pi(U_1287,U_1288),U_1284),U_1285))) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

cnf(f_363_5,plain,
    ( ~ hBOOL(hAPP(fun(U_1288,bool),bool,hAPP(U_1288,fun(fun(U_1288,bool),bool),member(U_1288),hAPP(U_1287,U_1288,U_1286,sK76(U_1288,U_1287,U_1286,U_1285,U_1284))),hAPP(U_1287,fun(U_1288,bool),U_1285,sK76(U_1288,U_1287,U_1286,U_1285,U_1284))))
    | hBOOL(hAPP(fun(fun(U_1287,U_1288),bool),bool,hAPP(fun(U_1287,U_1288),fun(fun(fun(U_1287,U_1288),bool),bool),member(fun(U_1287,U_1288)),U_1286),hAPP(fun(U_1287,fun(U_1288,bool)),fun(fun(U_1287,U_1288),bool),hAPP(fun(U_1287,bool),fun(fun(U_1287,fun(U_1288,bool)),fun(fun(U_1287,U_1288),bool)),pi(U_1287,U_1288),U_1284),U_1285))) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

fof(f_364_1,plain,
    ! [X_a,X_b,F,A_1,B] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
    inference(fof_nnf,[status(thm)],[fact_274_card__inj]) ).

fof(f_364_2,plain,
    ! [U_1293,U_1292,U_1291,U_1290,U_1289] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1293,bool),nat,finite_card(U_1293),U_1290)),hAPP(fun(U_1292,bool),nat,finite_card(U_1292),U_1289)))
      | ~ hBOOL(hAPP(fun(U_1292,bool),bool,finite_finite_1(U_1292),U_1289))
      | ~ hBOOL(hAPP(fun(U_1293,bool),bool,hAPP(fun(U_1293,U_1292),fun(fun(U_1293,bool),bool),inj_on(U_1293,U_1292),U_1291),U_1290))
      | ~ hBOOL(hAPP(fun(fun(U_1293,U_1292),bool),bool,hAPP(fun(U_1293,U_1292),fun(fun(fun(U_1293,U_1292),bool),bool),member(fun(U_1293,U_1292)),U_1291),hAPP(fun(U_1293,fun(U_1292,bool)),fun(fun(U_1293,U_1292),bool),hAPP(fun(U_1293,bool),fun(fun(U_1293,fun(U_1292,bool)),fun(fun(U_1293,U_1292),bool)),pi(U_1293,U_1292),U_1290),hAPP(fun(U_1292,bool),fun(U_1293,fun(U_1292,bool)),combk(fun(U_1292,bool),U_1293),U_1289)))) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

cnf(f_364_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1293,bool),nat,finite_card(U_1293),U_1290)),hAPP(fun(U_1292,bool),nat,finite_card(U_1292),U_1289)))
    | ~ hBOOL(hAPP(fun(U_1292,bool),bool,finite_finite_1(U_1292),U_1289))
    | ~ hBOOL(hAPP(fun(U_1293,bool),bool,hAPP(fun(U_1293,U_1292),fun(fun(U_1293,bool),bool),inj_on(U_1293,U_1292),U_1291),U_1290))
    | ~ hBOOL(hAPP(fun(fun(U_1293,U_1292),bool),bool,hAPP(fun(U_1293,U_1292),fun(fun(fun(U_1293,U_1292),bool),bool),member(fun(U_1293,U_1292)),U_1291),hAPP(fun(U_1293,fun(U_1292,bool)),fun(fun(U_1293,U_1292),bool),hAPP(fun(U_1293,bool),fun(fun(U_1293,fun(U_1292,bool)),fun(fun(U_1293,U_1292),bool)),pi(U_1293,U_1292),U_1290),hAPP(fun(U_1292,bool),fun(U_1293,fun(U_1292,bool)),combk(fun(U_1292,bool),U_1293),U_1289)))) ),
    inference(clausify,[status(thm)],[f_364_2]) ).

fof(f_365_1,plain,
    ! [X_b,X_a,G,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
      | ? [X_1] :
          ( hAPP(X_b,X_a,G,hAPP(X_a,X_b,F,X_1)) != ti(X_a,X_1)
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_275_inj__on__inverseI]) ).

fof(f_365_2,plain,
    ! [U_1299,U_1298,U_1297,U_1296,U_1295] :
      ( hBOOL(hAPP(fun(U_1298,bool),bool,hAPP(fun(U_1298,U_1299),fun(fun(U_1298,bool),bool),inj_on(U_1298,U_1299),U_1296),U_1295))
      | ? [U_1294] :
          ( hAPP(U_1299,U_1298,U_1297,hAPP(U_1298,U_1299,U_1296,U_1294)) != ti(U_1298,U_1294)
          & hBOOL(hAPP(fun(U_1298,bool),bool,hAPP(U_1298,fun(fun(U_1298,bool),bool),member(U_1298),U_1294),U_1295)) ) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ! [U_1299,U_1298,U_1297,U_1296,U_1295] :
      ( hBOOL(hAPP(fun(U_1298,bool),bool,hAPP(fun(U_1298,U_1299),fun(fun(U_1298,bool),bool),inj_on(U_1298,U_1299),U_1296),U_1295))
      | ( hAPP(U_1299,U_1298,U_1297,hAPP(U_1298,U_1299,U_1296,sK77(U_1299,U_1298,U_1297,U_1296,U_1295))) != ti(U_1298,sK77(U_1299,U_1298,U_1297,U_1296,U_1295))
        & hBOOL(hAPP(fun(U_1298,bool),bool,hAPP(U_1298,fun(fun(U_1298,bool),bool),member(U_1298),sK77(U_1299,U_1298,U_1297,U_1296,U_1295)),U_1295)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_1294,sK77(U_1299,U_1298,U_1297,U_1296,U_1295))],[f_365_2]) ).

cnf(f_365_4,plain,
    ( hBOOL(hAPP(fun(U_1298,bool),bool,hAPP(U_1298,fun(fun(U_1298,bool),bool),member(U_1298),sK77(U_1299,U_1298,U_1297,U_1296,U_1295)),U_1295))
    | hBOOL(hAPP(fun(U_1298,bool),bool,hAPP(fun(U_1298,U_1299),fun(fun(U_1298,bool),bool),inj_on(U_1298,U_1299),U_1296),U_1295)) ),
    inference(clausify,[status(thm)],[f_365_3]) ).

cnf(f_365_5,plain,
    ( hAPP(U_1299,U_1298,U_1297,hAPP(U_1298,U_1299,U_1296,sK77(U_1299,U_1298,U_1297,U_1296,U_1295))) != ti(U_1298,sK77(U_1299,U_1298,U_1297,U_1296,U_1295))
    | hBOOL(hAPP(fun(U_1298,bool),bool,hAPP(fun(U_1298,U_1299),fun(fun(U_1298,bool),bool),inj_on(U_1298,U_1299),U_1296),U_1295)) ),
    inference(clausify,[status(thm)],[f_365_3]) ).

fof(f_366_1,plain,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(fof_nnf,[status(thm)],[fact_276_finite__indi]) ).

cnf(f_366_2,plain,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(clausify,[status(thm)],[f_366_1]) ).

fof(f_367_1,plain,
    ! [X_a,X_b,G,F,A_1,B] :
      ( hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_b,bool),nat,finite_card(X_b),B)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),G),B))
      | ~ hBOOL(hAPP(fun(fun(X_b,X_a),bool),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,X_a),bool),bool),member(fun(X_b,X_a)),G),hAPP(fun(X_b,fun(X_a,bool)),fun(fun(X_b,X_a),bool),hAPP(fun(X_b,bool),fun(fun(X_b,fun(X_a,bool)),fun(fun(X_b,X_a),bool)),pi(X_b,X_a),B),hAPP(fun(X_a,bool),fun(X_b,fun(X_a,bool)),combk(fun(X_a,bool),X_b),A_1))))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
    inference(fof_nnf,[status(thm)],[fact_277_card__bij]) ).

fof(f_367_2,plain,
    ! [U_1305,U_1304,U_1303,U_1302,U_1301,U_1300] :
      ( hAPP(fun(U_1305,bool),nat,finite_card(U_1305),U_1301) = hAPP(fun(U_1304,bool),nat,finite_card(U_1304),U_1300)
      | ~ hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite_1(U_1304),U_1300))
      | ~ hBOOL(hAPP(fun(U_1305,bool),bool,finite_finite_1(U_1305),U_1301))
      | ~ hBOOL(hAPP(fun(U_1304,bool),bool,hAPP(fun(U_1304,U_1305),fun(fun(U_1304,bool),bool),inj_on(U_1304,U_1305),U_1303),U_1300))
      | ~ hBOOL(hAPP(fun(fun(U_1304,U_1305),bool),bool,hAPP(fun(U_1304,U_1305),fun(fun(fun(U_1304,U_1305),bool),bool),member(fun(U_1304,U_1305)),U_1303),hAPP(fun(U_1304,fun(U_1305,bool)),fun(fun(U_1304,U_1305),bool),hAPP(fun(U_1304,bool),fun(fun(U_1304,fun(U_1305,bool)),fun(fun(U_1304,U_1305),bool)),pi(U_1304,U_1305),U_1300),hAPP(fun(U_1305,bool),fun(U_1304,fun(U_1305,bool)),combk(fun(U_1305,bool),U_1304),U_1301))))
      | ~ hBOOL(hAPP(fun(U_1305,bool),bool,hAPP(fun(U_1305,U_1304),fun(fun(U_1305,bool),bool),inj_on(U_1305,U_1304),U_1302),U_1301))
      | ~ hBOOL(hAPP(fun(fun(U_1305,U_1304),bool),bool,hAPP(fun(U_1305,U_1304),fun(fun(fun(U_1305,U_1304),bool),bool),member(fun(U_1305,U_1304)),U_1302),hAPP(fun(U_1305,fun(U_1304,bool)),fun(fun(U_1305,U_1304),bool),hAPP(fun(U_1305,bool),fun(fun(U_1305,fun(U_1304,bool)),fun(fun(U_1305,U_1304),bool)),pi(U_1305,U_1304),U_1301),hAPP(fun(U_1304,bool),fun(U_1305,fun(U_1304,bool)),combk(fun(U_1304,bool),U_1305),U_1300)))) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

cnf(f_367_3,plain,
    ( hAPP(fun(U_1305,bool),nat,finite_card(U_1305),U_1301) = hAPP(fun(U_1304,bool),nat,finite_card(U_1304),U_1300)
    | ~ hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite_1(U_1304),U_1300))
    | ~ hBOOL(hAPP(fun(U_1305,bool),bool,finite_finite_1(U_1305),U_1301))
    | ~ hBOOL(hAPP(fun(U_1304,bool),bool,hAPP(fun(U_1304,U_1305),fun(fun(U_1304,bool),bool),inj_on(U_1304,U_1305),U_1303),U_1300))
    | ~ hBOOL(hAPP(fun(fun(U_1304,U_1305),bool),bool,hAPP(fun(U_1304,U_1305),fun(fun(fun(U_1304,U_1305),bool),bool),member(fun(U_1304,U_1305)),U_1303),hAPP(fun(U_1304,fun(U_1305,bool)),fun(fun(U_1304,U_1305),bool),hAPP(fun(U_1304,bool),fun(fun(U_1304,fun(U_1305,bool)),fun(fun(U_1304,U_1305),bool)),pi(U_1304,U_1305),U_1300),hAPP(fun(U_1305,bool),fun(U_1304,fun(U_1305,bool)),combk(fun(U_1305,bool),U_1304),U_1301))))
    | ~ hBOOL(hAPP(fun(U_1305,bool),bool,hAPP(fun(U_1305,U_1304),fun(fun(U_1305,bool),bool),inj_on(U_1305,U_1304),U_1302),U_1301))
    | ~ hBOOL(hAPP(fun(fun(U_1305,U_1304),bool),bool,hAPP(fun(U_1305,U_1304),fun(fun(fun(U_1305,U_1304),bool),bool),member(fun(U_1305,U_1304)),U_1302),hAPP(fun(U_1305,fun(U_1304,bool)),fun(fun(U_1305,U_1304),bool),hAPP(fun(U_1305,bool),fun(fun(U_1305,fun(U_1304,bool)),fun(fun(U_1305,U_1304),bool)),pi(U_1305,U_1304),U_1301),hAPP(fun(U_1304,bool),fun(U_1305,fun(U_1304,bool)),combk(fun(U_1304,bool),U_1305),U_1300)))) ),
    inference(clausify,[status(thm)],[f_367_2]) ).

fof(f_368_1,plain,
    ! [X_a,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_1))))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_278_finite__Collect__subsets]) ).

fof(f_368_2,plain,
    ! [U_1307,U_1306] :
      ( hBOOL(hAPP(fun(fun(U_1307,bool),bool),bool,finite_finite_1(fun(U_1307,bool)),hAPP(fun(fun(U_1307,bool),bool),fun(fun(U_1307,bool),bool),collect(fun(U_1307,bool)),hAPP(fun(U_1307,bool),fun(fun(U_1307,bool),bool),hAPP(fun(fun(U_1307,bool),fun(fun(U_1307,bool),bool)),fun(fun(U_1307,bool),fun(fun(U_1307,bool),bool)),combc(fun(U_1307,bool),fun(U_1307,bool),bool),ord_less_eq(fun(U_1307,bool))),U_1306))))
      | ~ hBOOL(hAPP(fun(U_1307,bool),bool,finite_finite_1(U_1307),U_1306)) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

cnf(f_368_3,plain,
    ( hBOOL(hAPP(fun(fun(U_1307,bool),bool),bool,finite_finite_1(fun(U_1307,bool)),hAPP(fun(fun(U_1307,bool),bool),fun(fun(U_1307,bool),bool),collect(fun(U_1307,bool)),hAPP(fun(U_1307,bool),fun(fun(U_1307,bool),bool),hAPP(fun(fun(U_1307,bool),fun(fun(U_1307,bool),bool)),fun(fun(U_1307,bool),fun(fun(U_1307,bool),bool)),combc(fun(U_1307,bool),fun(U_1307,bool),bool),ord_less_eq(fun(U_1307,bool))),U_1306))))
    | ~ hBOOL(hAPP(fun(U_1307,bool),bool,finite_finite_1(U_1307),U_1306)) ),
    inference(clausify,[status(thm)],[f_368_2]) ).

fof(f_369_1,plain,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B)) ),
    inference(fof_nnf,[status(thm)],[fact_279_card__psubset]) ).

fof(f_369_2,plain,
    ! [U_1310,U_1309,U_1308] :
      ( hBOOL(hAPP(fun(U_1310,bool),bool,hAPP(fun(U_1310,bool),fun(fun(U_1310,bool),bool),ord_less(fun(U_1310,bool)),U_1309),U_1308))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1310,bool),nat,finite_card(U_1310),U_1309)),hAPP(fun(U_1310,bool),nat,finite_card(U_1310),U_1308)))
      | ~ hBOOL(hAPP(fun(U_1310,bool),bool,hAPP(fun(U_1310,bool),fun(fun(U_1310,bool),bool),ord_less_eq(fun(U_1310,bool)),U_1309),U_1308))
      | ~ hBOOL(hAPP(fun(U_1310,bool),bool,finite_finite_1(U_1310),U_1308)) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

cnf(f_369_3,plain,
    ( hBOOL(hAPP(fun(U_1310,bool),bool,hAPP(fun(U_1310,bool),fun(fun(U_1310,bool),bool),ord_less(fun(U_1310,bool)),U_1309),U_1308))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1310,bool),nat,finite_card(U_1310),U_1309)),hAPP(fun(U_1310,bool),nat,finite_card(U_1310),U_1308)))
    | ~ hBOOL(hAPP(fun(U_1310,bool),bool,hAPP(fun(U_1310,bool),fun(fun(U_1310,bool),bool),ord_less_eq(fun(U_1310,bool)),U_1309),U_1308))
    | ~ hBOOL(hAPP(fun(U_1310,bool),bool,finite_finite_1(U_1310),U_1308)) ),
    inference(clausify,[status(thm)],[f_369_2]) ).

fof(f_370_1,plain,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B)) ),
    inference(fof_nnf,[status(thm)],[fact_280_psubset__card__mono]) ).

fof(f_370_2,plain,
    ! [U_1313,U_1312,U_1311] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1313,bool),nat,finite_card(U_1313),U_1312)),hAPP(fun(U_1313,bool),nat,finite_card(U_1313),U_1311)))
      | ~ hBOOL(hAPP(fun(U_1313,bool),bool,hAPP(fun(U_1313,bool),fun(fun(U_1313,bool),bool),ord_less(fun(U_1313,bool)),U_1312),U_1311))
      | ~ hBOOL(hAPP(fun(U_1313,bool),bool,finite_finite_1(U_1313),U_1311)) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

cnf(f_370_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1313,bool),nat,finite_card(U_1313),U_1312)),hAPP(fun(U_1313,bool),nat,finite_card(U_1313),U_1311)))
    | ~ hBOOL(hAPP(fun(U_1313,bool),bool,hAPP(fun(U_1313,bool),fun(fun(U_1313,bool),bool),ord_less(fun(U_1313,bool)),U_1312),U_1311))
    | ~ hBOOL(hAPP(fun(U_1313,bool),bool,finite_finite_1(U_1313),U_1311)) ),
    inference(clausify,[status(thm)],[f_370_2]) ).

fof(f_371_1,plain,
    ! [X_a,A_1,B] :
      ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B)) ),
    inference(fof_nnf,[status(thm)],[fact_281_card__seteq]) ).

fof(f_371_2,plain,
    ! [U_1316,U_1315,U_1314] :
      ( ti(fun(U_1316,bool),U_1315) = ti(fun(U_1316,bool),U_1314)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1316,bool),nat,finite_card(U_1316),U_1314)),hAPP(fun(U_1316,bool),nat,finite_card(U_1316),U_1315)))
      | ~ hBOOL(hAPP(fun(U_1316,bool),bool,hAPP(fun(U_1316,bool),fun(fun(U_1316,bool),bool),ord_less_eq(fun(U_1316,bool)),U_1315),U_1314))
      | ~ hBOOL(hAPP(fun(U_1316,bool),bool,finite_finite_1(U_1316),U_1314)) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

cnf(f_371_3,plain,
    ( ti(fun(U_1316,bool),U_1315) = ti(fun(U_1316,bool),U_1314)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1316,bool),nat,finite_card(U_1316),U_1314)),hAPP(fun(U_1316,bool),nat,finite_card(U_1316),U_1315)))
    | ~ hBOOL(hAPP(fun(U_1316,bool),bool,hAPP(fun(U_1316,bool),fun(fun(U_1316,bool),bool),ord_less_eq(fun(U_1316,bool)),U_1315),U_1314))
    | ~ hBOOL(hAPP(fun(U_1316,bool),bool,finite_finite_1(U_1316),U_1314)) ),
    inference(clausify,[status(thm)],[f_371_2]) ).

fof(f_372_1,plain,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B)) ),
    inference(fof_nnf,[status(thm)],[fact_282_card__mono]) ).

fof(f_372_2,plain,
    ! [U_1319,U_1318,U_1317] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1319,bool),nat,finite_card(U_1319),U_1318)),hAPP(fun(U_1319,bool),nat,finite_card(U_1319),U_1317)))
      | ~ hBOOL(hAPP(fun(U_1319,bool),bool,hAPP(fun(U_1319,bool),fun(fun(U_1319,bool),bool),ord_less_eq(fun(U_1319,bool)),U_1318),U_1317))
      | ~ hBOOL(hAPP(fun(U_1319,bool),bool,finite_finite_1(U_1319),U_1317)) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

cnf(f_372_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1319,bool),nat,finite_card(U_1319),U_1318)),hAPP(fun(U_1319,bool),nat,finite_card(U_1319),U_1317)))
    | ~ hBOOL(hAPP(fun(U_1319,bool),bool,hAPP(fun(U_1319,bool),fun(fun(U_1319,bool),bool),ord_less_eq(fun(U_1319,bool)),U_1318),U_1317))
    | ~ hBOOL(hAPP(fun(U_1319,bool),bool,finite_finite_1(U_1319),U_1317)) ),
    inference(clausify,[status(thm)],[f_372_2]) ).

fof(f_373_1,plain,
    ! [K] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K)))),
    inference(fof_nnf,[status(thm)],[fact_283_finite__Collect__le__nat]) ).

fof(f_373_2,plain,
    ! [U_1320] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),U_1320)))),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

cnf(f_373_3,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),U_1320)))),
    inference(clausify,[status(thm)],[f_373_2]) ).

fof(f_374_1,plain,
    ! [X_a,Q_1,Pa] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),Pa)),Q_1))))
      | ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
        & ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_284_finite__Collect__conjI]) ).

fof(f_374_2,plain,
    ! [U_1323,U_1322,U_1321] :
      ( hBOOL(hAPP(fun(U_1323,bool),bool,finite_finite_1(U_1323),hAPP(fun(U_1323,bool),fun(U_1323,bool),collect(U_1323),hAPP(fun(U_1323,bool),fun(U_1323,bool),hAPP(fun(U_1323,fun(bool,bool)),fun(fun(U_1323,bool),fun(U_1323,bool)),combs(U_1323,bool,bool),hAPP(fun(U_1323,bool),fun(U_1323,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1323,bool),fun(U_1323,fun(bool,bool))),combb(bool,fun(bool,bool),U_1323),fconj),U_1321)),U_1322))))
      | ( ~ hBOOL(hAPP(fun(U_1323,bool),bool,finite_finite_1(U_1323),hAPP(fun(U_1323,bool),fun(U_1323,bool),collect(U_1323),U_1322)))
        & ~ hBOOL(hAPP(fun(U_1323,bool),bool,finite_finite_1(U_1323),hAPP(fun(U_1323,bool),fun(U_1323,bool),collect(U_1323),U_1321))) ) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

cnf(f_374_3,plain,
    ( ~ hBOOL(hAPP(fun(U_1323,bool),bool,finite_finite_1(U_1323),hAPP(fun(U_1323,bool),fun(U_1323,bool),collect(U_1323),U_1321)))
    | hBOOL(hAPP(fun(U_1323,bool),bool,finite_finite_1(U_1323),hAPP(fun(U_1323,bool),fun(U_1323,bool),collect(U_1323),hAPP(fun(U_1323,bool),fun(U_1323,bool),hAPP(fun(U_1323,fun(bool,bool)),fun(fun(U_1323,bool),fun(U_1323,bool)),combs(U_1323,bool,bool),hAPP(fun(U_1323,bool),fun(U_1323,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1323,bool),fun(U_1323,fun(bool,bool))),combb(bool,fun(bool,bool),U_1323),fconj),U_1321)),U_1322)))) ),
    inference(clausify,[status(thm)],[f_374_2]) ).

cnf(f_374_4,plain,
    ( ~ hBOOL(hAPP(fun(U_1323,bool),bool,finite_finite_1(U_1323),hAPP(fun(U_1323,bool),fun(U_1323,bool),collect(U_1323),U_1322)))
    | hBOOL(hAPP(fun(U_1323,bool),bool,finite_finite_1(U_1323),hAPP(fun(U_1323,bool),fun(U_1323,bool),collect(U_1323),hAPP(fun(U_1323,bool),fun(U_1323,bool),hAPP(fun(U_1323,fun(bool,bool)),fun(fun(U_1323,bool),fun(U_1323,bool)),combs(U_1323,bool,bool),hAPP(fun(U_1323,bool),fun(U_1323,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1323,bool),fun(U_1323,fun(bool,bool))),combb(bool,fun(bool,bool),U_1323),fconj),U_1321)),U_1322)))) ),
    inference(clausify,[status(thm)],[f_374_2]) ).

fof(f_375_1,plain,
    ! [K] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K)))),
    inference(fof_nnf,[status(thm)],[fact_285_finite__Collect__less__nat]) ).

fof(f_375_2,plain,
    ! [U_1324] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1324)))),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

cnf(f_375_3,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1324)))),
    inference(clausify,[status(thm)],[f_375_2]) ).

fof(f_376_1,plain,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    inference(fof_nnf,[status(thm)],[fact_286_infinite__UNIV__nat]) ).

cnf(f_376_2,plain,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    inference(clausify,[status(thm)],[f_376_1]) ).

fof(f_377_1,plain,
    ! [X_a] :
      ( ! [A_1] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ finite_finite(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_287_finite__code]) ).

fof(f_377_2,plain,
    ! [U_1326] :
      ( ! [U_1325] : hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),U_1325))
      | ~ finite_finite(U_1326) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

cnf(f_377_3,plain,
    ( hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),U_1325))
    | ~ finite_finite(U_1326) ),
    inference(clausify,[status(thm)],[f_377_2]) ).

fof(f_378_1,plain,
    ! [X_a] :
      ( ! [A_1] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ finite_finite(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_288_finite]) ).

fof(f_378_2,plain,
    ! [U_1328] :
      ( ! [U_1327] : hBOOL(hAPP(fun(U_1328,bool),bool,finite_finite_1(U_1328),U_1327))
      | ~ finite_finite(U_1328) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

cnf(f_378_3,plain,
    ( hBOOL(hAPP(fun(U_1328,bool),bool,finite_finite_1(U_1328),U_1327))
    | ~ finite_finite(U_1328) ),
    inference(clausify,[status(thm)],[f_378_2]) ).

fof(f_379_1,plain,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    inference(fof_nnf,[status(thm)],[fact_289_card__UNIV__unit]) ).

cnf(f_379_2,plain,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    inference(clausify,[status(thm)],[f_379_1]) ).

fof(f_380_1,plain,
    ! [X_a,Pa,Q_1] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),Pa)),Q_1))))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa))) )
      & ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
          & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa))) )
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),Pa)),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_290_finite__Collect__disjI]) ).

fof(f_380_2,plain,
    ! [U_1331,U_1330,U_1329] :
      ( ( hBOOL(hAPP(fun(U_1331,bool),bool,finite_finite_1(U_1331),hAPP(fun(U_1331,bool),fun(U_1331,bool),collect(U_1331),hAPP(fun(U_1331,bool),fun(U_1331,bool),hAPP(fun(U_1331,fun(bool,bool)),fun(fun(U_1331,bool),fun(U_1331,bool)),combs(U_1331,bool,bool),hAPP(fun(U_1331,bool),fun(U_1331,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1331,bool),fun(U_1331,fun(bool,bool))),combb(bool,fun(bool,bool),U_1331),fdisj),U_1330)),U_1329))))
        | ~ hBOOL(hAPP(fun(U_1331,bool),bool,finite_finite_1(U_1331),hAPP(fun(U_1331,bool),fun(U_1331,bool),collect(U_1331),U_1329)))
        | ~ hBOOL(hAPP(fun(U_1331,bool),bool,finite_finite_1(U_1331),hAPP(fun(U_1331,bool),fun(U_1331,bool),collect(U_1331),U_1330))) )
      & ( ( hBOOL(hAPP(fun(U_1331,bool),bool,finite_finite_1(U_1331),hAPP(fun(U_1331,bool),fun(U_1331,bool),collect(U_1331),U_1329)))
          & hBOOL(hAPP(fun(U_1331,bool),bool,finite_finite_1(U_1331),hAPP(fun(U_1331,bool),fun(U_1331,bool),collect(U_1331),U_1330))) )
        | ~ hBOOL(hAPP(fun(U_1331,bool),bool,finite_finite_1(U_1331),hAPP(fun(U_1331,bool),fun(U_1331,bool),collect(U_1331),hAPP(fun(U_1331,bool),fun(U_1331,bool),hAPP(fun(U_1331,fun(bool,bool)),fun(fun(U_1331,bool),fun(U_1331,bool)),combs(U_1331,bool,bool),hAPP(fun(U_1331,bool),fun(U_1331,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1331,bool),fun(U_1331,fun(bool,bool))),combb(bool,fun(bool,bool),U_1331),fdisj),U_1330)),U_1329)))) ) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ( ! [U_1337,U_1335,U_1333] :
        ( hBOOL(hAPP(fun(U_1337,bool),bool,finite_finite_1(U_1337),hAPP(fun(U_1337,bool),fun(U_1337,bool),collect(U_1337),hAPP(fun(U_1337,bool),fun(U_1337,bool),hAPP(fun(U_1337,fun(bool,bool)),fun(fun(U_1337,bool),fun(U_1337,bool)),combs(U_1337,bool,bool),hAPP(fun(U_1337,bool),fun(U_1337,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1337,bool),fun(U_1337,fun(bool,bool))),combb(bool,fun(bool,bool),U_1337),fdisj),U_1335)),U_1333))))
        | ~ hBOOL(hAPP(fun(U_1337,bool),bool,finite_finite_1(U_1337),hAPP(fun(U_1337,bool),fun(U_1337,bool),collect(U_1337),U_1333)))
        | ~ hBOOL(hAPP(fun(U_1337,bool),bool,finite_finite_1(U_1337),hAPP(fun(U_1337,bool),fun(U_1337,bool),collect(U_1337),U_1335))) )
    & ! [U_1336,U_1334,U_1332] :
        ( ( hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),hAPP(fun(U_1336,bool),fun(U_1336,bool),collect(U_1336),U_1332)))
          & hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),hAPP(fun(U_1336,bool),fun(U_1336,bool),collect(U_1336),U_1334))) )
        | ~ hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),hAPP(fun(U_1336,bool),fun(U_1336,bool),collect(U_1336),hAPP(fun(U_1336,bool),fun(U_1336,bool),hAPP(fun(U_1336,fun(bool,bool)),fun(fun(U_1336,bool),fun(U_1336,bool)),combs(U_1336,bool,bool),hAPP(fun(U_1336,bool),fun(U_1336,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1336,bool),fun(U_1336,fun(bool,bool))),combb(bool,fun(bool,bool),U_1336),fdisj),U_1334)),U_1332)))) ) ),
    inference(miniscope,[status(thm)],[f_380_2]) ).

cnf(f_380_4,plain,
    ( hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),hAPP(fun(U_1336,bool),fun(U_1336,bool),collect(U_1336),U_1334)))
    | ~ hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),hAPP(fun(U_1336,bool),fun(U_1336,bool),collect(U_1336),hAPP(fun(U_1336,bool),fun(U_1336,bool),hAPP(fun(U_1336,fun(bool,bool)),fun(fun(U_1336,bool),fun(U_1336,bool)),combs(U_1336,bool,bool),hAPP(fun(U_1336,bool),fun(U_1336,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1336,bool),fun(U_1336,fun(bool,bool))),combb(bool,fun(bool,bool),U_1336),fdisj),U_1334)),U_1332)))) ),
    inference(clausify,[status(thm)],[f_380_3]) ).

cnf(f_380_5,plain,
    ( hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),hAPP(fun(U_1336,bool),fun(U_1336,bool),collect(U_1336),U_1332)))
    | ~ hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),hAPP(fun(U_1336,bool),fun(U_1336,bool),collect(U_1336),hAPP(fun(U_1336,bool),fun(U_1336,bool),hAPP(fun(U_1336,fun(bool,bool)),fun(fun(U_1336,bool),fun(U_1336,bool)),combs(U_1336,bool,bool),hAPP(fun(U_1336,bool),fun(U_1336,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1336,bool),fun(U_1336,fun(bool,bool))),combb(bool,fun(bool,bool),U_1336),fdisj),U_1334)),U_1332)))) ),
    inference(clausify,[status(thm)],[f_380_3]) ).

cnf(f_380_6,plain,
    ( hBOOL(hAPP(fun(U_1337,bool),bool,finite_finite_1(U_1337),hAPP(fun(U_1337,bool),fun(U_1337,bool),collect(U_1337),hAPP(fun(U_1337,bool),fun(U_1337,bool),hAPP(fun(U_1337,fun(bool,bool)),fun(fun(U_1337,bool),fun(U_1337,bool)),combs(U_1337,bool,bool),hAPP(fun(U_1337,bool),fun(U_1337,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1337,bool),fun(U_1337,fun(bool,bool))),combb(bool,fun(bool,bool),U_1337),fdisj),U_1335)),U_1333))))
    | ~ hBOOL(hAPP(fun(U_1337,bool),bool,finite_finite_1(U_1337),hAPP(fun(U_1337,bool),fun(U_1337,bool),collect(U_1337),U_1333)))
    | ~ hBOOL(hAPP(fun(U_1337,bool),bool,finite_finite_1(U_1337),hAPP(fun(U_1337,bool),fun(U_1337,bool),collect(U_1337),U_1335))) ),
    inference(clausify,[status(thm)],[f_380_3]) ).

fof(f_381_1,plain,
    ! [Na] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na))) = Na,
    inference(fof_nnf,[status(thm)],[fact_291_card__Collect__less__nat]) ).

fof(f_381_2,plain,
    ! [U_1338] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1338))) = U_1338,
    inference(variable_rename,[status(thm)],[f_381_1]) ).

cnf(f_381_3,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1338))) = U_1338,
    inference(clausify,[status(thm)],[f_381_2]) ).

fof(f_382_1,plain,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B)) ),
    inference(fof_nnf,[status(thm)],[fact_292_rev__finite__subset]) ).

fof(f_382_2,plain,
    ! [U_1341,U_1340,U_1339] :
      ( hBOOL(hAPP(fun(U_1341,bool),bool,finite_finite_1(U_1341),U_1340))
      | ~ hBOOL(hAPP(fun(U_1341,bool),bool,hAPP(fun(U_1341,bool),fun(fun(U_1341,bool),bool),ord_less_eq(fun(U_1341,bool)),U_1340),U_1339))
      | ~ hBOOL(hAPP(fun(U_1341,bool),bool,finite_finite_1(U_1341),U_1339)) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

cnf(f_382_3,plain,
    ( hBOOL(hAPP(fun(U_1341,bool),bool,finite_finite_1(U_1341),U_1340))
    | ~ hBOOL(hAPP(fun(U_1341,bool),bool,hAPP(fun(U_1341,bool),fun(fun(U_1341,bool),bool),ord_less_eq(fun(U_1341,bool)),U_1340),U_1339))
    | ~ hBOOL(hAPP(fun(U_1341,bool),bool,finite_finite_1(U_1341),U_1339)) ),
    inference(clausify,[status(thm)],[f_382_2]) ).

fof(f_383_1,plain,
    ! [X_a,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_293_finite__subset]) ).

fof(f_383_2,plain,
    ! [U_1344,U_1343,U_1342] :
      ( hBOOL(hAPP(fun(U_1344,bool),bool,finite_finite_1(U_1344),U_1343))
      | ~ hBOOL(hAPP(fun(U_1344,bool),bool,finite_finite_1(U_1344),U_1342))
      | ~ hBOOL(hAPP(fun(U_1344,bool),bool,hAPP(fun(U_1344,bool),fun(fun(U_1344,bool),bool),ord_less_eq(fun(U_1344,bool)),U_1343),U_1342)) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

cnf(f_383_3,plain,
    ( hBOOL(hAPP(fun(U_1344,bool),bool,finite_finite_1(U_1344),U_1343))
    | ~ hBOOL(hAPP(fun(U_1344,bool),bool,finite_finite_1(U_1344),U_1342))
    | ~ hBOOL(hAPP(fun(U_1344,bool),bool,hAPP(fun(U_1344,bool),fun(fun(U_1344,bool),bool),ord_less_eq(fun(U_1344,bool)),U_1343),U_1342)) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

fof(f_384_1,plain,
    ! [X_a] :
      ( ( hBOOL(hAPP(fun(option(X_a),bool),bool,finite_finite_1(option(X_a)),top_top(fun(option(X_a),bool))))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) )
      & ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
        | ~ hBOOL(hAPP(fun(option(X_a),bool),bool,finite_finite_1(option(X_a)),top_top(fun(option(X_a),bool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_294_finite__option__UNIV]) ).

fof(f_384_2,plain,
    ! [U_1345] :
      ( ( hBOOL(hAPP(fun(option(U_1345),bool),bool,finite_finite_1(option(U_1345)),top_top(fun(option(U_1345),bool))))
        | ~ hBOOL(hAPP(fun(U_1345,bool),bool,finite_finite_1(U_1345),top_top(fun(U_1345,bool)))) )
      & ( hBOOL(hAPP(fun(U_1345,bool),bool,finite_finite_1(U_1345),top_top(fun(U_1345,bool))))
        | ~ hBOOL(hAPP(fun(option(U_1345),bool),bool,finite_finite_1(option(U_1345)),top_top(fun(option(U_1345),bool)))) ) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ( ! [U_1347] :
        ( hBOOL(hAPP(fun(option(U_1347),bool),bool,finite_finite_1(option(U_1347)),top_top(fun(option(U_1347),bool))))
        | ~ hBOOL(hAPP(fun(U_1347,bool),bool,finite_finite_1(U_1347),top_top(fun(U_1347,bool)))) )
    & ! [U_1346] :
        ( hBOOL(hAPP(fun(U_1346,bool),bool,finite_finite_1(U_1346),top_top(fun(U_1346,bool))))
        | ~ hBOOL(hAPP(fun(option(U_1346),bool),bool,finite_finite_1(option(U_1346)),top_top(fun(option(U_1346),bool)))) ) ),
    inference(miniscope,[status(thm)],[f_384_2]) ).

cnf(f_384_4,plain,
    ( hBOOL(hAPP(fun(U_1346,bool),bool,finite_finite_1(U_1346),top_top(fun(U_1346,bool))))
    | ~ hBOOL(hAPP(fun(option(U_1346),bool),bool,finite_finite_1(option(U_1346)),top_top(fun(option(U_1346),bool)))) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

cnf(f_384_5,plain,
    ( hBOOL(hAPP(fun(option(U_1347),bool),bool,finite_finite_1(option(U_1347)),top_top(fun(option(U_1347),bool))))
    | ~ hBOOL(hAPP(fun(U_1347,bool),bool,finite_finite_1(U_1347),top_top(fun(U_1347,bool)))) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_1,plain,
    ! [X_a,X_b] :
      ( ( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),top_top(fun(sum_sum(X_a,X_b),bool))))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),top_top(fun(X_b,bool))))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) )
      & ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),top_top(fun(X_b,bool))))
          & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) )
        | ~ hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),top_top(fun(sum_sum(X_a,X_b),bool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_295_finite__Plus__UNIV__iff]) ).

fof(f_385_2,plain,
    ! [U_1349,U_1348] :
      ( ( hBOOL(hAPP(fun(sum_sum(U_1349,U_1348),bool),bool,finite_finite_1(sum_sum(U_1349,U_1348)),top_top(fun(sum_sum(U_1349,U_1348),bool))))
        | ~ hBOOL(hAPP(fun(U_1348,bool),bool,finite_finite_1(U_1348),top_top(fun(U_1348,bool))))
        | ~ hBOOL(hAPP(fun(U_1349,bool),bool,finite_finite_1(U_1349),top_top(fun(U_1349,bool)))) )
      & ( ( hBOOL(hAPP(fun(U_1348,bool),bool,finite_finite_1(U_1348),top_top(fun(U_1348,bool))))
          & hBOOL(hAPP(fun(U_1349,bool),bool,finite_finite_1(U_1349),top_top(fun(U_1349,bool)))) )
        | ~ hBOOL(hAPP(fun(sum_sum(U_1349,U_1348),bool),bool,finite_finite_1(sum_sum(U_1349,U_1348)),top_top(fun(sum_sum(U_1349,U_1348),bool)))) ) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ( ! [U_1353,U_1351] :
        ( hBOOL(hAPP(fun(sum_sum(U_1353,U_1351),bool),bool,finite_finite_1(sum_sum(U_1353,U_1351)),top_top(fun(sum_sum(U_1353,U_1351),bool))))
        | ~ hBOOL(hAPP(fun(U_1351,bool),bool,finite_finite_1(U_1351),top_top(fun(U_1351,bool))))
        | ~ hBOOL(hAPP(fun(U_1353,bool),bool,finite_finite_1(U_1353),top_top(fun(U_1353,bool)))) )
    & ! [U_1352,U_1350] :
        ( ( hBOOL(hAPP(fun(U_1350,bool),bool,finite_finite_1(U_1350),top_top(fun(U_1350,bool))))
          & hBOOL(hAPP(fun(U_1352,bool),bool,finite_finite_1(U_1352),top_top(fun(U_1352,bool)))) )
        | ~ hBOOL(hAPP(fun(sum_sum(U_1352,U_1350),bool),bool,finite_finite_1(sum_sum(U_1352,U_1350)),top_top(fun(sum_sum(U_1352,U_1350),bool)))) ) ),
    inference(miniscope,[status(thm)],[f_385_2]) ).

cnf(f_385_4,plain,
    ( hBOOL(hAPP(fun(U_1352,bool),bool,finite_finite_1(U_1352),top_top(fun(U_1352,bool))))
    | ~ hBOOL(hAPP(fun(sum_sum(U_1352,U_1350),bool),bool,finite_finite_1(sum_sum(U_1352,U_1350)),top_top(fun(sum_sum(U_1352,U_1350),bool)))) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

cnf(f_385_5,plain,
    ( hBOOL(hAPP(fun(U_1350,bool),bool,finite_finite_1(U_1350),top_top(fun(U_1350,bool))))
    | ~ hBOOL(hAPP(fun(sum_sum(U_1352,U_1350),bool),bool,finite_finite_1(sum_sum(U_1352,U_1350)),top_top(fun(sum_sum(U_1352,U_1350),bool)))) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

cnf(f_385_6,plain,
    ( hBOOL(hAPP(fun(sum_sum(U_1353,U_1351),bool),bool,finite_finite_1(sum_sum(U_1353,U_1351)),top_top(fun(sum_sum(U_1353,U_1351),bool))))
    | ~ hBOOL(hAPP(fun(U_1351,bool),bool,finite_finite_1(U_1351),top_top(fun(U_1351,bool))))
    | ~ hBOOL(hAPP(fun(U_1353,bool),bool,finite_finite_1(U_1353),top_top(fun(U_1353,bool)))) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

fof(f_386_1,plain,
    ! [X_b,X_a] :
      ( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,finite_finite_1(product_prod(X_a,X_b)),top_top(fun(product_prod(X_a,X_b),bool))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),top_top(fun(X_b,bool))))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_296_finite__Prod__UNIV]) ).

fof(f_386_2,plain,
    ! [U_1355,U_1354] :
      ( hBOOL(hAPP(fun(product_prod(U_1354,U_1355),bool),bool,finite_finite_1(product_prod(U_1354,U_1355)),top_top(fun(product_prod(U_1354,U_1355),bool))))
      | ~ hBOOL(hAPP(fun(U_1355,bool),bool,finite_finite_1(U_1355),top_top(fun(U_1355,bool))))
      | ~ hBOOL(hAPP(fun(U_1354,bool),bool,finite_finite_1(U_1354),top_top(fun(U_1354,bool)))) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

cnf(f_386_3,plain,
    ( hBOOL(hAPP(fun(product_prod(U_1354,U_1355),bool),bool,finite_finite_1(product_prod(U_1354,U_1355)),top_top(fun(product_prod(U_1354,U_1355),bool))))
    | ~ hBOOL(hAPP(fun(U_1355,bool),bool,finite_finite_1(U_1355),top_top(fun(U_1355,bool))))
    | ~ hBOOL(hAPP(fun(U_1354,bool),bool,finite_finite_1(U_1354),top_top(fun(U_1354,bool)))) ),
    inference(clausify,[status(thm)],[f_386_2]) ).

fof(f_387_1,plain,
    ! [X_a] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
      | ~ finite_finite(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_297_finite__UNIV]) ).

fof(f_387_2,plain,
    ! [U_1356] :
      ( hBOOL(hAPP(fun(U_1356,bool),bool,finite_finite_1(U_1356),top_top(fun(U_1356,bool))))
      | ~ finite_finite(U_1356) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

cnf(f_387_3,plain,
    ( hBOOL(hAPP(fun(U_1356,bool),bool,finite_finite_1(U_1356),top_top(fun(U_1356,bool))))
    | ~ finite_finite(U_1356) ),
    inference(clausify,[status(thm)],[f_387_2]) ).

fof(f_388_1,plain,
    ! [X_a,Pa] :
      ( ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),Pa))))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) )
        & ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),Pa)))) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa))) ),
    inference(fof_nnf,[status(thm)],[fact_298_finite__Collect__not]) ).

fof(f_388_2,plain,
    ! [U_1358,U_1357] :
      ( ( ( hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),collect(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),hAPP(fun(bool,bool),fun(fun(U_1358,bool),fun(U_1358,bool)),combb(bool,bool,U_1358),fNot),U_1357))))
          | ~ hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),top_top(fun(U_1358,bool)))) )
        & ( hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),top_top(fun(U_1358,bool))))
          | ~ hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),collect(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),hAPP(fun(bool,bool),fun(fun(U_1358,bool),fun(U_1358,bool)),combb(bool,bool,U_1358),fNot),U_1357)))) ) )
      | ~ hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),collect(U_1358),U_1357))) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

cnf(f_388_3,plain,
    ( hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),top_top(fun(U_1358,bool))))
    | ~ hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),collect(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),hAPP(fun(bool,bool),fun(fun(U_1358,bool),fun(U_1358,bool)),combb(bool,bool,U_1358),fNot),U_1357))))
    | ~ hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),collect(U_1358),U_1357))) ),
    inference(clausify,[status(thm)],[f_388_2]) ).

cnf(f_388_4,plain,
    ( hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),collect(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),hAPP(fun(bool,bool),fun(fun(U_1358,bool),fun(U_1358,bool)),combb(bool,bool,U_1358),fNot),U_1357))))
    | ~ hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),top_top(fun(U_1358,bool))))
    | ~ hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),hAPP(fun(U_1358,bool),fun(U_1358,bool),collect(U_1358),U_1357))) ),
    inference(clausify,[status(thm)],[f_388_2]) ).

fof(f_389_1,plain,
    ! [X_a,A_1] :
      ( ti(fun(X_a,bool),A_1) = top_top(fun(X_a,bool))
      | hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) != hAPP(fun(X_a,bool),nat,finite_card(X_a),top_top(fun(X_a,bool)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_299_card__eq__UNIV__imp__eq__UNIV]) ).

fof(f_389_2,plain,
    ! [U_1360,U_1359] :
      ( ti(fun(U_1360,bool),U_1359) = top_top(fun(U_1360,bool))
      | hAPP(fun(U_1360,bool),nat,finite_card(U_1360),U_1359) != hAPP(fun(U_1360,bool),nat,finite_card(U_1360),top_top(fun(U_1360,bool)))
      | ~ hBOOL(hAPP(fun(U_1360,bool),bool,finite_finite_1(U_1360),top_top(fun(U_1360,bool)))) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ! [U_1360] :
      ( ! [U_1359] :
          ( ti(fun(U_1360,bool),U_1359) = top_top(fun(U_1360,bool))
          | hAPP(fun(U_1360,bool),nat,finite_card(U_1360),U_1359) != hAPP(fun(U_1360,bool),nat,finite_card(U_1360),top_top(fun(U_1360,bool))) )
      | ~ hBOOL(hAPP(fun(U_1360,bool),bool,finite_finite_1(U_1360),top_top(fun(U_1360,bool)))) ),
    inference(miniscope,[status(thm)],[f_389_2]) ).

cnf(f_389_4,plain,
    ( ti(fun(U_1360,bool),U_1359) = top_top(fun(U_1360,bool))
    | hAPP(fun(U_1360,bool),nat,finite_card(U_1360),U_1359) != hAPP(fun(U_1360,bool),nat,finite_card(U_1360),top_top(fun(U_1360,bool)))
    | ~ hBOOL(hAPP(fun(U_1360,bool),bool,finite_finite_1(U_1360),top_top(fun(U_1360,bool)))) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_1,plain,
    ! [X_a,X_b] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),top_top(fun(X_b,bool))))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,finite_finite_1(fun(X_a,X_b)),top_top(fun(fun(X_a,X_b),bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_300_finite__fun__UNIVD2]) ).

fof(f_390_2,plain,
    ! [U_1362,U_1361] :
      ( hBOOL(hAPP(fun(U_1361,bool),bool,finite_finite_1(U_1361),top_top(fun(U_1361,bool))))
      | ~ hBOOL(hAPP(fun(fun(U_1362,U_1361),bool),bool,finite_finite_1(fun(U_1362,U_1361)),top_top(fun(fun(U_1362,U_1361),bool)))) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

cnf(f_390_3,plain,
    ( hBOOL(hAPP(fun(U_1361,bool),bool,finite_finite_1(U_1361),top_top(fun(U_1361,bool))))
    | ~ hBOOL(hAPP(fun(fun(U_1362,U_1361),bool),bool,finite_finite_1(fun(U_1362,U_1361)),top_top(fun(fun(U_1362,U_1361),bool)))) ),
    inference(clausify,[status(thm)],[f_390_2]) ).

fof(f_391_1,plain,
    ! [Pa,I] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I))))),
    inference(fof_nnf,[status(thm)],[fact_301_finite__M__bounded__by__nat]) ).

fof(f_391_2,plain,
    ! [U_1364,U_1363] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),U_1364)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1363))))),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

cnf(f_391_3,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),U_1364)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1363))))),
    inference(clausify,[status(thm)],[f_391_2]) ).

fof(f_392_1,plain,
    ! [X_a,A_1] :
      ( ? [A_4] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_302_ex__new__if__finite]) ).

fof(f_392_2,plain,
    ! [U_1367,U_1366] :
      ( ? [U_1365] : ~ hBOOL(hAPP(fun(U_1367,bool),bool,hAPP(U_1367,fun(fun(U_1367,bool),bool),member(U_1367),U_1365),U_1366))
      | ~ hBOOL(hAPP(fun(U_1367,bool),bool,finite_finite_1(U_1367),U_1366))
      | hBOOL(hAPP(fun(U_1367,bool),bool,finite_finite_1(U_1367),top_top(fun(U_1367,bool)))) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ! [U_1367] :
      ( ! [U_1366] :
          ( ? [U_1365] : ~ hBOOL(hAPP(fun(U_1367,bool),bool,hAPP(U_1367,fun(fun(U_1367,bool),bool),member(U_1367),U_1365),U_1366))
          | ~ hBOOL(hAPP(fun(U_1367,bool),bool,finite_finite_1(U_1367),U_1366)) )
      | hBOOL(hAPP(fun(U_1367,bool),bool,finite_finite_1(U_1367),top_top(fun(U_1367,bool)))) ),
    inference(miniscope,[status(thm)],[f_392_2]) ).

fof(f_392_4,plain,
    ! [U_1367] :
      ( ! [U_1366] :
          ( ~ hBOOL(hAPP(fun(U_1367,bool),bool,hAPP(U_1367,fun(fun(U_1367,bool),bool),member(U_1367),sK78(U_1367,U_1366)),U_1366))
          | ~ hBOOL(hAPP(fun(U_1367,bool),bool,finite_finite_1(U_1367),U_1366)) )
      | hBOOL(hAPP(fun(U_1367,bool),bool,finite_finite_1(U_1367),top_top(fun(U_1367,bool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_1365,sK78(U_1367,U_1366))],[f_392_3]) ).

cnf(f_392_5,plain,
    ( ~ hBOOL(hAPP(fun(U_1367,bool),bool,hAPP(U_1367,fun(fun(U_1367,bool),bool),member(U_1367),sK78(U_1367,U_1366)),U_1366))
    | ~ hBOOL(hAPP(fun(U_1367,bool),bool,finite_finite_1(U_1367),U_1366))
    | hBOOL(hAPP(fun(U_1367,bool),bool,finite_finite_1(U_1367),top_top(fun(U_1367,bool)))) ),
    inference(clausify,[status(thm)],[f_392_4]) ).

fof(f_393_1,plain,
    ! [N_1] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_1))
        | ! [M_1] :
          ? [X_1] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),M_1))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_1)) ) )
      & ( ? [M_1] :
          ! [X_1] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),M_1))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_1)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_303_finite__nat__set__iff__bounded__le]) ).

fof(f_393_2,plain,
    ! [U_1372] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1372))
        | ! [U_1371] :
          ? [U_1370] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1370),U_1371))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1370),U_1372)) ) )
      & ( ? [U_1369] :
          ! [U_1368] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1368),U_1369))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1368),U_1372)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1372)) ) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ( ! [U_1374] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1374))
        | ! [U_1371] :
          ? [U_1370] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1370),U_1371))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1370),U_1374)) ) )
    & ! [U_1373] :
        ( ? [U_1369] :
          ! [U_1368] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1368),U_1369))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1368),U_1373)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1373)) ) ),
    inference(miniscope,[status(thm)],[f_393_2]) ).

fof(f_393_4,plain,
    ( ! [U_1374] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1374))
        | ! [U_1371] :
          ? [U_1370] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1370),U_1371))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1370),U_1374)) ) )
    & ! [U_1373] :
        ( ! [U_1368] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1368),sK79(U_1373)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1368),U_1373)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1373)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_1369,sK79(U_1373))],[f_393_3]) ).

fof(f_393_5,plain,
    ( ! [U_1374] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1374))
        | ! [U_1371] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK80(U_1374,U_1371)),U_1371))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK80(U_1374,U_1371)),U_1374)) ) )
    & ! [U_1373] :
        ( ! [U_1368] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1368),sK79(U_1373)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1368),U_1373)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1373)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_1370,sK80(U_1374,U_1371))],[f_393_4]) ).

cnf(f_393_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1368),sK79(U_1373)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1368),U_1373))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1373)) ),
    inference(clausify,[status(thm)],[f_393_5]) ).

cnf(f_393_7,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK80(U_1374,U_1371)),U_1374))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1374)) ),
    inference(clausify,[status(thm)],[f_393_5]) ).

cnf(f_393_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK80(U_1374,U_1371)),U_1371))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1374)) ),
    inference(clausify,[status(thm)],[f_393_5]) ).

fof(f_394_1,plain,
    ! [N_1] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_1))
        | ! [M_1] :
          ? [X_1] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),M_1))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_1)) ) )
      & ( ? [M_1] :
          ! [X_1] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),M_1))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_1)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_304_finite__nat__set__iff__bounded]) ).

fof(f_394_2,plain,
    ! [U_1379] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1379))
        | ! [U_1378] :
          ? [U_1377] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1377),U_1378))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1377),U_1379)) ) )
      & ( ? [U_1376] :
          ! [U_1375] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1375),U_1376))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1375),U_1379)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1379)) ) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ( ! [U_1381] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1381))
        | ! [U_1378] :
          ? [U_1377] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1377),U_1378))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1377),U_1381)) ) )
    & ! [U_1380] :
        ( ? [U_1376] :
          ! [U_1375] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1375),U_1376))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1375),U_1380)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1380)) ) ),
    inference(miniscope,[status(thm)],[f_394_2]) ).

fof(f_394_4,plain,
    ( ! [U_1381] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1381))
        | ! [U_1378] :
          ? [U_1377] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1377),U_1378))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1377),U_1381)) ) )
    & ! [U_1380] :
        ( ! [U_1375] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1375),sK81(U_1380)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1375),U_1380)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1380)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_1376,sK81(U_1380))],[f_394_3]) ).

fof(f_394_5,plain,
    ( ! [U_1381] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1381))
        | ! [U_1378] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK82(U_1381,U_1378)),U_1378))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK82(U_1381,U_1378)),U_1381)) ) )
    & ! [U_1380] :
        ( ! [U_1375] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1375),sK81(U_1380)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1375),U_1380)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1380)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_1377,sK82(U_1381,U_1378))],[f_394_4]) ).

cnf(f_394_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1375),sK81(U_1380)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1375),U_1380))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1380)) ),
    inference(clausify,[status(thm)],[f_394_5]) ).

cnf(f_394_7,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK82(U_1381,U_1378)),U_1381))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1381)) ),
    inference(clausify,[status(thm)],[f_394_5]) ).

cnf(f_394_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK82(U_1381,U_1378)),U_1378))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1381)) ),
    inference(clausify,[status(thm)],[f_394_5]) ).

fof(f_395_1,plain,
    ! [X_b,X_a,B,A_1] :
      ( hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_305_card__Plus]) ).

fof(f_395_2,plain,
    ! [U_1385,U_1384,U_1383,U_1382] :
      ( hAPP(fun(sum_sum(U_1384,U_1385),bool),nat,finite_card(sum_sum(U_1384,U_1385)),hAPP(fun(U_1385,bool),fun(sum_sum(U_1384,U_1385),bool),hAPP(fun(U_1384,bool),fun(fun(U_1385,bool),fun(sum_sum(U_1384,U_1385),bool)),sum_Plus(U_1384,U_1385),U_1382),U_1383)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1384,bool),nat,finite_card(U_1384),U_1382)),hAPP(fun(U_1385,bool),nat,finite_card(U_1385),U_1383))
      | ~ hBOOL(hAPP(fun(U_1385,bool),bool,finite_finite_1(U_1385),U_1383))
      | ~ hBOOL(hAPP(fun(U_1384,bool),bool,finite_finite_1(U_1384),U_1382)) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

cnf(f_395_3,plain,
    ( hAPP(fun(sum_sum(U_1384,U_1385),bool),nat,finite_card(sum_sum(U_1384,U_1385)),hAPP(fun(U_1385,bool),fun(sum_sum(U_1384,U_1385),bool),hAPP(fun(U_1384,bool),fun(fun(U_1385,bool),fun(sum_sum(U_1384,U_1385),bool)),sum_Plus(U_1384,U_1385),U_1382),U_1383)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1384,bool),nat,finite_card(U_1384),U_1382)),hAPP(fun(U_1385,bool),nat,finite_card(U_1385),U_1383))
    | ~ hBOOL(hAPP(fun(U_1385,bool),bool,finite_finite_1(U_1385),U_1383))
    | ~ hBOOL(hAPP(fun(U_1384,bool),bool,finite_finite_1(U_1384),U_1382)) ),
    inference(clausify,[status(thm)],[f_395_2]) ).

fof(f_396_1,plain,
    ! [X_b,X_a,B,A_1,F,Z_1,G,Fa] :
      ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,B)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_306_folding__image__simple__idem_Osubset__idem]) ).

fof(f_396_2,plain,
    ! [U_1393,U_1392,U_1391,U_1390,U_1389,U_1388,U_1387,U_1386] :
      ( hAPP(U_1392,U_1392,hAPP(U_1392,fun(U_1392,U_1392),U_1389,hAPP(fun(U_1393,bool),U_1392,U_1386,U_1391)),hAPP(fun(U_1393,bool),U_1392,U_1386,U_1390)) = hAPP(fun(U_1393,bool),U_1392,U_1386,U_1390)
      | ~ hBOOL(hAPP(fun(U_1393,bool),bool,hAPP(fun(U_1393,bool),fun(fun(U_1393,bool),bool),ord_less_eq(fun(U_1393,bool)),U_1391),U_1390))
      | ~ hBOOL(hAPP(fun(U_1393,bool),bool,finite_finite_1(U_1393),U_1390))
      | ~ hBOOL(hAPP(fun(fun(U_1393,bool),U_1392),bool,hAPP(fun(U_1393,U_1392),fun(fun(fun(U_1393,bool),U_1392),bool),hAPP(U_1392,fun(fun(U_1393,U_1392),fun(fun(fun(U_1393,bool),U_1392),bool)),hAPP(fun(U_1392,fun(U_1392,U_1392)),fun(U_1392,fun(fun(U_1393,U_1392),fun(fun(fun(U_1393,bool),U_1392),bool))),finite908156982e_idem(U_1392,U_1393),U_1389),U_1388),U_1387),U_1386)) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

cnf(f_396_3,plain,
    ( hAPP(U_1392,U_1392,hAPP(U_1392,fun(U_1392,U_1392),U_1389,hAPP(fun(U_1393,bool),U_1392,U_1386,U_1391)),hAPP(fun(U_1393,bool),U_1392,U_1386,U_1390)) = hAPP(fun(U_1393,bool),U_1392,U_1386,U_1390)
    | ~ hBOOL(hAPP(fun(U_1393,bool),bool,hAPP(fun(U_1393,bool),fun(fun(U_1393,bool),bool),ord_less_eq(fun(U_1393,bool)),U_1391),U_1390))
    | ~ hBOOL(hAPP(fun(U_1393,bool),bool,finite_finite_1(U_1393),U_1390))
    | ~ hBOOL(hAPP(fun(fun(U_1393,bool),U_1392),bool,hAPP(fun(U_1393,U_1392),fun(fun(fun(U_1393,bool),U_1392),bool),hAPP(U_1392,fun(fun(U_1393,U_1392),fun(fun(fun(U_1393,bool),U_1392),bool)),hAPP(fun(U_1392,fun(U_1392,U_1392)),fun(U_1392,fun(fun(U_1393,U_1392),fun(fun(fun(U_1393,bool),U_1392),bool))),finite908156982e_idem(U_1392,U_1393),U_1389),U_1388),U_1387),U_1386)) ),
    inference(clausify,[status(thm)],[f_396_2]) ).

fof(f_397_1,plain,
    ! [X_b,X_a,X_2,F,Z_1,G,Fa] :
      ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),X_2) = ti(X_a,X_2)
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_307_folding__image__simple__idem_Oidem]) ).

fof(f_397_2,plain,
    ! [U_1400,U_1399,U_1398,U_1397,U_1396,U_1395,U_1394] :
      ( hAPP(U_1399,U_1399,hAPP(U_1399,fun(U_1399,U_1399),U_1397,U_1398),U_1398) = ti(U_1399,U_1398)
      | ~ hBOOL(hAPP(fun(fun(U_1400,bool),U_1399),bool,hAPP(fun(U_1400,U_1399),fun(fun(fun(U_1400,bool),U_1399),bool),hAPP(U_1399,fun(fun(U_1400,U_1399),fun(fun(fun(U_1400,bool),U_1399),bool)),hAPP(fun(U_1399,fun(U_1399,U_1399)),fun(U_1399,fun(fun(U_1400,U_1399),fun(fun(fun(U_1400,bool),U_1399),bool))),finite908156982e_idem(U_1399,U_1400),U_1397),U_1396),U_1395),U_1394)) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_1400,U_1399,U_1398,U_1397] :
      ( ! [U_1396,U_1395,U_1394] : ~ hBOOL(hAPP(fun(fun(U_1400,bool),U_1399),bool,hAPP(fun(U_1400,U_1399),fun(fun(fun(U_1400,bool),U_1399),bool),hAPP(U_1399,fun(fun(U_1400,U_1399),fun(fun(fun(U_1400,bool),U_1399),bool)),hAPP(fun(U_1399,fun(U_1399,U_1399)),fun(U_1399,fun(fun(U_1400,U_1399),fun(fun(fun(U_1400,bool),U_1399),bool))),finite908156982e_idem(U_1399,U_1400),U_1397),U_1396),U_1395),U_1394))
      | hAPP(U_1399,U_1399,hAPP(U_1399,fun(U_1399,U_1399),U_1397,U_1398),U_1398) = ti(U_1399,U_1398) ),
    inference(miniscope,[status(thm)],[f_397_2]) ).

cnf(f_397_4,plain,
    ( ~ hBOOL(hAPP(fun(fun(U_1400,bool),U_1399),bool,hAPP(fun(U_1400,U_1399),fun(fun(fun(U_1400,bool),U_1399),bool),hAPP(U_1399,fun(fun(U_1400,U_1399),fun(fun(fun(U_1400,bool),U_1399),bool)),hAPP(fun(U_1399,fun(U_1399,U_1399)),fun(U_1399,fun(fun(U_1400,U_1399),fun(fun(fun(U_1400,bool),U_1399),bool))),finite908156982e_idem(U_1399,U_1400),U_1397),U_1396),U_1395),U_1394))
    | hAPP(U_1399,U_1399,hAPP(U_1399,fun(U_1399,U_1399),U_1397,U_1398),U_1398) = ti(U_1399,U_1398) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

fof(f_398_1,plain,
    ! [X_a,X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
      | ~ hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B))) ),
    inference(fof_nnf,[status(thm)],[fact_308_finite__PlusD_I2_J]) ).

fof(f_398_2,plain,
    ! [U_1404,U_1403,U_1402,U_1401] :
      ( hBOOL(hAPP(fun(U_1403,bool),bool,finite_finite_1(U_1403),U_1401))
      | ~ hBOOL(hAPP(fun(sum_sum(U_1404,U_1403),bool),bool,finite_finite_1(sum_sum(U_1404,U_1403)),hAPP(fun(U_1403,bool),fun(sum_sum(U_1404,U_1403),bool),hAPP(fun(U_1404,bool),fun(fun(U_1403,bool),fun(sum_sum(U_1404,U_1403),bool)),sum_Plus(U_1404,U_1403),U_1402),U_1401))) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

cnf(f_398_3,plain,
    ( hBOOL(hAPP(fun(U_1403,bool),bool,finite_finite_1(U_1403),U_1401))
    | ~ hBOOL(hAPP(fun(sum_sum(U_1404,U_1403),bool),bool,finite_finite_1(sum_sum(U_1404,U_1403)),hAPP(fun(U_1403,bool),fun(sum_sum(U_1404,U_1403),bool),hAPP(fun(U_1404,bool),fun(fun(U_1403,bool),fun(sum_sum(U_1404,U_1403),bool)),sum_Plus(U_1404,U_1403),U_1402),U_1401))) ),
    inference(clausify,[status(thm)],[f_398_2]) ).

fof(f_399_1,plain,
    ! [X_a,X_b,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B))) ),
    inference(fof_nnf,[status(thm)],[fact_309_finite__PlusD_I1_J]) ).

fof(f_399_2,plain,
    ! [U_1408,U_1407,U_1406,U_1405] :
      ( hBOOL(hAPP(fun(U_1408,bool),bool,finite_finite_1(U_1408),U_1406))
      | ~ hBOOL(hAPP(fun(sum_sum(U_1408,U_1407),bool),bool,finite_finite_1(sum_sum(U_1408,U_1407)),hAPP(fun(U_1407,bool),fun(sum_sum(U_1408,U_1407),bool),hAPP(fun(U_1408,bool),fun(fun(U_1407,bool),fun(sum_sum(U_1408,U_1407),bool)),sum_Plus(U_1408,U_1407),U_1406),U_1405))) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ! [U_1408,U_1407,U_1406] :
      ( ! [U_1405] : ~ hBOOL(hAPP(fun(sum_sum(U_1408,U_1407),bool),bool,finite_finite_1(sum_sum(U_1408,U_1407)),hAPP(fun(U_1407,bool),fun(sum_sum(U_1408,U_1407),bool),hAPP(fun(U_1408,bool),fun(fun(U_1407,bool),fun(sum_sum(U_1408,U_1407),bool)),sum_Plus(U_1408,U_1407),U_1406),U_1405)))
      | hBOOL(hAPP(fun(U_1408,bool),bool,finite_finite_1(U_1408),U_1406)) ),
    inference(miniscope,[status(thm)],[f_399_2]) ).

cnf(f_399_4,plain,
    ( ~ hBOOL(hAPP(fun(sum_sum(U_1408,U_1407),bool),bool,finite_finite_1(sum_sum(U_1408,U_1407)),hAPP(fun(U_1407,bool),fun(sum_sum(U_1408,U_1407),bool),hAPP(fun(U_1408,bool),fun(fun(U_1407,bool),fun(sum_sum(U_1408,U_1407),bool)),sum_Plus(U_1408,U_1407),U_1406),U_1405)))
    | hBOOL(hAPP(fun(U_1408,bool),bool,finite_finite_1(U_1408),U_1406)) ),
    inference(clausify,[status(thm)],[f_399_3]) ).

fof(f_400_1,plain,
    ! [X_b,X_a,B,A_1] :
      ( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_310_finite__Plus]) ).

fof(f_400_2,plain,
    ! [U_1412,U_1411,U_1410,U_1409] :
      ( hBOOL(hAPP(fun(sum_sum(U_1411,U_1412),bool),bool,finite_finite_1(sum_sum(U_1411,U_1412)),hAPP(fun(U_1412,bool),fun(sum_sum(U_1411,U_1412),bool),hAPP(fun(U_1411,bool),fun(fun(U_1412,bool),fun(sum_sum(U_1411,U_1412),bool)),sum_Plus(U_1411,U_1412),U_1409),U_1410)))
      | ~ hBOOL(hAPP(fun(U_1412,bool),bool,finite_finite_1(U_1412),U_1410))
      | ~ hBOOL(hAPP(fun(U_1411,bool),bool,finite_finite_1(U_1411),U_1409)) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

cnf(f_400_3,plain,
    ( hBOOL(hAPP(fun(sum_sum(U_1411,U_1412),bool),bool,finite_finite_1(sum_sum(U_1411,U_1412)),hAPP(fun(U_1412,bool),fun(sum_sum(U_1411,U_1412),bool),hAPP(fun(U_1411,bool),fun(fun(U_1412,bool),fun(sum_sum(U_1411,U_1412),bool)),sum_Plus(U_1411,U_1412),U_1409),U_1410)))
    | ~ hBOOL(hAPP(fun(U_1412,bool),bool,finite_finite_1(U_1412),U_1410))
    | ~ hBOOL(hAPP(fun(U_1411,bool),bool,finite_finite_1(U_1411),U_1409)) ),
    inference(clausify,[status(thm)],[f_400_2]) ).

fof(f_401_1,plain,
    ! [X_a,X_b,A_1,B] :
      ( ( hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      & ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
          & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
        | ~ hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_311_finite__Plus__iff]) ).

fof(f_401_2,plain,
    ! [U_1416,U_1415,U_1414,U_1413] :
      ( ( hBOOL(hAPP(fun(sum_sum(U_1416,U_1415),bool),bool,finite_finite_1(sum_sum(U_1416,U_1415)),hAPP(fun(U_1415,bool),fun(sum_sum(U_1416,U_1415),bool),hAPP(fun(U_1416,bool),fun(fun(U_1415,bool),fun(sum_sum(U_1416,U_1415),bool)),sum_Plus(U_1416,U_1415),U_1414),U_1413)))
        | ~ hBOOL(hAPP(fun(U_1415,bool),bool,finite_finite_1(U_1415),U_1413))
        | ~ hBOOL(hAPP(fun(U_1416,bool),bool,finite_finite_1(U_1416),U_1414)) )
      & ( ( hBOOL(hAPP(fun(U_1415,bool),bool,finite_finite_1(U_1415),U_1413))
          & hBOOL(hAPP(fun(U_1416,bool),bool,finite_finite_1(U_1416),U_1414)) )
        | ~ hBOOL(hAPP(fun(sum_sum(U_1416,U_1415),bool),bool,finite_finite_1(sum_sum(U_1416,U_1415)),hAPP(fun(U_1415,bool),fun(sum_sum(U_1416,U_1415),bool),hAPP(fun(U_1416,bool),fun(fun(U_1415,bool),fun(sum_sum(U_1416,U_1415),bool)),sum_Plus(U_1416,U_1415),U_1414),U_1413))) ) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ( ! [U_1424,U_1422,U_1420,U_1418] :
        ( hBOOL(hAPP(fun(sum_sum(U_1424,U_1422),bool),bool,finite_finite_1(sum_sum(U_1424,U_1422)),hAPP(fun(U_1422,bool),fun(sum_sum(U_1424,U_1422),bool),hAPP(fun(U_1424,bool),fun(fun(U_1422,bool),fun(sum_sum(U_1424,U_1422),bool)),sum_Plus(U_1424,U_1422),U_1420),U_1418)))
        | ~ hBOOL(hAPP(fun(U_1422,bool),bool,finite_finite_1(U_1422),U_1418))
        | ~ hBOOL(hAPP(fun(U_1424,bool),bool,finite_finite_1(U_1424),U_1420)) )
    & ! [U_1423,U_1421,U_1419,U_1417] :
        ( ( hBOOL(hAPP(fun(U_1421,bool),bool,finite_finite_1(U_1421),U_1417))
          & hBOOL(hAPP(fun(U_1423,bool),bool,finite_finite_1(U_1423),U_1419)) )
        | ~ hBOOL(hAPP(fun(sum_sum(U_1423,U_1421),bool),bool,finite_finite_1(sum_sum(U_1423,U_1421)),hAPP(fun(U_1421,bool),fun(sum_sum(U_1423,U_1421),bool),hAPP(fun(U_1423,bool),fun(fun(U_1421,bool),fun(sum_sum(U_1423,U_1421),bool)),sum_Plus(U_1423,U_1421),U_1419),U_1417))) ) ),
    inference(miniscope,[status(thm)],[f_401_2]) ).

cnf(f_401_4,plain,
    ( hBOOL(hAPP(fun(U_1423,bool),bool,finite_finite_1(U_1423),U_1419))
    | ~ hBOOL(hAPP(fun(sum_sum(U_1423,U_1421),bool),bool,finite_finite_1(sum_sum(U_1423,U_1421)),hAPP(fun(U_1421,bool),fun(sum_sum(U_1423,U_1421),bool),hAPP(fun(U_1423,bool),fun(fun(U_1421,bool),fun(sum_sum(U_1423,U_1421),bool)),sum_Plus(U_1423,U_1421),U_1419),U_1417))) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

cnf(f_401_5,plain,
    ( hBOOL(hAPP(fun(U_1421,bool),bool,finite_finite_1(U_1421),U_1417))
    | ~ hBOOL(hAPP(fun(sum_sum(U_1423,U_1421),bool),bool,finite_finite_1(sum_sum(U_1423,U_1421)),hAPP(fun(U_1421,bool),fun(sum_sum(U_1423,U_1421),bool),hAPP(fun(U_1423,bool),fun(fun(U_1421,bool),fun(sum_sum(U_1423,U_1421),bool)),sum_Plus(U_1423,U_1421),U_1419),U_1417))) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

cnf(f_401_6,plain,
    ( hBOOL(hAPP(fun(sum_sum(U_1424,U_1422),bool),bool,finite_finite_1(sum_sum(U_1424,U_1422)),hAPP(fun(U_1422,bool),fun(sum_sum(U_1424,U_1422),bool),hAPP(fun(U_1424,bool),fun(fun(U_1422,bool),fun(sum_sum(U_1424,U_1422),bool)),sum_Plus(U_1424,U_1422),U_1420),U_1418)))
    | ~ hBOOL(hAPP(fun(U_1422,bool),bool,finite_finite_1(U_1422),U_1418))
    | ~ hBOOL(hAPP(fun(U_1424,bool),bool,finite_finite_1(U_1424),U_1420)) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

fof(f_402_1,plain,
    ! [X_b,X_a,X_2,A_1,F,Z_1,G,Fa] :
      ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_312_folding__image__simple__idem_Oin__idem]) ).

fof(f_402_2,plain,
    ! [U_1432,U_1431,U_1430,U_1429,U_1428,U_1427,U_1426,U_1425] :
      ( hAPP(U_1431,U_1431,hAPP(U_1431,fun(U_1431,U_1431),U_1428,hAPP(U_1432,U_1431,U_1426,U_1430)),hAPP(fun(U_1432,bool),U_1431,U_1425,U_1429)) = hAPP(fun(U_1432,bool),U_1431,U_1425,U_1429)
      | ~ hBOOL(hAPP(fun(U_1432,bool),bool,hAPP(U_1432,fun(fun(U_1432,bool),bool),member(U_1432),U_1430),U_1429))
      | ~ hBOOL(hAPP(fun(U_1432,bool),bool,finite_finite_1(U_1432),U_1429))
      | ~ hBOOL(hAPP(fun(fun(U_1432,bool),U_1431),bool,hAPP(fun(U_1432,U_1431),fun(fun(fun(U_1432,bool),U_1431),bool),hAPP(U_1431,fun(fun(U_1432,U_1431),fun(fun(fun(U_1432,bool),U_1431),bool)),hAPP(fun(U_1431,fun(U_1431,U_1431)),fun(U_1431,fun(fun(U_1432,U_1431),fun(fun(fun(U_1432,bool),U_1431),bool))),finite908156982e_idem(U_1431,U_1432),U_1428),U_1427),U_1426),U_1425)) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

cnf(f_402_3,plain,
    ( hAPP(U_1431,U_1431,hAPP(U_1431,fun(U_1431,U_1431),U_1428,hAPP(U_1432,U_1431,U_1426,U_1430)),hAPP(fun(U_1432,bool),U_1431,U_1425,U_1429)) = hAPP(fun(U_1432,bool),U_1431,U_1425,U_1429)
    | ~ hBOOL(hAPP(fun(U_1432,bool),bool,hAPP(U_1432,fun(fun(U_1432,bool),bool),member(U_1432),U_1430),U_1429))
    | ~ hBOOL(hAPP(fun(U_1432,bool),bool,finite_finite_1(U_1432),U_1429))
    | ~ hBOOL(hAPP(fun(fun(U_1432,bool),U_1431),bool,hAPP(fun(U_1432,U_1431),fun(fun(fun(U_1432,bool),U_1431),bool),hAPP(U_1431,fun(fun(U_1432,U_1431),fun(fun(fun(U_1432,bool),U_1431),bool)),hAPP(fun(U_1431,fun(U_1431,U_1431)),fun(U_1431,fun(fun(U_1432,U_1431),fun(fun(fun(U_1432,bool),U_1431),bool))),finite908156982e_idem(U_1431,U_1432),U_1428),U_1427),U_1426),U_1425)) ),
    inference(clausify,[status(thm)],[f_402_2]) ).

fof(f_403_1,plain,
    ! [X_b,X_a] : hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),top_top(fun(X_a,bool))),top_top(fun(X_b,bool))) = top_top(fun(sum_sum(X_a,X_b),bool)),
    inference(fof_nnf,[status(thm)],[fact_313_UNIV__Plus__UNIV]) ).

fof(f_403_2,plain,
    ! [U_1434,U_1433] : hAPP(fun(U_1434,bool),fun(sum_sum(U_1433,U_1434),bool),hAPP(fun(U_1433,bool),fun(fun(U_1434,bool),fun(sum_sum(U_1433,U_1434),bool)),sum_Plus(U_1433,U_1434),top_top(fun(U_1433,bool))),top_top(fun(U_1434,bool))) = top_top(fun(sum_sum(U_1433,U_1434),bool)),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

cnf(f_403_3,plain,
    hAPP(fun(U_1434,bool),fun(sum_sum(U_1433,U_1434),bool),hAPP(fun(U_1433,bool),fun(fun(U_1434,bool),fun(sum_sum(U_1433,U_1434),bool)),sum_Plus(U_1433,U_1434),top_top(fun(U_1433,bool))),top_top(fun(U_1434,bool))) = top_top(fun(sum_sum(U_1433,U_1434),bool)),
    inference(clausify,[status(thm)],[f_403_2]) ).

fof(f_404_1,plain,
    ! [U,F] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U))))
      | ? [N_2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,F,N_2))) ),
    inference(fof_nnf,[status(thm)],[fact_314_finite__less__ub]) ).

fof(f_404_2,plain,
    ! [U_1437,U_1436] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),U_1436)),U_1437))))
      | ? [U_1435] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1435),hAPP(nat,nat,U_1436,U_1435))) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ! [U_1437,U_1436] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),U_1436)),U_1437))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK83(U_1437,U_1436)),hAPP(nat,nat,U_1436,sK83(U_1437,U_1436)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_1435,sK83(U_1437,U_1436))],[f_404_2]) ).

cnf(f_404_4,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),U_1436)),U_1437))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK83(U_1437,U_1436)),hAPP(nat,nat,U_1436,sK83(U_1437,U_1436)))) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_1,plain,
    ! [Na,N_1] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_1))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Na))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_315_bounded__nat__set__is__finite]) ).

fof(f_405_2,plain,
    ! [U_1440,U_1439] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1439))
      | ? [U_1438] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1438),U_1440))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1438),U_1439)) ) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ! [U_1440,U_1439] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1439))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK84(U_1440,U_1439)),U_1440))
        & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK84(U_1440,U_1439)),U_1439)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_1438,sK84(U_1440,U_1439))],[f_405_2]) ).

cnf(f_405_4,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK84(U_1440,U_1439)),U_1439))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1439)) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK84(U_1440,U_1439)),U_1440))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1439)) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

fof(f_406_1,plain,
    ! [X_b,X_a,B,A_1] :
      ( ( hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
          & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) )
      & ( hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_316_card__Plus__conv__if]) ).

fof(f_406_2,plain,
    ! [U_1444,U_1443,U_1442,U_1441] :
      ( ( hAPP(fun(sum_sum(U_1443,U_1444),bool),nat,finite_card(sum_sum(U_1443,U_1444)),hAPP(fun(U_1444,bool),fun(sum_sum(U_1443,U_1444),bool),hAPP(fun(U_1443,bool),fun(fun(U_1444,bool),fun(sum_sum(U_1443,U_1444),bool)),sum_Plus(U_1443,U_1444),U_1441),U_1442)) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(U_1444,bool),bool,finite_finite_1(U_1444),U_1442))
          & hBOOL(hAPP(fun(U_1443,bool),bool,finite_finite_1(U_1443),U_1441)) ) )
      & ( hAPP(fun(sum_sum(U_1443,U_1444),bool),nat,finite_card(sum_sum(U_1443,U_1444)),hAPP(fun(U_1444,bool),fun(sum_sum(U_1443,U_1444),bool),hAPP(fun(U_1443,bool),fun(fun(U_1444,bool),fun(sum_sum(U_1443,U_1444),bool)),sum_Plus(U_1443,U_1444),U_1441),U_1442)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1443,bool),nat,finite_card(U_1443),U_1441)),hAPP(fun(U_1444,bool),nat,finite_card(U_1444),U_1442))
        | ~ hBOOL(hAPP(fun(U_1444,bool),bool,finite_finite_1(U_1444),U_1442))
        | ~ hBOOL(hAPP(fun(U_1443,bool),bool,finite_finite_1(U_1443),U_1441)) ) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ( ! [U_1452,U_1450,U_1448,U_1446] :
        ( hAPP(fun(sum_sum(U_1450,U_1452),bool),nat,finite_card(sum_sum(U_1450,U_1452)),hAPP(fun(U_1452,bool),fun(sum_sum(U_1450,U_1452),bool),hAPP(fun(U_1450,bool),fun(fun(U_1452,bool),fun(sum_sum(U_1450,U_1452),bool)),sum_Plus(U_1450,U_1452),U_1446),U_1448)) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(U_1452,bool),bool,finite_finite_1(U_1452),U_1448))
          & hBOOL(hAPP(fun(U_1450,bool),bool,finite_finite_1(U_1450),U_1446)) ) )
    & ! [U_1451,U_1449,U_1447,U_1445] :
        ( hAPP(fun(sum_sum(U_1449,U_1451),bool),nat,finite_card(sum_sum(U_1449,U_1451)),hAPP(fun(U_1451,bool),fun(sum_sum(U_1449,U_1451),bool),hAPP(fun(U_1449,bool),fun(fun(U_1451,bool),fun(sum_sum(U_1449,U_1451),bool)),sum_Plus(U_1449,U_1451),U_1445),U_1447)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1449,bool),nat,finite_card(U_1449),U_1445)),hAPP(fun(U_1451,bool),nat,finite_card(U_1451),U_1447))
        | ~ hBOOL(hAPP(fun(U_1451,bool),bool,finite_finite_1(U_1451),U_1447))
        | ~ hBOOL(hAPP(fun(U_1449,bool),bool,finite_finite_1(U_1449),U_1445)) ) ),
    inference(miniscope,[status(thm)],[f_406_2]) ).

cnf(f_406_4,plain,
    ( hAPP(fun(sum_sum(U_1449,U_1451),bool),nat,finite_card(sum_sum(U_1449,U_1451)),hAPP(fun(U_1451,bool),fun(sum_sum(U_1449,U_1451),bool),hAPP(fun(U_1449,bool),fun(fun(U_1451,bool),fun(sum_sum(U_1449,U_1451),bool)),sum_Plus(U_1449,U_1451),U_1445),U_1447)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1449,bool),nat,finite_card(U_1449),U_1445)),hAPP(fun(U_1451,bool),nat,finite_card(U_1451),U_1447))
    | ~ hBOOL(hAPP(fun(U_1451,bool),bool,finite_finite_1(U_1451),U_1447))
    | ~ hBOOL(hAPP(fun(U_1449,bool),bool,finite_finite_1(U_1449),U_1445)) ),
    inference(clausify,[status(thm)],[f_406_3]) ).

cnf(f_406_5,plain,
    ( hBOOL(hAPP(fun(U_1450,bool),bool,finite_finite_1(U_1450),U_1446))
    | hAPP(fun(sum_sum(U_1450,U_1452),bool),nat,finite_card(sum_sum(U_1450,U_1452)),hAPP(fun(U_1452,bool),fun(sum_sum(U_1450,U_1452),bool),hAPP(fun(U_1450,bool),fun(fun(U_1452,bool),fun(sum_sum(U_1450,U_1452),bool)),sum_Plus(U_1450,U_1452),U_1446),U_1448)) = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_406_3]) ).

cnf(f_406_6,plain,
    ( hBOOL(hAPP(fun(U_1452,bool),bool,finite_finite_1(U_1452),U_1448))
    | hAPP(fun(sum_sum(U_1450,U_1452),bool),nat,finite_card(sum_sum(U_1450,U_1452)),hAPP(fun(U_1452,bool),fun(sum_sum(U_1450,U_1452),bool),hAPP(fun(U_1450,bool),fun(fun(U_1452,bool),fun(sum_sum(U_1450,U_1452),bool)),sum_Plus(U_1450,U_1452),U_1446),U_1448)) = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_406_3]) ).

fof(f_407_1,plain,
    ! [X_b,X_a,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
      | ? [X_1,Y_2] :
          ( ti(X_a,X_1) != ti(X_a,Y_2)
          & hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2)
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_317_inj__onI]) ).

fof(f_407_2,plain,
    ! [U_1458,U_1457,U_1456,U_1455] :
      ( hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(fun(U_1457,U_1458),fun(fun(U_1457,bool),bool),inj_on(U_1457,U_1458),U_1456),U_1455))
      | ? [U_1454,U_1453] :
          ( ti(U_1457,U_1454) != ti(U_1457,U_1453)
          & hAPP(U_1457,U_1458,U_1456,U_1454) = hAPP(U_1457,U_1458,U_1456,U_1453)
          & hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(U_1457,fun(fun(U_1457,bool),bool),member(U_1457),U_1453),U_1455))
          & hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(U_1457,fun(fun(U_1457,bool),bool),member(U_1457),U_1454),U_1455)) ) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ! [U_1458,U_1457,U_1456,U_1455] :
      ( hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(fun(U_1457,U_1458),fun(fun(U_1457,bool),bool),inj_on(U_1457,U_1458),U_1456),U_1455))
      | ? [U_1454] :
          ( ? [U_1453] :
              ( ti(U_1457,U_1454) != ti(U_1457,U_1453)
              & hAPP(U_1457,U_1458,U_1456,U_1454) = hAPP(U_1457,U_1458,U_1456,U_1453)
              & hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(U_1457,fun(fun(U_1457,bool),bool),member(U_1457),U_1453),U_1455)) )
          & hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(U_1457,fun(fun(U_1457,bool),bool),member(U_1457),U_1454),U_1455)) ) ),
    inference(miniscope,[status(thm)],[f_407_2]) ).

fof(f_407_4,plain,
    ! [U_1458,U_1457,U_1456,U_1455] :
      ( hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(fun(U_1457,U_1458),fun(fun(U_1457,bool),bool),inj_on(U_1457,U_1458),U_1456),U_1455))
      | ( ? [U_1453] :
            ( ti(U_1457,sK85(U_1458,U_1457,U_1456,U_1455)) != ti(U_1457,U_1453)
            & hAPP(U_1457,U_1458,U_1456,sK85(U_1458,U_1457,U_1456,U_1455)) = hAPP(U_1457,U_1458,U_1456,U_1453)
            & hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(U_1457,fun(fun(U_1457,bool),bool),member(U_1457),U_1453),U_1455)) )
        & hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(U_1457,fun(fun(U_1457,bool),bool),member(U_1457),sK85(U_1458,U_1457,U_1456,U_1455)),U_1455)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_1454,sK85(U_1458,U_1457,U_1456,U_1455))],[f_407_3]) ).

fof(f_407_5,plain,
    ! [U_1458,U_1457,U_1456,U_1455] :
      ( hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(fun(U_1457,U_1458),fun(fun(U_1457,bool),bool),inj_on(U_1457,U_1458),U_1456),U_1455))
      | ( ti(U_1457,sK85(U_1458,U_1457,U_1456,U_1455)) != ti(U_1457,sK86(U_1458,U_1457,U_1456,U_1455))
        & hAPP(U_1457,U_1458,U_1456,sK85(U_1458,U_1457,U_1456,U_1455)) = hAPP(U_1457,U_1458,U_1456,sK86(U_1458,U_1457,U_1456,U_1455))
        & hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(U_1457,fun(fun(U_1457,bool),bool),member(U_1457),sK86(U_1458,U_1457,U_1456,U_1455)),U_1455))
        & hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(U_1457,fun(fun(U_1457,bool),bool),member(U_1457),sK85(U_1458,U_1457,U_1456,U_1455)),U_1455)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_1453,sK86(U_1458,U_1457,U_1456,U_1455))],[f_407_4]) ).

cnf(f_407_6,plain,
    ( hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(U_1457,fun(fun(U_1457,bool),bool),member(U_1457),sK85(U_1458,U_1457,U_1456,U_1455)),U_1455))
    | hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(fun(U_1457,U_1458),fun(fun(U_1457,bool),bool),inj_on(U_1457,U_1458),U_1456),U_1455)) ),
    inference(clausify,[status(thm)],[f_407_5]) ).

cnf(f_407_7,plain,
    ( hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(U_1457,fun(fun(U_1457,bool),bool),member(U_1457),sK86(U_1458,U_1457,U_1456,U_1455)),U_1455))
    | hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(fun(U_1457,U_1458),fun(fun(U_1457,bool),bool),inj_on(U_1457,U_1458),U_1456),U_1455)) ),
    inference(clausify,[status(thm)],[f_407_5]) ).

cnf(f_407_8,plain,
    ( hAPP(U_1457,U_1458,U_1456,sK85(U_1458,U_1457,U_1456,U_1455)) = hAPP(U_1457,U_1458,U_1456,sK86(U_1458,U_1457,U_1456,U_1455))
    | hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(fun(U_1457,U_1458),fun(fun(U_1457,bool),bool),inj_on(U_1457,U_1458),U_1456),U_1455)) ),
    inference(clausify,[status(thm)],[f_407_5]) ).

cnf(f_407_9,plain,
    ( ti(U_1457,sK85(U_1458,U_1457,U_1456,U_1455)) != ti(U_1457,sK86(U_1458,U_1457,U_1456,U_1455))
    | hBOOL(hAPP(fun(U_1457,bool),bool,hAPP(fun(U_1457,U_1458),fun(fun(U_1457,bool),bool),inj_on(U_1457,U_1458),U_1456),U_1455)) ),
    inference(clausify,[status(thm)],[f_407_5]) ).

fof(f_408_1,plain,
    ! [X_b,X_a,F,G,A_1] :
      ( ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),A_1)) )
        & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),A_1))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ) )
      | ? [A_4] :
          ( hAPP(X_a,X_b,F,A_4) != hAPP(X_a,X_b,G,A_4)
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_318_inj__on__cong]) ).

fof(f_408_2,plain,
    ! [U_1464,U_1463,U_1462,U_1461,U_1460] :
      ( ( ( hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1462),U_1460))
          | ~ hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1461),U_1460)) )
        & ( hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1461),U_1460))
          | ~ hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1462),U_1460)) ) )
      | ? [U_1459] :
          ( hAPP(U_1463,U_1464,U_1462,U_1459) != hAPP(U_1463,U_1464,U_1461,U_1459)
          & hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(U_1463,fun(fun(U_1463,bool),bool),member(U_1463),U_1459),U_1460)) ) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ! [U_1464,U_1463,U_1462,U_1461,U_1460] :
      ( ( ( hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1462),U_1460))
          | ~ hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1461),U_1460)) )
        & ( hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1461),U_1460))
          | ~ hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1462),U_1460)) ) )
      | ( hAPP(U_1463,U_1464,U_1462,sK87(U_1464,U_1463,U_1462,U_1461,U_1460)) != hAPP(U_1463,U_1464,U_1461,sK87(U_1464,U_1463,U_1462,U_1461,U_1460))
        & hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(U_1463,fun(fun(U_1463,bool),bool),member(U_1463),sK87(U_1464,U_1463,U_1462,U_1461,U_1460)),U_1460)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_1459,sK87(U_1464,U_1463,U_1462,U_1461,U_1460))],[f_408_2]) ).

cnf(f_408_4,plain,
    ( hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1461),U_1460))
    | ~ hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1462),U_1460))
    | hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(U_1463,fun(fun(U_1463,bool),bool),member(U_1463),sK87(U_1464,U_1463,U_1462,U_1461,U_1460)),U_1460)) ),
    inference(clausify,[status(thm)],[f_408_3]) ).

cnf(f_408_5,plain,
    ( hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1462),U_1460))
    | ~ hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1461),U_1460))
    | hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(U_1463,fun(fun(U_1463,bool),bool),member(U_1463),sK87(U_1464,U_1463,U_1462,U_1461,U_1460)),U_1460)) ),
    inference(clausify,[status(thm)],[f_408_3]) ).

cnf(f_408_6,plain,
    ( hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1461),U_1460))
    | ~ hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1462),U_1460))
    | hAPP(U_1463,U_1464,U_1462,sK87(U_1464,U_1463,U_1462,U_1461,U_1460)) != hAPP(U_1463,U_1464,U_1461,sK87(U_1464,U_1463,U_1462,U_1461,U_1460)) ),
    inference(clausify,[status(thm)],[f_408_3]) ).

cnf(f_408_7,plain,
    ( hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1462),U_1460))
    | ~ hBOOL(hAPP(fun(U_1463,bool),bool,hAPP(fun(U_1463,U_1464),fun(fun(U_1463,bool),bool),inj_on(U_1463,U_1464),U_1461),U_1460))
    | hAPP(U_1463,U_1464,U_1462,sK87(U_1464,U_1463,U_1462,U_1461,U_1460)) != hAPP(U_1463,U_1464,U_1461,sK87(U_1464,U_1463,U_1462,U_1461,U_1460)) ),
    inference(clausify,[status(thm)],[f_408_3]) ).

fof(f_409_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    inference(fof_nnf,[status(thm)],[fact_319_less__zeroE]) ).

fof(f_409_2,plain,
    ! [U_1465] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1465),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

cnf(f_409_3,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1465),zero_zero(nat))),
    inference(clausify,[status(thm)],[f_409_2]) ).

fof(f_410_1,plain,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N)),
    inference(fof_nnf,[status(thm)],[fact_320_le0]) ).

fof(f_410_2,plain,
    ! [U_1466] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1466)),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

cnf(f_410_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1466)),
    inference(clausify,[status(thm)],[f_410_2]) ).

fof(f_411_1,plain,
    ! [X_a] :
      ( ! [X_2] :
          ( ( zero_zero(X_a) = ti(X_a,X_2)
            | ti(X_a,X_2) != zero_zero(X_a) )
          & ( ti(X_a,X_2) = zero_zero(X_a)
            | zero_zero(X_a) != ti(X_a,X_2) ) )
      | ~ zero(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_321_zero__reorient]) ).

fof(f_411_2,plain,
    ! [U_1468] :
      ( ! [U_1467] :
          ( ( zero_zero(U_1468) = ti(U_1468,U_1467)
            | ti(U_1468,U_1467) != zero_zero(U_1468) )
          & ( ti(U_1468,U_1467) = zero_zero(U_1468)
            | zero_zero(U_1468) != ti(U_1468,U_1467) ) )
      | ~ zero(U_1468) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1468] :
      ( ( ! [U_1470] :
            ( zero_zero(U_1468) = ti(U_1468,U_1470)
            | ti(U_1468,U_1470) != zero_zero(U_1468) )
        & ! [U_1469] :
            ( ti(U_1468,U_1469) = zero_zero(U_1468)
            | zero_zero(U_1468) != ti(U_1468,U_1469) ) )
      | ~ zero(U_1468) ),
    inference(miniscope,[status(thm)],[f_411_2]) ).

cnf(f_411_4,plain,
    ( ti(U_1468,U_1469) = zero_zero(U_1468)
    | zero_zero(U_1468) != ti(U_1468,U_1469)
    | ~ zero(U_1468) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

cnf(f_411_5,plain,
    ( zero_zero(U_1468) = ti(U_1468,U_1470)
    | ti(U_1468,U_1470) != zero_zero(U_1468)
    | ~ zero(U_1468) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2)
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_322_add_Ocomm__neutral]) ).

fof(f_412_2,plain,
    ! [U_1472] :
      ( ! [U_1471] : hAPP(U_1472,U_1472,hAPP(U_1472,fun(U_1472,U_1472),plus_plus(U_1472),U_1471),zero_zero(U_1472)) = ti(U_1472,U_1471)
      | ~ comm_monoid_add(U_1472) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

cnf(f_412_3,plain,
    ( hAPP(U_1472,U_1472,hAPP(U_1472,fun(U_1472,U_1472),plus_plus(U_1472),U_1471),zero_zero(U_1472)) = ti(U_1472,U_1471)
    | ~ comm_monoid_add(U_1472) ),
    inference(clausify,[status(thm)],[f_412_2]) ).

fof(f_413_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2)
      | ~ monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_323_add__0__right]) ).

fof(f_413_2,plain,
    ! [U_1474] :
      ( ! [U_1473] : hAPP(U_1474,U_1474,hAPP(U_1474,fun(U_1474,U_1474),plus_plus(U_1474),U_1473),zero_zero(U_1474)) = ti(U_1474,U_1473)
      | ~ monoid_add(U_1474) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

cnf(f_413_3,plain,
    ( hAPP(U_1474,U_1474,hAPP(U_1474,fun(U_1474,U_1474),plus_plus(U_1474),U_1473),zero_zero(U_1474)) = ti(U_1474,U_1473)
    | ~ monoid_add(U_1474) ),
    inference(clausify,[status(thm)],[f_413_2]) ).

fof(f_414_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)
            | ti(X_a,Aa) != zero_zero(X_a) )
          & ( ti(X_a,Aa) = zero_zero(X_a)
            | zero_zero(X_a) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) ) )
      | ~ linord219039673up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_324_double__zero__sym]) ).

fof(f_414_2,plain,
    ! [U_1476] :
      ( ! [U_1475] :
          ( ( zero_zero(U_1476) = hAPP(U_1476,U_1476,hAPP(U_1476,fun(U_1476,U_1476),plus_plus(U_1476),U_1475),U_1475)
            | ti(U_1476,U_1475) != zero_zero(U_1476) )
          & ( ti(U_1476,U_1475) = zero_zero(U_1476)
            | zero_zero(U_1476) != hAPP(U_1476,U_1476,hAPP(U_1476,fun(U_1476,U_1476),plus_plus(U_1476),U_1475),U_1475) ) )
      | ~ linord219039673up_add(U_1476) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1476] :
      ( ( ! [U_1478] :
            ( zero_zero(U_1476) = hAPP(U_1476,U_1476,hAPP(U_1476,fun(U_1476,U_1476),plus_plus(U_1476),U_1478),U_1478)
            | ti(U_1476,U_1478) != zero_zero(U_1476) )
        & ! [U_1477] :
            ( ti(U_1476,U_1477) = zero_zero(U_1476)
            | zero_zero(U_1476) != hAPP(U_1476,U_1476,hAPP(U_1476,fun(U_1476,U_1476),plus_plus(U_1476),U_1477),U_1477) ) )
      | ~ linord219039673up_add(U_1476) ),
    inference(miniscope,[status(thm)],[f_414_2]) ).

cnf(f_414_4,plain,
    ( ti(U_1476,U_1477) = zero_zero(U_1476)
    | zero_zero(U_1476) != hAPP(U_1476,U_1476,hAPP(U_1476,fun(U_1476,U_1476),plus_plus(U_1476),U_1477),U_1477)
    | ~ linord219039673up_add(U_1476) ),
    inference(clausify,[status(thm)],[f_414_3]) ).

cnf(f_414_5,plain,
    ( zero_zero(U_1476) = hAPP(U_1476,U_1476,hAPP(U_1476,fun(U_1476,U_1476),plus_plus(U_1476),U_1478),U_1478)
    | ti(U_1476,U_1478) != zero_zero(U_1476)
    | ~ linord219039673up_add(U_1476) ),
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2)
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_325_add__0]) ).

fof(f_415_2,plain,
    ! [U_1480] :
      ( ! [U_1479] : hAPP(U_1480,U_1480,hAPP(U_1480,fun(U_1480,U_1480),plus_plus(U_1480),zero_zero(U_1480)),U_1479) = ti(U_1480,U_1479)
      | ~ comm_monoid_add(U_1480) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

cnf(f_415_3,plain,
    ( hAPP(U_1480,U_1480,hAPP(U_1480,fun(U_1480,U_1480),plus_plus(U_1480),zero_zero(U_1480)),U_1479) = ti(U_1480,U_1479)
    | ~ comm_monoid_add(U_1480) ),
    inference(clausify,[status(thm)],[f_415_2]) ).

fof(f_416_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2)
      | ~ monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_326_add__0__left]) ).

fof(f_416_2,plain,
    ! [U_1482] :
      ( ! [U_1481] : hAPP(U_1482,U_1482,hAPP(U_1482,fun(U_1482,U_1482),plus_plus(U_1482),zero_zero(U_1482)),U_1481) = ti(U_1482,U_1481)
      | ~ monoid_add(U_1482) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

cnf(f_416_3,plain,
    ( hAPP(U_1482,U_1482,hAPP(U_1482,fun(U_1482,U_1482),plus_plus(U_1482),zero_zero(U_1482)),U_1481) = ti(U_1482,U_1481)
    | ~ monoid_add(U_1482) ),
    inference(clausify,[status(thm)],[f_416_2]) ).

fof(f_417_1,plain,
    ! [X_a] :
      ( zero_zero(X_a) != one_one(X_a)
      | ~ zero_neq_one(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_327_zero__neq__one]) ).

fof(f_417_2,plain,
    ! [U_1483] :
      ( zero_zero(U_1483) != one_one(U_1483)
      | ~ zero_neq_one(U_1483) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

cnf(f_417_3,plain,
    ( zero_zero(U_1483) != one_one(U_1483)
    | ~ zero_neq_one(U_1483) ),
    inference(clausify,[status(thm)],[f_417_2]) ).

fof(f_418_1,plain,
    ! [X_a] :
      ( one_one(X_a) != zero_zero(X_a)
      | ~ zero_neq_one(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_328_one__neq__zero]) ).

fof(f_418_2,plain,
    ! [U_1484] :
      ( one_one(U_1484) != zero_zero(U_1484)
      | ~ zero_neq_one(U_1484) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

cnf(f_418_3,plain,
    ( one_one(U_1484) != zero_zero(U_1484)
    | ~ zero_neq_one(U_1484) ),
    inference(clausify,[status(thm)],[f_418_2]) ).

fof(f_419_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    inference(fof_nnf,[status(thm)],[fact_329_not__less0]) ).

fof(f_419_2,plain,
    ! [U_1485] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1485),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

cnf(f_419_3,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1485),zero_zero(nat))),
    inference(clausify,[status(thm)],[f_419_2]) ).

fof(f_420_1,plain,
    ! [Na] :
      ( ( Na != zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | Na = zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_330_neq0__conv]) ).

fof(f_420_2,plain,
    ! [U_1486] :
      ( ( U_1486 != zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1486)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1486))
        | U_1486 = zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ( ! [U_1488] :
        ( U_1488 != zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1488)) )
    & ! [U_1487] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1487))
        | U_1487 = zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_420_2]) ).

cnf(f_420_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1487))
    | U_1487 = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

cnf(f_420_5,plain,
    ( U_1488 != zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1488)) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

fof(f_421_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    inference(fof_nnf,[status(thm)],[fact_331_less__nat__zero__code]) ).

fof(f_421_2,plain,
    ! [U_1489] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1489),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

cnf(f_421_3,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1489),zero_zero(nat))),
    inference(clausify,[status(thm)],[f_421_2]) ).

fof(f_422_1,plain,
    ! [M_3,N] :
      ( N != zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_332_gr__implies__not0]) ).

fof(f_422_2,plain,
    ! [U_1491,U_1490] :
      ( U_1490 != zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1491),U_1490)) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

cnf(f_422_3,plain,
    ( U_1490 != zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1491),U_1490)) ),
    inference(clausify,[status(thm)],[f_422_2]) ).

fof(f_423_1,plain,
    ! [N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))
      | N = zero_zero(nat) ),
    inference(fof_nnf,[status(thm)],[fact_333_gr0I]) ).

fof(f_423_2,plain,
    ! [U_1492] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1492))
      | U_1492 = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

cnf(f_423_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1492))
    | U_1492 = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_423_2]) ).

fof(f_424_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_334_plus__nat_Oadd__0]) ).

fof(f_424_2,plain,
    ! [U_1493] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),U_1493) = U_1493,
    inference(variable_rename,[status(thm)],[f_424_1]) ).

cnf(f_424_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),U_1493) = U_1493,
    inference(clausify,[status(thm)],[f_424_2]) ).

fof(f_425_1,plain,
    ! [M_3] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),zero_zero(nat)) = M_3,
    inference(fof_nnf,[status(thm)],[fact_335_Nat_Oadd__0__right]) ).

fof(f_425_2,plain,
    ! [U_1494] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1494),zero_zero(nat)) = U_1494,
    inference(variable_rename,[status(thm)],[f_425_1]) ).

cnf(f_425_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1494),zero_zero(nat)) = U_1494,
    inference(clausify,[status(thm)],[f_425_2]) ).

fof(f_426_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) = zero_zero(nat)
        | Na != zero_zero(nat)
        | M != zero_zero(nat) )
      & ( ( Na = zero_zero(nat)
          & M = zero_zero(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) != zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_336_add__is__0]) ).

fof(f_426_2,plain,
    ! [U_1496,U_1495] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1496),U_1495) = zero_zero(nat)
        | U_1495 != zero_zero(nat)
        | U_1496 != zero_zero(nat) )
      & ( ( U_1495 = zero_zero(nat)
          & U_1496 = zero_zero(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1496),U_1495) != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

fof(f_426_3,plain,
    ( ! [U_1500,U_1498] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1500),U_1498) = zero_zero(nat)
        | U_1498 != zero_zero(nat)
        | U_1500 != zero_zero(nat) )
    & ! [U_1499,U_1497] :
        ( ( U_1497 = zero_zero(nat)
          & U_1499 = zero_zero(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1499),U_1497) != zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_426_2]) ).

cnf(f_426_4,plain,
    ( U_1499 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1499),U_1497) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_426_3]) ).

cnf(f_426_5,plain,
    ( U_1497 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1499),U_1497) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_426_3]) ).

cnf(f_426_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1500),U_1498) = zero_zero(nat)
    | U_1498 != zero_zero(nat)
    | U_1500 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_426_3]) ).

fof(f_427_1,plain,
    ! [M_3,N] :
      ( N = zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N) != M_3 ),
    inference(fof_nnf,[status(thm)],[fact_337_add__eq__self__zero]) ).

fof(f_427_2,plain,
    ! [U_1502,U_1501] :
      ( U_1501 = zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1502),U_1501) != U_1502 ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

cnf(f_427_3,plain,
    ( U_1501 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1502),U_1501) != U_1502 ),
    inference(clausify,[status(thm)],[f_427_2]) ).

fof(f_428_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat)))
        | Na != zero_zero(nat) )
      & ( Na = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_338_le__0__eq]) ).

fof(f_428_2,plain,
    ! [U_1503] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1503),zero_zero(nat)))
        | U_1503 != zero_zero(nat) )
      & ( U_1503 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1503),zero_zero(nat))) ) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

fof(f_428_3,plain,
    ( ! [U_1505] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1505),zero_zero(nat)))
        | U_1505 != zero_zero(nat) )
    & ! [U_1504] :
        ( U_1504 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1504),zero_zero(nat))) ) ),
    inference(miniscope,[status(thm)],[f_428_2]) ).

cnf(f_428_4,plain,
    ( U_1504 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1504),zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

cnf(f_428_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1505),zero_zero(nat)))
    | U_1505 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

fof(f_429_1,plain,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N)),
    inference(fof_nnf,[status(thm)],[fact_339_less__eq__nat_Osimps_I1_J]) ).

fof(f_429_2,plain,
    ! [U_1506] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1506)),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

cnf(f_429_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1506)),
    inference(clausify,[status(thm)],[f_429_2]) ).

fof(f_430_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_340_add__nonpos__nonpos]) ).

fof(f_430_2,plain,
    ! [U_1509] :
      ( ! [U_1508,U_1507] :
          ( hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less_eq(U_1509),hAPP(U_1509,U_1509,hAPP(U_1509,fun(U_1509,U_1509),plus_plus(U_1509),U_1507),U_1508)),zero_zero(U_1509)))
          | ~ hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less_eq(U_1509),U_1508),zero_zero(U_1509)))
          | ~ hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less_eq(U_1509),U_1507),zero_zero(U_1509))) )
      | ~ ordere216010020id_add(U_1509) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

cnf(f_430_3,plain,
    ( hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less_eq(U_1509),hAPP(U_1509,U_1509,hAPP(U_1509,fun(U_1509,U_1509),plus_plus(U_1509),U_1507),U_1508)),zero_zero(U_1509)))
    | ~ hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less_eq(U_1509),U_1508),zero_zero(U_1509)))
    | ~ hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less_eq(U_1509),U_1507),zero_zero(U_1509)))
    | ~ ordere216010020id_add(U_1509) ),
    inference(clausify,[status(thm)],[f_430_2]) ).

fof(f_431_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2,C_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_341_add__increasing2]) ).

fof(f_431_2,plain,
    ! [U_1513] :
      ( ! [U_1512,U_1511,U_1510] :
          ( hBOOL(hAPP(U_1513,bool,hAPP(U_1513,fun(U_1513,bool),ord_less_eq(U_1513),U_1512),hAPP(U_1513,U_1513,hAPP(U_1513,fun(U_1513,U_1513),plus_plus(U_1513),U_1511),U_1510)))
          | ~ hBOOL(hAPP(U_1513,bool,hAPP(U_1513,fun(U_1513,bool),ord_less_eq(U_1513),U_1512),U_1511))
          | ~ hBOOL(hAPP(U_1513,bool,hAPP(U_1513,fun(U_1513,bool),ord_less_eq(U_1513),zero_zero(U_1513)),U_1510)) )
      | ~ ordere216010020id_add(U_1513) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

cnf(f_431_3,plain,
    ( hBOOL(hAPP(U_1513,bool,hAPP(U_1513,fun(U_1513,bool),ord_less_eq(U_1513),U_1512),hAPP(U_1513,U_1513,hAPP(U_1513,fun(U_1513,U_1513),plus_plus(U_1513),U_1511),U_1510)))
    | ~ hBOOL(hAPP(U_1513,bool,hAPP(U_1513,fun(U_1513,bool),ord_less_eq(U_1513),U_1512),U_1511))
    | ~ hBOOL(hAPP(U_1513,bool,hAPP(U_1513,fun(U_1513,bool),ord_less_eq(U_1513),zero_zero(U_1513)),U_1510))
    | ~ ordere216010020id_add(U_1513) ),
    inference(clausify,[status(thm)],[f_431_2]) ).

fof(f_432_1,plain,
    ! [X_a] :
      ( ! [B_1,C_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_342_add__increasing]) ).

fof(f_432_2,plain,
    ! [U_1517] :
      ( ! [U_1516,U_1515,U_1514] :
          ( hBOOL(hAPP(U_1517,bool,hAPP(U_1517,fun(U_1517,bool),ord_less_eq(U_1517),U_1516),hAPP(U_1517,U_1517,hAPP(U_1517,fun(U_1517,U_1517),plus_plus(U_1517),U_1514),U_1515)))
          | ~ hBOOL(hAPP(U_1517,bool,hAPP(U_1517,fun(U_1517,bool),ord_less_eq(U_1517),U_1516),U_1515))
          | ~ hBOOL(hAPP(U_1517,bool,hAPP(U_1517,fun(U_1517,bool),ord_less_eq(U_1517),zero_zero(U_1517)),U_1514)) )
      | ~ ordere216010020id_add(U_1517) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

cnf(f_432_3,plain,
    ( hBOOL(hAPP(U_1517,bool,hAPP(U_1517,fun(U_1517,bool),ord_less_eq(U_1517),U_1516),hAPP(U_1517,U_1517,hAPP(U_1517,fun(U_1517,U_1517),plus_plus(U_1517),U_1514),U_1515)))
    | ~ hBOOL(hAPP(U_1517,bool,hAPP(U_1517,fun(U_1517,bool),ord_less_eq(U_1517),U_1516),U_1515))
    | ~ hBOOL(hAPP(U_1517,bool,hAPP(U_1517,fun(U_1517,bool),ord_less_eq(U_1517),zero_zero(U_1517)),U_1514))
    | ~ ordere216010020id_add(U_1517) ),
    inference(clausify,[status(thm)],[f_432_2]) ).

fof(f_433_1,plain,
    ! [X_a] :
      ( ! [Y_1,X_2] :
          ( ( ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Y_1) = zero_zero(X_a)
              | ti(X_a,Y_1) != zero_zero(X_a)
              | ti(X_a,X_2) != zero_zero(X_a) )
            & ( ( ti(X_a,Y_1) = zero_zero(X_a)
                & ti(X_a,X_2) = zero_zero(X_a) )
              | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Y_1) != zero_zero(X_a) ) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_2)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_343_add__nonneg__eq__0__iff]) ).

fof(f_433_2,plain,
    ! [U_1520] :
      ( ! [U_1519,U_1518] :
          ( ( ( hAPP(U_1520,U_1520,hAPP(U_1520,fun(U_1520,U_1520),plus_plus(U_1520),U_1518),U_1519) = zero_zero(U_1520)
              | ti(U_1520,U_1519) != zero_zero(U_1520)
              | ti(U_1520,U_1518) != zero_zero(U_1520) )
            & ( ( ti(U_1520,U_1519) = zero_zero(U_1520)
                & ti(U_1520,U_1518) = zero_zero(U_1520) )
              | hAPP(U_1520,U_1520,hAPP(U_1520,fun(U_1520,U_1520),plus_plus(U_1520),U_1518),U_1519) != zero_zero(U_1520) ) )
          | ~ hBOOL(hAPP(U_1520,bool,hAPP(U_1520,fun(U_1520,bool),ord_less_eq(U_1520),zero_zero(U_1520)),U_1519))
          | ~ hBOOL(hAPP(U_1520,bool,hAPP(U_1520,fun(U_1520,bool),ord_less_eq(U_1520),zero_zero(U_1520)),U_1518)) )
      | ~ ordere216010020id_add(U_1520) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

cnf(f_433_3,plain,
    ( ti(U_1520,U_1518) = zero_zero(U_1520)
    | hAPP(U_1520,U_1520,hAPP(U_1520,fun(U_1520,U_1520),plus_plus(U_1520),U_1518),U_1519) != zero_zero(U_1520)
    | ~ hBOOL(hAPP(U_1520,bool,hAPP(U_1520,fun(U_1520,bool),ord_less_eq(U_1520),zero_zero(U_1520)),U_1519))
    | ~ hBOOL(hAPP(U_1520,bool,hAPP(U_1520,fun(U_1520,bool),ord_less_eq(U_1520),zero_zero(U_1520)),U_1518))
    | ~ ordere216010020id_add(U_1520) ),
    inference(clausify,[status(thm)],[f_433_2]) ).

cnf(f_433_4,plain,
    ( ti(U_1520,U_1519) = zero_zero(U_1520)
    | hAPP(U_1520,U_1520,hAPP(U_1520,fun(U_1520,U_1520),plus_plus(U_1520),U_1518),U_1519) != zero_zero(U_1520)
    | ~ hBOOL(hAPP(U_1520,bool,hAPP(U_1520,fun(U_1520,bool),ord_less_eq(U_1520),zero_zero(U_1520)),U_1519))
    | ~ hBOOL(hAPP(U_1520,bool,hAPP(U_1520,fun(U_1520,bool),ord_less_eq(U_1520),zero_zero(U_1520)),U_1518))
    | ~ ordere216010020id_add(U_1520) ),
    inference(clausify,[status(thm)],[f_433_2]) ).

cnf(f_433_5,plain,
    ( hAPP(U_1520,U_1520,hAPP(U_1520,fun(U_1520,U_1520),plus_plus(U_1520),U_1518),U_1519) = zero_zero(U_1520)
    | ti(U_1520,U_1519) != zero_zero(U_1520)
    | ti(U_1520,U_1518) != zero_zero(U_1520)
    | ~ hBOOL(hAPP(U_1520,bool,hAPP(U_1520,fun(U_1520,bool),ord_less_eq(U_1520),zero_zero(U_1520)),U_1519))
    | ~ hBOOL(hAPP(U_1520,bool,hAPP(U_1520,fun(U_1520,bool),ord_less_eq(U_1520),zero_zero(U_1520)),U_1518))
    | ~ ordere216010020id_add(U_1520) ),
    inference(clausify,[status(thm)],[f_433_2]) ).

fof(f_434_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_344_add__nonneg__nonneg]) ).

fof(f_434_2,plain,
    ! [U_1523] :
      ( ! [U_1522,U_1521] :
          ( hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less_eq(U_1523),zero_zero(U_1523)),hAPP(U_1523,U_1523,hAPP(U_1523,fun(U_1523,U_1523),plus_plus(U_1523),U_1521),U_1522)))
          | ~ hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less_eq(U_1523),zero_zero(U_1523)),U_1522))
          | ~ hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less_eq(U_1523),zero_zero(U_1523)),U_1521)) )
      | ~ ordere216010020id_add(U_1523) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

cnf(f_434_3,plain,
    ( hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less_eq(U_1523),zero_zero(U_1523)),hAPP(U_1523,U_1523,hAPP(U_1523,fun(U_1523,U_1523),plus_plus(U_1523),U_1521),U_1522)))
    | ~ hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less_eq(U_1523),zero_zero(U_1523)),U_1522))
    | ~ hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less_eq(U_1523),zero_zero(U_1523)),U_1521))
    | ~ ordere216010020id_add(U_1523) ),
    inference(clausify,[status(thm)],[f_434_2]) ).

fof(f_435_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) ) )
      | ~ linord219039673up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_345_double__add__le__zero__iff__single__add__le__zero]) ).

fof(f_435_2,plain,
    ! [U_1525] :
      ( ! [U_1524] :
          ( ( hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),hAPP(U_1525,U_1525,hAPP(U_1525,fun(U_1525,U_1525),plus_plus(U_1525),U_1524),U_1524)),zero_zero(U_1525)))
            | ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),U_1524),zero_zero(U_1525))) )
          & ( hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),U_1524),zero_zero(U_1525)))
            | ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),hAPP(U_1525,U_1525,hAPP(U_1525,fun(U_1525,U_1525),plus_plus(U_1525),U_1524),U_1524)),zero_zero(U_1525))) ) )
      | ~ linord219039673up_add(U_1525) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

fof(f_435_3,plain,
    ! [U_1525] :
      ( ( ! [U_1527] :
            ( hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),hAPP(U_1525,U_1525,hAPP(U_1525,fun(U_1525,U_1525),plus_plus(U_1525),U_1527),U_1527)),zero_zero(U_1525)))
            | ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),U_1527),zero_zero(U_1525))) )
        & ! [U_1526] :
            ( hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),U_1526),zero_zero(U_1525)))
            | ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),hAPP(U_1525,U_1525,hAPP(U_1525,fun(U_1525,U_1525),plus_plus(U_1525),U_1526),U_1526)),zero_zero(U_1525))) ) )
      | ~ linord219039673up_add(U_1525) ),
    inference(miniscope,[status(thm)],[f_435_2]) ).

cnf(f_435_4,plain,
    ( hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),U_1526),zero_zero(U_1525)))
    | ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),hAPP(U_1525,U_1525,hAPP(U_1525,fun(U_1525,U_1525),plus_plus(U_1525),U_1526),U_1526)),zero_zero(U_1525)))
    | ~ linord219039673up_add(U_1525) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

cnf(f_435_5,plain,
    ( hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),hAPP(U_1525,U_1525,hAPP(U_1525,fun(U_1525,U_1525),plus_plus(U_1525),U_1527),U_1527)),zero_zero(U_1525)))
    | ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less_eq(U_1525),U_1527),zero_zero(U_1525)))
    | ~ linord219039673up_add(U_1525) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

fof(f_436_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa))) ) )
      | ~ linord219039673up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_346_zero__le__double__add__iff__zero__le__single__add]) ).

fof(f_436_2,plain,
    ! [U_1529] :
      ( ! [U_1528] :
          ( ( hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),hAPP(U_1529,U_1529,hAPP(U_1529,fun(U_1529,U_1529),plus_plus(U_1529),U_1528),U_1528)))
            | ~ hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),U_1528)) )
          & ( hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),U_1528))
            | ~ hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),hAPP(U_1529,U_1529,hAPP(U_1529,fun(U_1529,U_1529),plus_plus(U_1529),U_1528),U_1528))) ) )
      | ~ linord219039673up_add(U_1529) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

fof(f_436_3,plain,
    ! [U_1529] :
      ( ( ! [U_1531] :
            ( hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),hAPP(U_1529,U_1529,hAPP(U_1529,fun(U_1529,U_1529),plus_plus(U_1529),U_1531),U_1531)))
            | ~ hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),U_1531)) )
        & ! [U_1530] :
            ( hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),U_1530))
            | ~ hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),hAPP(U_1529,U_1529,hAPP(U_1529,fun(U_1529,U_1529),plus_plus(U_1529),U_1530),U_1530))) ) )
      | ~ linord219039673up_add(U_1529) ),
    inference(miniscope,[status(thm)],[f_436_2]) ).

cnf(f_436_4,plain,
    ( hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),U_1530))
    | ~ hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),hAPP(U_1529,U_1529,hAPP(U_1529,fun(U_1529,U_1529),plus_plus(U_1529),U_1530),U_1530)))
    | ~ linord219039673up_add(U_1529) ),
    inference(clausify,[status(thm)],[f_436_3]) ).

cnf(f_436_5,plain,
    ( hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),hAPP(U_1529,U_1529,hAPP(U_1529,fun(U_1529,U_1529),plus_plus(U_1529),U_1531),U_1531)))
    | ~ hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less_eq(U_1529),zero_zero(U_1529)),U_1531))
    | ~ linord219039673up_add(U_1529) ),
    inference(clausify,[status(thm)],[f_436_3]) ).

fof(f_437_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_347_add__neg__neg]) ).

fof(f_437_2,plain,
    ! [U_1534] :
      ( ! [U_1533,U_1532] :
          ( hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less(U_1534),hAPP(U_1534,U_1534,hAPP(U_1534,fun(U_1534,U_1534),plus_plus(U_1534),U_1532),U_1533)),zero_zero(U_1534)))
          | ~ hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less(U_1534),U_1533),zero_zero(U_1534)))
          | ~ hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less(U_1534),U_1532),zero_zero(U_1534))) )
      | ~ ordere216010020id_add(U_1534) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

cnf(f_437_3,plain,
    ( hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less(U_1534),hAPP(U_1534,U_1534,hAPP(U_1534,fun(U_1534,U_1534),plus_plus(U_1534),U_1532),U_1533)),zero_zero(U_1534)))
    | ~ hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less(U_1534),U_1533),zero_zero(U_1534)))
    | ~ hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less(U_1534),U_1532),zero_zero(U_1534)))
    | ~ ordere216010020id_add(U_1534) ),
    inference(clausify,[status(thm)],[f_437_2]) ).

fof(f_438_1,plain,
    ! [X_a] :
      ( ! [B_1,C_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) )
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_348_pos__add__strict]) ).

fof(f_438_2,plain,
    ! [U_1538] :
      ( ! [U_1537,U_1536,U_1535] :
          ( hBOOL(hAPP(U_1538,bool,hAPP(U_1538,fun(U_1538,bool),ord_less(U_1538),U_1537),hAPP(U_1538,U_1538,hAPP(U_1538,fun(U_1538,U_1538),plus_plus(U_1538),U_1535),U_1536)))
          | ~ hBOOL(hAPP(U_1538,bool,hAPP(U_1538,fun(U_1538,bool),ord_less(U_1538),U_1537),U_1536))
          | ~ hBOOL(hAPP(U_1538,bool,hAPP(U_1538,fun(U_1538,bool),ord_less(U_1538),zero_zero(U_1538)),U_1535)) )
      | ~ linordered_semidom(U_1538) ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

cnf(f_438_3,plain,
    ( hBOOL(hAPP(U_1538,bool,hAPP(U_1538,fun(U_1538,bool),ord_less(U_1538),U_1537),hAPP(U_1538,U_1538,hAPP(U_1538,fun(U_1538,U_1538),plus_plus(U_1538),U_1535),U_1536)))
    | ~ hBOOL(hAPP(U_1538,bool,hAPP(U_1538,fun(U_1538,bool),ord_less(U_1538),U_1537),U_1536))
    | ~ hBOOL(hAPP(U_1538,bool,hAPP(U_1538,fun(U_1538,bool),ord_less(U_1538),zero_zero(U_1538)),U_1535))
    | ~ linordered_semidom(U_1538) ),
    inference(clausify,[status(thm)],[f_438_2]) ).

fof(f_439_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_349_add__pos__pos]) ).

fof(f_439_2,plain,
    ! [U_1541] :
      ( ! [U_1540,U_1539] :
          ( hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),zero_zero(U_1541)),hAPP(U_1541,U_1541,hAPP(U_1541,fun(U_1541,U_1541),plus_plus(U_1541),U_1539),U_1540)))
          | ~ hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),zero_zero(U_1541)),U_1540))
          | ~ hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),zero_zero(U_1541)),U_1539)) )
      | ~ ordere216010020id_add(U_1541) ),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

cnf(f_439_3,plain,
    ( hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),zero_zero(U_1541)),hAPP(U_1541,U_1541,hAPP(U_1541,fun(U_1541,U_1541),plus_plus(U_1541),U_1539),U_1540)))
    | ~ hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),zero_zero(U_1541)),U_1540))
    | ~ hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),zero_zero(U_1541)),U_1539))
    | ~ ordere216010020id_add(U_1541) ),
    inference(clausify,[status(thm)],[f_439_2]) ).

fof(f_440_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) ) )
      | ~ linord219039673up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_350_double__add__less__zero__iff__single__add__less__zero]) ).

fof(f_440_2,plain,
    ! [U_1543] :
      ( ! [U_1542] :
          ( ( hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),hAPP(U_1543,U_1543,hAPP(U_1543,fun(U_1543,U_1543),plus_plus(U_1543),U_1542),U_1542)),zero_zero(U_1543)))
            | ~ hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),U_1542),zero_zero(U_1543))) )
          & ( hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),U_1542),zero_zero(U_1543)))
            | ~ hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),hAPP(U_1543,U_1543,hAPP(U_1543,fun(U_1543,U_1543),plus_plus(U_1543),U_1542),U_1542)),zero_zero(U_1543))) ) )
      | ~ linord219039673up_add(U_1543) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

fof(f_440_3,plain,
    ! [U_1543] :
      ( ( ! [U_1545] :
            ( hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),hAPP(U_1543,U_1543,hAPP(U_1543,fun(U_1543,U_1543),plus_plus(U_1543),U_1545),U_1545)),zero_zero(U_1543)))
            | ~ hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),U_1545),zero_zero(U_1543))) )
        & ! [U_1544] :
            ( hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),U_1544),zero_zero(U_1543)))
            | ~ hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),hAPP(U_1543,U_1543,hAPP(U_1543,fun(U_1543,U_1543),plus_plus(U_1543),U_1544),U_1544)),zero_zero(U_1543))) ) )
      | ~ linord219039673up_add(U_1543) ),
    inference(miniscope,[status(thm)],[f_440_2]) ).

cnf(f_440_4,plain,
    ( hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),U_1544),zero_zero(U_1543)))
    | ~ hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),hAPP(U_1543,U_1543,hAPP(U_1543,fun(U_1543,U_1543),plus_plus(U_1543),U_1544),U_1544)),zero_zero(U_1543)))
    | ~ linord219039673up_add(U_1543) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

cnf(f_440_5,plain,
    ( hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),hAPP(U_1543,U_1543,hAPP(U_1543,fun(U_1543,U_1543),plus_plus(U_1543),U_1545),U_1545)),zero_zero(U_1543)))
    | ~ hBOOL(hAPP(U_1543,bool,hAPP(U_1543,fun(U_1543,bool),ord_less(U_1543),U_1545),zero_zero(U_1543)))
    | ~ linord219039673up_add(U_1543) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

fof(f_441_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa))) ) )
      | ~ linord219039673up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_351_zero__less__double__add__iff__zero__less__single__add]) ).

fof(f_441_2,plain,
    ! [U_1547] :
      ( ! [U_1546] :
          ( ( hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),hAPP(U_1547,U_1547,hAPP(U_1547,fun(U_1547,U_1547),plus_plus(U_1547),U_1546),U_1546)))
            | ~ hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),U_1546)) )
          & ( hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),U_1546))
            | ~ hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),hAPP(U_1547,U_1547,hAPP(U_1547,fun(U_1547,U_1547),plus_plus(U_1547),U_1546),U_1546))) ) )
      | ~ linord219039673up_add(U_1547) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

fof(f_441_3,plain,
    ! [U_1547] :
      ( ( ! [U_1549] :
            ( hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),hAPP(U_1547,U_1547,hAPP(U_1547,fun(U_1547,U_1547),plus_plus(U_1547),U_1549),U_1549)))
            | ~ hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),U_1549)) )
        & ! [U_1548] :
            ( hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),U_1548))
            | ~ hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),hAPP(U_1547,U_1547,hAPP(U_1547,fun(U_1547,U_1547),plus_plus(U_1547),U_1548),U_1548))) ) )
      | ~ linord219039673up_add(U_1547) ),
    inference(miniscope,[status(thm)],[f_441_2]) ).

cnf(f_441_4,plain,
    ( hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),U_1548))
    | ~ hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),hAPP(U_1547,U_1547,hAPP(U_1547,fun(U_1547,U_1547),plus_plus(U_1547),U_1548),U_1548)))
    | ~ linord219039673up_add(U_1547) ),
    inference(clausify,[status(thm)],[f_441_3]) ).

cnf(f_441_5,plain,
    ( hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),hAPP(U_1547,U_1547,hAPP(U_1547,fun(U_1547,U_1547),plus_plus(U_1547),U_1549),U_1549)))
    | ~ hBOOL(hAPP(U_1547,bool,hAPP(U_1547,fun(U_1547,bool),ord_less(U_1547),zero_zero(U_1547)),U_1549))
    | ~ linord219039673up_add(U_1547) ),
    inference(clausify,[status(thm)],[f_441_3]) ).

fof(f_442_1,plain,
    ! [X_a] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_352_zero__le__one]) ).

fof(f_442_2,plain,
    ! [U_1550] :
      ( hBOOL(hAPP(U_1550,bool,hAPP(U_1550,fun(U_1550,bool),ord_less_eq(U_1550),zero_zero(U_1550)),one_one(U_1550)))
      | ~ linordered_semidom(U_1550) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

cnf(f_442_3,plain,
    ( hBOOL(hAPP(U_1550,bool,hAPP(U_1550,fun(U_1550,bool),ord_less_eq(U_1550),zero_zero(U_1550)),one_one(U_1550)))
    | ~ linordered_semidom(U_1550) ),
    inference(clausify,[status(thm)],[f_442_2]) ).

fof(f_443_1,plain,
    ! [X_a] :
      ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_353_not__one__le__zero]) ).

fof(f_443_2,plain,
    ! [U_1551] :
      ( ~ hBOOL(hAPP(U_1551,bool,hAPP(U_1551,fun(U_1551,bool),ord_less_eq(U_1551),one_one(U_1551)),zero_zero(U_1551)))
      | ~ linordered_semidom(U_1551) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

cnf(f_443_3,plain,
    ( ~ hBOOL(hAPP(U_1551,bool,hAPP(U_1551,fun(U_1551,bool),ord_less_eq(U_1551),one_one(U_1551)),zero_zero(U_1551)))
    | ~ linordered_semidom(U_1551) ),
    inference(clausify,[status(thm)],[f_443_2]) ).

fof(f_444_1,plain,
    ! [X_a] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_354_zero__less__one]) ).

fof(f_444_2,plain,
    ! [U_1552] :
      ( hBOOL(hAPP(U_1552,bool,hAPP(U_1552,fun(U_1552,bool),ord_less(U_1552),zero_zero(U_1552)),one_one(U_1552)))
      | ~ linordered_semidom(U_1552) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

cnf(f_444_3,plain,
    ( hBOOL(hAPP(U_1552,bool,hAPP(U_1552,fun(U_1552,bool),ord_less(U_1552),zero_zero(U_1552)),one_one(U_1552)))
    | ~ linordered_semidom(U_1552) ),
    inference(clausify,[status(thm)],[f_444_2]) ).

fof(f_445_1,plain,
    ! [X_a] :
      ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_355_not__one__less__zero]) ).

fof(f_445_2,plain,
    ! [U_1553] :
      ( ~ hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less(U_1553),one_one(U_1553)),zero_zero(U_1553)))
      | ~ linordered_semidom(U_1553) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

cnf(f_445_3,plain,
    ( ~ hBOOL(hAPP(U_1553,bool,hAPP(U_1553,fun(U_1553,bool),ord_less(U_1553),one_one(U_1553)),zero_zero(U_1553)))
    | ~ linordered_semidom(U_1553) ),
    inference(clausify,[status(thm)],[f_445_2]) ).

fof(f_446_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_356_add__gr__0]) ).

fof(f_446_2,plain,
    ! [U_1555,U_1554] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1555),U_1554)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1554))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1555)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1554))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1555))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1555),U_1554))) ) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

fof(f_446_3,plain,
    ( ! [U_1559,U_1557] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1559),U_1557)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1557))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1559)) ) )
    & ! [U_1558,U_1556] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1556))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1558))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1558),U_1556))) ) ),
    inference(miniscope,[status(thm)],[f_446_2]) ).

cnf(f_446_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1556))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1558))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1558),U_1556))) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

cnf(f_446_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1559))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1559),U_1557))) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

cnf(f_446_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1557))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1559),U_1557))) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

fof(f_447_1,plain,
    ! [X_a,A_1] :
      ( hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = zero_zero(nat)
      | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_357_card__infinite]) ).

fof(f_447_2,plain,
    ! [U_1561,U_1560] :
      ( hAPP(fun(U_1561,bool),nat,finite_card(U_1561),U_1560) = zero_zero(nat)
      | hBOOL(hAPP(fun(U_1561,bool),bool,finite_finite_1(U_1561),U_1560)) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

cnf(f_447_3,plain,
    ( hAPP(fun(U_1561,bool),nat,finite_card(U_1561),U_1560) = zero_zero(nat)
    | hBOOL(hAPP(fun(U_1561,bool),bool,finite_finite_1(U_1561),U_1560)) ),
    inference(clausify,[status(thm)],[f_447_2]) ).

fof(f_448_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_358_add__nonpos__neg]) ).

fof(f_448_2,plain,
    ! [U_1564] :
      ( ! [U_1563,U_1562] :
          ( hBOOL(hAPP(U_1564,bool,hAPP(U_1564,fun(U_1564,bool),ord_less(U_1564),hAPP(U_1564,U_1564,hAPP(U_1564,fun(U_1564,U_1564),plus_plus(U_1564),U_1562),U_1563)),zero_zero(U_1564)))
          | ~ hBOOL(hAPP(U_1564,bool,hAPP(U_1564,fun(U_1564,bool),ord_less(U_1564),U_1563),zero_zero(U_1564)))
          | ~ hBOOL(hAPP(U_1564,bool,hAPP(U_1564,fun(U_1564,bool),ord_less_eq(U_1564),U_1562),zero_zero(U_1564))) )
      | ~ ordere216010020id_add(U_1564) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

cnf(f_448_3,plain,
    ( hBOOL(hAPP(U_1564,bool,hAPP(U_1564,fun(U_1564,bool),ord_less(U_1564),hAPP(U_1564,U_1564,hAPP(U_1564,fun(U_1564,U_1564),plus_plus(U_1564),U_1562),U_1563)),zero_zero(U_1564)))
    | ~ hBOOL(hAPP(U_1564,bool,hAPP(U_1564,fun(U_1564,bool),ord_less(U_1564),U_1563),zero_zero(U_1564)))
    | ~ hBOOL(hAPP(U_1564,bool,hAPP(U_1564,fun(U_1564,bool),ord_less_eq(U_1564),U_1562),zero_zero(U_1564)))
    | ~ ordere216010020id_add(U_1564) ),
    inference(clausify,[status(thm)],[f_448_2]) ).

fof(f_449_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_359_add__neg__nonpos]) ).

fof(f_449_2,plain,
    ! [U_1567] :
      ( ! [U_1566,U_1565] :
          ( hBOOL(hAPP(U_1567,bool,hAPP(U_1567,fun(U_1567,bool),ord_less(U_1567),hAPP(U_1567,U_1567,hAPP(U_1567,fun(U_1567,U_1567),plus_plus(U_1567),U_1565),U_1566)),zero_zero(U_1567)))
          | ~ hBOOL(hAPP(U_1567,bool,hAPP(U_1567,fun(U_1567,bool),ord_less_eq(U_1567),U_1566),zero_zero(U_1567)))
          | ~ hBOOL(hAPP(U_1567,bool,hAPP(U_1567,fun(U_1567,bool),ord_less(U_1567),U_1565),zero_zero(U_1567))) )
      | ~ ordere216010020id_add(U_1567) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

cnf(f_449_3,plain,
    ( hBOOL(hAPP(U_1567,bool,hAPP(U_1567,fun(U_1567,bool),ord_less(U_1567),hAPP(U_1567,U_1567,hAPP(U_1567,fun(U_1567,U_1567),plus_plus(U_1567),U_1565),U_1566)),zero_zero(U_1567)))
    | ~ hBOOL(hAPP(U_1567,bool,hAPP(U_1567,fun(U_1567,bool),ord_less_eq(U_1567),U_1566),zero_zero(U_1567)))
    | ~ hBOOL(hAPP(U_1567,bool,hAPP(U_1567,fun(U_1567,bool),ord_less(U_1567),U_1565),zero_zero(U_1567)))
    | ~ ordere216010020id_add(U_1567) ),
    inference(clausify,[status(thm)],[f_449_2]) ).

fof(f_450_1,plain,
    ! [X_a] :
      ( ! [B_1,C_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_360_add__strict__increasing2]) ).

fof(f_450_2,plain,
    ! [U_1571] :
      ( ! [U_1570,U_1569,U_1568] :
          ( hBOOL(hAPP(U_1571,bool,hAPP(U_1571,fun(U_1571,bool),ord_less(U_1571),U_1570),hAPP(U_1571,U_1571,hAPP(U_1571,fun(U_1571,U_1571),plus_plus(U_1571),U_1568),U_1569)))
          | ~ hBOOL(hAPP(U_1571,bool,hAPP(U_1571,fun(U_1571,bool),ord_less(U_1571),U_1570),U_1569))
          | ~ hBOOL(hAPP(U_1571,bool,hAPP(U_1571,fun(U_1571,bool),ord_less_eq(U_1571),zero_zero(U_1571)),U_1568)) )
      | ~ ordere216010020id_add(U_1571) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

cnf(f_450_3,plain,
    ( hBOOL(hAPP(U_1571,bool,hAPP(U_1571,fun(U_1571,bool),ord_less(U_1571),U_1570),hAPP(U_1571,U_1571,hAPP(U_1571,fun(U_1571,U_1571),plus_plus(U_1571),U_1568),U_1569)))
    | ~ hBOOL(hAPP(U_1571,bool,hAPP(U_1571,fun(U_1571,bool),ord_less(U_1571),U_1570),U_1569))
    | ~ hBOOL(hAPP(U_1571,bool,hAPP(U_1571,fun(U_1571,bool),ord_less_eq(U_1571),zero_zero(U_1571)),U_1568))
    | ~ ordere216010020id_add(U_1571) ),
    inference(clausify,[status(thm)],[f_450_2]) ).

fof(f_451_1,plain,
    ! [X_a] :
      ( ! [B_1,C_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_361_add__strict__increasing]) ).

fof(f_451_2,plain,
    ! [U_1575] :
      ( ! [U_1574,U_1573,U_1572] :
          ( hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),U_1574),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1572),U_1573)))
          | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less_eq(U_1575),U_1574),U_1573))
          | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),zero_zero(U_1575)),U_1572)) )
      | ~ ordere216010020id_add(U_1575) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

cnf(f_451_3,plain,
    ( hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),U_1574),hAPP(U_1575,U_1575,hAPP(U_1575,fun(U_1575,U_1575),plus_plus(U_1575),U_1572),U_1573)))
    | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less_eq(U_1575),U_1574),U_1573))
    | ~ hBOOL(hAPP(U_1575,bool,hAPP(U_1575,fun(U_1575,bool),ord_less(U_1575),zero_zero(U_1575)),U_1572))
    | ~ ordere216010020id_add(U_1575) ),
    inference(clausify,[status(thm)],[f_451_2]) ).

fof(f_452_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_362_add__nonneg__pos]) ).

fof(f_452_2,plain,
    ! [U_1578] :
      ( ! [U_1577,U_1576] :
          ( hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),zero_zero(U_1578)),hAPP(U_1578,U_1578,hAPP(U_1578,fun(U_1578,U_1578),plus_plus(U_1578),U_1576),U_1577)))
          | ~ hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),zero_zero(U_1578)),U_1577))
          | ~ hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less_eq(U_1578),zero_zero(U_1578)),U_1576)) )
      | ~ ordere216010020id_add(U_1578) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

cnf(f_452_3,plain,
    ( hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),zero_zero(U_1578)),hAPP(U_1578,U_1578,hAPP(U_1578,fun(U_1578,U_1578),plus_plus(U_1578),U_1576),U_1577)))
    | ~ hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),zero_zero(U_1578)),U_1577))
    | ~ hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less_eq(U_1578),zero_zero(U_1578)),U_1576))
    | ~ ordere216010020id_add(U_1578) ),
    inference(clausify,[status(thm)],[f_452_2]) ).

fof(f_453_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_363_add__pos__nonneg]) ).

fof(f_453_2,plain,
    ! [U_1581] :
      ( ! [U_1580,U_1579] :
          ( hBOOL(hAPP(U_1581,bool,hAPP(U_1581,fun(U_1581,bool),ord_less(U_1581),zero_zero(U_1581)),hAPP(U_1581,U_1581,hAPP(U_1581,fun(U_1581,U_1581),plus_plus(U_1581),U_1579),U_1580)))
          | ~ hBOOL(hAPP(U_1581,bool,hAPP(U_1581,fun(U_1581,bool),ord_less_eq(U_1581),zero_zero(U_1581)),U_1580))
          | ~ hBOOL(hAPP(U_1581,bool,hAPP(U_1581,fun(U_1581,bool),ord_less(U_1581),zero_zero(U_1581)),U_1579)) )
      | ~ ordere216010020id_add(U_1581) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

cnf(f_453_3,plain,
    ( hBOOL(hAPP(U_1581,bool,hAPP(U_1581,fun(U_1581,bool),ord_less(U_1581),zero_zero(U_1581)),hAPP(U_1581,U_1581,hAPP(U_1581,fun(U_1581,U_1581),plus_plus(U_1581),U_1579),U_1580)))
    | ~ hBOOL(hAPP(U_1581,bool,hAPP(U_1581,fun(U_1581,bool),ord_less_eq(U_1581),zero_zero(U_1581)),U_1580))
    | ~ hBOOL(hAPP(U_1581,bool,hAPP(U_1581,fun(U_1581,bool),ord_less(U_1581),zero_zero(U_1581)),U_1579))
    | ~ ordere216010020id_add(U_1581) ),
    inference(clausify,[status(thm)],[f_453_2]) ).

fof(f_454_1,plain,
    ! [X_a] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_364_zero__less__two]) ).

fof(f_454_2,plain,
    ! [U_1582] :
      ( hBOOL(hAPP(U_1582,bool,hAPP(U_1582,fun(U_1582,bool),ord_less(U_1582),zero_zero(U_1582)),hAPP(U_1582,U_1582,hAPP(U_1582,fun(U_1582,U_1582),plus_plus(U_1582),one_one(U_1582)),one_one(U_1582))))
      | ~ linordered_semidom(U_1582) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

cnf(f_454_3,plain,
    ( hBOOL(hAPP(U_1582,bool,hAPP(U_1582,fun(U_1582,bool),ord_less(U_1582),zero_zero(U_1582)),hAPP(U_1582,U_1582,hAPP(U_1582,fun(U_1582,U_1582),plus_plus(U_1582),one_one(U_1582)),one_one(U_1582))))
    | ~ linordered_semidom(U_1582) ),
    inference(clausify,[status(thm)],[f_454_2]) ).

fof(f_455_1,plain,
    ! [X_a,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_365_card__ge__0__finite]) ).

fof(f_455_2,plain,
    ! [U_1584,U_1583] :
      ( hBOOL(hAPP(fun(U_1584,bool),bool,finite_finite_1(U_1584),U_1583))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_1584,bool),nat,finite_card(U_1584),U_1583))) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

cnf(f_455_3,plain,
    ( hBOOL(hAPP(fun(U_1584,bool),bool,finite_finite_1(U_1584),U_1583))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_1584,bool),nat,finite_card(U_1584),U_1583))) ),
    inference(clausify,[status(thm)],[f_455_2]) ).

fof(f_456_1,plain,
    ! [X_a] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,finite_card(X_a),top_top(fun(X_a,bool)))))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_366_finite__UNIV__card__ge__0]) ).

fof(f_456_2,plain,
    ! [U_1585] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_1585,bool),nat,finite_card(U_1585),top_top(fun(U_1585,bool)))))
      | ~ hBOOL(hAPP(fun(U_1585,bool),bool,finite_finite_1(U_1585),top_top(fun(U_1585,bool)))) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

cnf(f_456_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_1585,bool),nat,finite_card(U_1585),top_top(fun(U_1585,bool)))))
    | ~ hBOOL(hAPP(fun(U_1585,bool),bool,finite_finite_1(U_1585),top_top(fun(U_1585,bool)))) ),
    inference(clausify,[status(thm)],[f_456_2]) ).

fof(f_457_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(nat,fun(nat,bool),ord_less_eq(nat),I_1),K_1)) )
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_367_ex__least__nat__less]) ).

fof(f_457_2,plain,
    ! [U_1589,U_1588] :
      ( ? [U_1587] :
          ( hBOOL(hAPP(nat,bool,U_1588,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1587),one_one(nat))))
          & ! [U_1586] :
              ( ~ hBOOL(hAPP(nat,bool,U_1588,U_1586))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1586),U_1587)) )
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1587),U_1589)) )
      | ~ hBOOL(hAPP(nat,bool,U_1588,U_1589))
      | hBOOL(hAPP(nat,bool,U_1588,zero_zero(nat))) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

fof(f_457_3,plain,
    ! [U_1589,U_1588] :
      ( ( hBOOL(hAPP(nat,bool,U_1588,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK88(U_1589,U_1588)),one_one(nat))))
        & ! [U_1586] :
            ( ~ hBOOL(hAPP(nat,bool,U_1588,U_1586))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1586),sK88(U_1589,U_1588))) )
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK88(U_1589,U_1588)),U_1589)) )
      | ~ hBOOL(hAPP(nat,bool,U_1588,U_1589))
      | hBOOL(hAPP(nat,bool,U_1588,zero_zero(nat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_1587,sK88(U_1589,U_1588))],[f_457_2]) ).

cnf(f_457_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK88(U_1589,U_1588)),U_1589))
    | ~ hBOOL(hAPP(nat,bool,U_1588,U_1589))
    | hBOOL(hAPP(nat,bool,U_1588,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

cnf(f_457_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_1588,U_1586))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1586),sK88(U_1589,U_1588)))
    | ~ hBOOL(hAPP(nat,bool,U_1588,U_1589))
    | hBOOL(hAPP(nat,bool,U_1588,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

cnf(f_457_6,plain,
    ( hBOOL(hAPP(nat,bool,U_1588,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK88(U_1589,U_1588)),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,U_1588,U_1589))
    | hBOOL(hAPP(nat,bool,U_1588,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

fof(f_458_1,plain,
    ! [X_a,A_1] :
      ( hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = zero_zero(nat)
      | ( one_one(nat) != zero_zero(nat)
        & ? [X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_368_card_Oneutral]) ).

fof(f_458_2,plain,
    ! [U_1592,U_1591] :
      ( hAPP(fun(U_1592,bool),nat,finite_card(U_1592),U_1591) = zero_zero(nat)
      | ( one_one(nat) != zero_zero(nat)
        & ? [U_1590] : hBOOL(hAPP(fun(U_1592,bool),bool,hAPP(U_1592,fun(fun(U_1592,bool),bool),member(U_1592),U_1590),U_1591)) )
      | ~ hBOOL(hAPP(fun(U_1592,bool),bool,finite_finite_1(U_1592),U_1591)) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

fof(f_458_3,plain,
    ! [U_1592,U_1591] :
      ( hAPP(fun(U_1592,bool),nat,finite_card(U_1592),U_1591) = zero_zero(nat)
      | ( one_one(nat) != zero_zero(nat)
        & hBOOL(hAPP(fun(U_1592,bool),bool,hAPP(U_1592,fun(fun(U_1592,bool),bool),member(U_1592),sK89(U_1592,U_1591)),U_1591)) )
      | ~ hBOOL(hAPP(fun(U_1592,bool),bool,finite_finite_1(U_1592),U_1591)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_1590,sK89(U_1592,U_1591))],[f_458_2]) ).

cnf(f_458_4,plain,
    ( hBOOL(hAPP(fun(U_1592,bool),bool,hAPP(U_1592,fun(fun(U_1592,bool),bool),member(U_1592),sK89(U_1592,U_1591)),U_1591))
    | hAPP(fun(U_1592,bool),nat,finite_card(U_1592),U_1591) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(U_1592,bool),bool,finite_finite_1(U_1592),U_1591)) ),
    inference(clausify,[status(thm)],[f_458_3]) ).

cnf(f_458_5,plain,
    ( one_one(nat) != zero_zero(nat)
    | hAPP(fun(U_1592,bool),nat,finite_card(U_1592),U_1591) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(U_1592,bool),bool,finite_finite_1(U_1592),U_1591)) ),
    inference(clausify,[status(thm)],[f_458_3]) ).

fof(f_459_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(nat,fun(nat,bool),ord_less(nat),I_1),K_1)) )
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_369_ex__least__nat__le]) ).

fof(f_459_2,plain,
    ! [U_1596,U_1595] :
      ( ? [U_1594] :
          ( hBOOL(hAPP(nat,bool,U_1595,U_1594))
          & ! [U_1593] :
              ( ~ hBOOL(hAPP(nat,bool,U_1595,U_1593))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1593),U_1594)) )
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1594),U_1596)) )
      | ~ hBOOL(hAPP(nat,bool,U_1595,U_1596))
      | hBOOL(hAPP(nat,bool,U_1595,zero_zero(nat))) ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

fof(f_459_3,plain,
    ! [U_1596,U_1595] :
      ( ( hBOOL(hAPP(nat,bool,U_1595,sK90(U_1596,U_1595)))
        & ! [U_1593] :
            ( ~ hBOOL(hAPP(nat,bool,U_1595,U_1593))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1593),sK90(U_1596,U_1595))) )
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK90(U_1596,U_1595)),U_1596)) )
      | ~ hBOOL(hAPP(nat,bool,U_1595,U_1596))
      | hBOOL(hAPP(nat,bool,U_1595,zero_zero(nat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_1594,sK90(U_1596,U_1595))],[f_459_2]) ).

cnf(f_459_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK90(U_1596,U_1595)),U_1596))
    | ~ hBOOL(hAPP(nat,bool,U_1595,U_1596))
    | hBOOL(hAPP(nat,bool,U_1595,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_459_3]) ).

cnf(f_459_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_1595,U_1593))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1593),sK90(U_1596,U_1595)))
    | ~ hBOOL(hAPP(nat,bool,U_1595,U_1596))
    | hBOOL(hAPP(nat,bool,U_1595,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_459_3]) ).

cnf(f_459_6,plain,
    ( hBOOL(hAPP(nat,bool,U_1595,sK90(U_1596,U_1595)))
    | ~ hBOOL(hAPP(nat,bool,U_1595,U_1596))
    | hBOOL(hAPP(nat,bool,U_1595,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_459_3]) ).

fof(f_460_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(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_370_less__imp__add__positive]) ).

fof(f_460_2,plain,
    ! [U_1599,U_1598] :
      ( ? [U_1597] :
          ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1599),U_1597) = U_1598
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1597)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1599),U_1598)) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

fof(f_460_3,plain,
    ! [U_1599,U_1598] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1599),sK91(U_1599,U_1598)) = U_1598
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sK91(U_1599,U_1598))) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1599),U_1598)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_1597,sK91(U_1599,U_1598))],[f_460_2]) ).

cnf(f_460_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sK91(U_1599,U_1598)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1599),U_1598)) ),
    inference(clausify,[status(thm)],[f_460_3]) ).

cnf(f_460_5,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1599),sK91(U_1599,U_1598)) = U_1598
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1599),U_1598)) ),
    inference(clausify,[status(thm)],[f_460_3]) ).

fof(f_461_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) ) )
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_371_even__less__0__iff]) ).

fof(f_461_2,plain,
    ! [U_1601] :
      ( ! [U_1600] :
          ( ( hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),hAPP(U_1601,U_1601,hAPP(U_1601,fun(U_1601,U_1601),plus_plus(U_1601),U_1600),U_1600)),zero_zero(U_1601)))
            | ~ hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),U_1600),zero_zero(U_1601))) )
          & ( hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),U_1600),zero_zero(U_1601)))
            | ~ hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),hAPP(U_1601,U_1601,hAPP(U_1601,fun(U_1601,U_1601),plus_plus(U_1601),U_1600),U_1600)),zero_zero(U_1601))) ) )
      | ~ linordered_idom(U_1601) ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

fof(f_461_3,plain,
    ! [U_1601] :
      ( ( ! [U_1603] :
            ( hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),hAPP(U_1601,U_1601,hAPP(U_1601,fun(U_1601,U_1601),plus_plus(U_1601),U_1603),U_1603)),zero_zero(U_1601)))
            | ~ hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),U_1603),zero_zero(U_1601))) )
        & ! [U_1602] :
            ( hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),U_1602),zero_zero(U_1601)))
            | ~ hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),hAPP(U_1601,U_1601,hAPP(U_1601,fun(U_1601,U_1601),plus_plus(U_1601),U_1602),U_1602)),zero_zero(U_1601))) ) )
      | ~ linordered_idom(U_1601) ),
    inference(miniscope,[status(thm)],[f_461_2]) ).

cnf(f_461_4,plain,
    ( hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),U_1602),zero_zero(U_1601)))
    | ~ hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),hAPP(U_1601,U_1601,hAPP(U_1601,fun(U_1601,U_1601),plus_plus(U_1601),U_1602),U_1602)),zero_zero(U_1601)))
    | ~ linordered_idom(U_1601) ),
    inference(clausify,[status(thm)],[f_461_3]) ).

cnf(f_461_5,plain,
    ( hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),hAPP(U_1601,U_1601,hAPP(U_1601,fun(U_1601,U_1601),plus_plus(U_1601),U_1603),U_1603)),zero_zero(U_1601)))
    | ~ hBOOL(hAPP(U_1601,bool,hAPP(U_1601,fun(U_1601,bool),ord_less(U_1601),U_1603),zero_zero(U_1601)))
    | ~ linordered_idom(U_1601) ),
    inference(clausify,[status(thm)],[f_461_3]) ).

fof(f_462_1,plain,
    ! [X_a,X_b] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool))))
      | hAPP(fun(X_b,bool),nat,finite_card(X_b),top_top(fun(X_b,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,finite_finite_1(fun(X_a,X_b)),top_top(fun(fun(X_a,X_b),bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_372_finite__fun__UNIVD1]) ).

fof(f_462_2,plain,
    ! [U_1605,U_1604] :
      ( hBOOL(hAPP(fun(U_1605,bool),bool,finite_finite_1(U_1605),top_top(fun(U_1605,bool))))
      | hAPP(fun(U_1604,bool),nat,finite_card(U_1604),top_top(fun(U_1604,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
      | ~ hBOOL(hAPP(fun(fun(U_1605,U_1604),bool),bool,finite_finite_1(fun(U_1605,U_1604)),top_top(fun(fun(U_1605,U_1604),bool)))) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

cnf(f_462_3,plain,
    ( hBOOL(hAPP(fun(U_1605,bool),bool,finite_finite_1(U_1605),top_top(fun(U_1605,bool))))
    | hAPP(fun(U_1604,bool),nat,finite_card(U_1604),top_top(fun(U_1604,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(fun(U_1605,U_1604),bool),bool,finite_finite_1(fun(U_1605,U_1604)),top_top(fun(fun(U_1605,U_1604),bool)))) ),
    inference(clausify,[status(thm)],[f_462_2]) ).

fof(f_463_1,plain,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N))),
    inference(fof_nnf,[status(thm)],[fact_373_lessI]) ).

fof(f_463_2,plain,
    ! [U_1606] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1606),hAPP(nat,nat,suc,U_1606))),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

cnf(f_463_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1606),hAPP(nat,nat,suc,U_1606))),
    inference(clausify,[status(thm)],[f_463_2]) ).

fof(f_464_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_374_Suc__mono]) ).

fof(f_464_2,plain,
    ! [U_1608,U_1607] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1608)),hAPP(nat,nat,suc,U_1607)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1608),U_1607)) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

cnf(f_464_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1608)),hAPP(nat,nat,suc,U_1607)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1608),U_1607)) ),
    inference(clausify,[status(thm)],[f_464_2]) ).

fof(f_465_1,plain,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))),
    inference(fof_nnf,[status(thm)],[fact_375_zero__less__Suc]) ).

fof(f_465_2,plain,
    ! [U_1609] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,U_1609))),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

cnf(f_465_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,U_1609))),
    inference(clausify,[status(thm)],[f_465_2]) ).

fof(f_466_1,plain,
    ! [X,Y] :
      ( X = Y
      | hAPP(nat,nat,suc,X) != hAPP(nat,nat,suc,Y) ),
    inference(fof_nnf,[status(thm)],[fact_376_Suc__inject]) ).

fof(f_466_2,plain,
    ! [U_1611,U_1610] :
      ( U_1611 = U_1610
      | hAPP(nat,nat,suc,U_1611) != hAPP(nat,nat,suc,U_1610) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

cnf(f_466_3,plain,
    ( U_1611 = U_1610
    | hAPP(nat,nat,suc,U_1611) != hAPP(nat,nat,suc,U_1610) ),
    inference(clausify,[status(thm)],[f_466_2]) ).

fof(f_467_1,plain,
    ! [Nat_1,Nat_5] :
      ( ( hAPP(nat,nat,suc,Nat_1) = hAPP(nat,nat,suc,Nat_5)
        | Nat_1 != Nat_5 )
      & ( Nat_1 = Nat_5
        | hAPP(nat,nat,suc,Nat_1) != hAPP(nat,nat,suc,Nat_5) ) ),
    inference(fof_nnf,[status(thm)],[fact_377_nat_Oinject]) ).

fof(f_467_2,plain,
    ! [U_1613,U_1612] :
      ( ( hAPP(nat,nat,suc,U_1613) = hAPP(nat,nat,suc,U_1612)
        | U_1613 != U_1612 )
      & ( U_1613 = U_1612
        | hAPP(nat,nat,suc,U_1613) != hAPP(nat,nat,suc,U_1612) ) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

fof(f_467_3,plain,
    ( ! [U_1617,U_1615] :
        ( hAPP(nat,nat,suc,U_1617) = hAPP(nat,nat,suc,U_1615)
        | U_1617 != U_1615 )
    & ! [U_1616,U_1614] :
        ( U_1616 = U_1614
        | hAPP(nat,nat,suc,U_1616) != hAPP(nat,nat,suc,U_1614) ) ),
    inference(miniscope,[status(thm)],[f_467_2]) ).

cnf(f_467_4,plain,
    ( U_1616 = U_1614
    | hAPP(nat,nat,suc,U_1616) != hAPP(nat,nat,suc,U_1614) ),
    inference(clausify,[status(thm)],[f_467_3]) ).

cnf(f_467_5,plain,
    ( hAPP(nat,nat,suc,U_1617) = hAPP(nat,nat,suc,U_1615)
    | U_1617 != U_1615 ),
    inference(clausify,[status(thm)],[f_467_3]) ).

fof(f_468_1,plain,
    ! [N] : hAPP(nat,nat,suc,N) != N,
    inference(fof_nnf,[status(thm)],[fact_378_Suc__n__not__n]) ).

fof(f_468_2,plain,
    ! [U_1618] : hAPP(nat,nat,suc,U_1618) != U_1618,
    inference(variable_rename,[status(thm)],[f_468_1]) ).

cnf(f_468_3,plain,
    hAPP(nat,nat,suc,U_1618) != U_1618,
    inference(clausify,[status(thm)],[f_468_2]) ).

fof(f_469_1,plain,
    ! [N] : N != hAPP(nat,nat,suc,N),
    inference(fof_nnf,[status(thm)],[fact_379_n__not__Suc__n]) ).

fof(f_469_2,plain,
    ! [U_1619] : U_1619 != hAPP(nat,nat,suc,U_1619),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

cnf(f_469_3,plain,
    U_1619 != hAPP(nat,nat,suc,U_1619),
    inference(clausify,[status(thm)],[f_469_2]) ).

fof(f_470_1,plain,
    ! [M_3] : hAPP(nat,nat,suc,M_3) != zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_380_Suc__neq__Zero]) ).

fof(f_470_2,plain,
    ! [U_1620] : hAPP(nat,nat,suc,U_1620) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

cnf(f_470_3,plain,
    hAPP(nat,nat,suc,U_1620) != zero_zero(nat),
    inference(clausify,[status(thm)],[f_470_2]) ).

fof(f_471_1,plain,
    ! [M_3] : zero_zero(nat) != hAPP(nat,nat,suc,M_3),
    inference(fof_nnf,[status(thm)],[fact_381_Zero__neq__Suc]) ).

fof(f_471_2,plain,
    ! [U_1621] : zero_zero(nat) != hAPP(nat,nat,suc,U_1621),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

cnf(f_471_3,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,U_1621),
    inference(clausify,[status(thm)],[f_471_2]) ).

fof(f_472_1,plain,
    ! [Nat_4] : hAPP(nat,nat,suc,Nat_4) != zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_382_nat_Osimps_I3_J]) ).

fof(f_472_2,plain,
    ! [U_1622] : hAPP(nat,nat,suc,U_1622) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

cnf(f_472_3,plain,
    hAPP(nat,nat,suc,U_1622) != zero_zero(nat),
    inference(clausify,[status(thm)],[f_472_2]) ).

fof(f_473_1,plain,
    ! [M_3] : hAPP(nat,nat,suc,M_3) != zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_383_Suc__not__Zero]) ).

fof(f_473_2,plain,
    ! [U_1623] : hAPP(nat,nat,suc,U_1623) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

cnf(f_473_3,plain,
    hAPP(nat,nat,suc,U_1623) != zero_zero(nat),
    inference(clausify,[status(thm)],[f_473_2]) ).

fof(f_474_1,plain,
    ! [Nat_3] : zero_zero(nat) != hAPP(nat,nat,suc,Nat_3),
    inference(fof_nnf,[status(thm)],[fact_384_nat_Osimps_I2_J]) ).

fof(f_474_2,plain,
    ! [U_1624] : zero_zero(nat) != hAPP(nat,nat,suc,U_1624),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

cnf(f_474_3,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,U_1624),
    inference(clausify,[status(thm)],[f_474_2]) ).

fof(f_475_1,plain,
    ! [M_3] : zero_zero(nat) != hAPP(nat,nat,suc,M_3),
    inference(fof_nnf,[status(thm)],[fact_385_Zero__not__Suc]) ).

fof(f_475_2,plain,
    ! [U_1625] : zero_zero(nat) != hAPP(nat,nat,suc,U_1625),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

cnf(f_475_3,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,U_1625),
    inference(clausify,[status(thm)],[f_475_2]) ).

fof(f_476_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),hAPP(nat,nat,suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_386_Suc__less__SucD]) ).

fof(f_476_2,plain,
    ! [U_1627,U_1626] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1627),U_1626))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1627)),hAPP(nat,nat,suc,U_1626))) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

cnf(f_476_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1627),U_1626))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1627)),hAPP(nat,nat,suc,U_1626))) ),
    inference(clausify,[status(thm)],[f_476_2]) ).

fof(f_477_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_387_Suc__lessD]) ).

fof(f_477_2,plain,
    ! [U_1629,U_1628] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1629),U_1628))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1629)),U_1628)) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

cnf(f_477_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1629),U_1628))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1629)),U_1628)) ),
    inference(clausify,[status(thm)],[f_477_2]) ).

fof(f_478_1,plain,
    ! [M_3,N] :
      ( M_3 = N
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_388_less__SucE]) ).

fof(f_478_2,plain,
    ! [U_1631,U_1630] :
      ( U_1631 = U_1630
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),U_1630))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),hAPP(nat,nat,suc,U_1630))) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

cnf(f_478_3,plain,
    ( U_1631 = U_1630
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),U_1630))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),hAPP(nat,nat,suc,U_1630))) ),
    inference(clausify,[status(thm)],[f_478_2]) ).

fof(f_479_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_389_less__trans__Suc]) ).

fof(f_479_2,plain,
    ! [U_1634,U_1633,U_1632] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1633)),U_1634))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1632),U_1634))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),U_1632)) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

cnf(f_479_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1633)),U_1634))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1632),U_1634))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1633),U_1632)) ),
    inference(clausify,[status(thm)],[f_479_2]) ).

fof(f_480_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),N))
      | hAPP(nat,nat,suc,M_3) = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_390_Suc__lessI]) ).

fof(f_480_2,plain,
    ! [U_1636,U_1635] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1636)),U_1635))
      | hAPP(nat,nat,suc,U_1636) = U_1635
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1636),U_1635)) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

cnf(f_480_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1636)),U_1635))
    | hAPP(nat,nat,suc,U_1636) = U_1635
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1636),U_1635)) ),
    inference(clausify,[status(thm)],[f_480_2]) ).

fof(f_481_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_391_less__SucI]) ).

fof(f_481_2,plain,
    ! [U_1638,U_1637] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1638),hAPP(nat,nat,suc,U_1637)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1638),U_1637)) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

cnf(f_481_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1638),hAPP(nat,nat,suc,U_1637)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1638),U_1637)) ),
    inference(clausify,[status(thm)],[f_481_2]) ).

fof(f_482_1,plain,
    ! [N,M_3] :
      ( M_3 = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M_3)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_392_less__antisym]) ).

fof(f_482_2,plain,
    ! [U_1640,U_1639] :
      ( U_1639 = U_1640
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1640),hAPP(nat,nat,suc,U_1639)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1640),U_1639)) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

cnf(f_482_3,plain,
    ( U_1639 = U_1640
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1640),hAPP(nat,nat,suc,U_1639)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1640),U_1639)) ),
    inference(clausify,[status(thm)],[f_482_2]) ).

fof(f_483_1,plain,
    ! [Na,M] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))
          | Na != M )
        & ( Na = M
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))) ) )
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) ),
    inference(fof_nnf,[status(thm)],[fact_393_not__less__less__Suc__eq]) ).

fof(f_483_2,plain,
    ! [U_1642,U_1641] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1642),hAPP(nat,nat,suc,U_1641)))
          | U_1642 != U_1641 )
        & ( U_1642 = U_1641
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1642),hAPP(nat,nat,suc,U_1641))) ) )
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1642),U_1641)) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

cnf(f_483_3,plain,
    ( U_1642 = U_1641
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1642),hAPP(nat,nat,suc,U_1641)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1642),U_1641)) ),
    inference(clausify,[status(thm)],[f_483_2]) ).

cnf(f_483_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1642),hAPP(nat,nat,suc,U_1641)))
    | U_1642 != U_1641
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1642),U_1641)) ),
    inference(clausify,[status(thm)],[f_483_2]) ).

fof(f_484_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_394_Suc__less__eq]) ).

fof(f_484_2,plain,
    ! [U_1644,U_1643] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1644)),hAPP(nat,nat,suc,U_1643)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),U_1643)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),U_1643))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1644)),hAPP(nat,nat,suc,U_1643))) ) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

fof(f_484_3,plain,
    ( ! [U_1648,U_1646] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1648)),hAPP(nat,nat,suc,U_1646)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1648),U_1646)) )
    & ! [U_1647,U_1645] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1647),U_1645))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1647)),hAPP(nat,nat,suc,U_1645))) ) ),
    inference(miniscope,[status(thm)],[f_484_2]) ).

cnf(f_484_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1647),U_1645))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1647)),hAPP(nat,nat,suc,U_1645))) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

cnf(f_484_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1648)),hAPP(nat,nat,suc,U_1646)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1648),U_1646)) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

fof(f_485_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
        | ( M != Na
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) )
      & ( M = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_395_less__Suc__eq]) ).

fof(f_485_2,plain,
    ! [U_1650,U_1649] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1650),hAPP(nat,nat,suc,U_1649)))
        | ( U_1650 != U_1649
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1650),U_1649)) ) )
      & ( U_1650 = U_1649
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1650),U_1649))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1650),hAPP(nat,nat,suc,U_1649))) ) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

fof(f_485_3,plain,
    ( ! [U_1654,U_1652] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1654),hAPP(nat,nat,suc,U_1652)))
        | ( U_1654 != U_1652
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1654),U_1652)) ) )
    & ! [U_1653,U_1651] :
        ( U_1653 = U_1651
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1653),U_1651))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1653),hAPP(nat,nat,suc,U_1651))) ) ),
    inference(miniscope,[status(thm)],[f_485_2]) ).

cnf(f_485_4,plain,
    ( U_1653 = U_1651
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1653),U_1651))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1653),hAPP(nat,nat,suc,U_1651))) ),
    inference(clausify,[status(thm)],[f_485_3]) ).

cnf(f_485_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1654),U_1652))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1654),hAPP(nat,nat,suc,U_1652))) ),
    inference(clausify,[status(thm)],[f_485_3]) ).

cnf(f_485_6,plain,
    ( U_1654 != U_1652
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1654),hAPP(nat,nat,suc,U_1652))) ),
    inference(clausify,[status(thm)],[f_485_3]) ).

fof(f_486_1,plain,
    ! [M,Na] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_396_not__less__eq]) ).

fof(f_486_2,plain,
    ! [U_1656,U_1655] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1656),U_1655))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1655),hAPP(nat,nat,suc,U_1656))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1655),hAPP(nat,nat,suc,U_1656)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1656),U_1655)) ) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

fof(f_486_3,plain,
    ( ! [U_1660,U_1658] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1660),U_1658))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1658),hAPP(nat,nat,suc,U_1660))) )
    & ! [U_1659,U_1657] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1657),hAPP(nat,nat,suc,U_1659)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1659),U_1657)) ) ),
    inference(miniscope,[status(thm)],[f_486_2]) ).

cnf(f_486_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1657),hAPP(nat,nat,suc,U_1659)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1659),U_1657)) ),
    inference(clausify,[status(thm)],[f_486_3]) ).

cnf(f_486_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1660),U_1658))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1658),hAPP(nat,nat,suc,U_1660))) ),
    inference(clausify,[status(thm)],[f_486_3]) ).

fof(f_487_1,plain,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,suc,N)),
    inference(fof_nnf,[status(thm)],[fact_397_add__Suc__shift]) ).

fof(f_487_2,plain,
    ! [U_1662,U_1661] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1662)),U_1661) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1662),hAPP(nat,nat,suc,U_1661)),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

cnf(f_487_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1662)),U_1661) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1662),hAPP(nat,nat,suc,U_1661)),
    inference(clausify,[status(thm)],[f_487_2]) ).

fof(f_488_1,plain,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N)),
    inference(fof_nnf,[status(thm)],[fact_398_add__Suc]) ).

fof(f_488_2,plain,
    ! [U_1664,U_1663] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1664)),U_1663) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1664),U_1663)),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

cnf(f_488_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1664)),U_1663) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1664),U_1663)),
    inference(clausify,[status(thm)],[f_488_2]) ).

fof(f_489_1,plain,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N)),
    inference(fof_nnf,[status(thm)],[fact_399_add__Suc__right]) ).

fof(f_489_2,plain,
    ! [U_1666,U_1665] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1666),hAPP(nat,nat,suc,U_1665)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1666),U_1665)),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

cnf(f_489_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1666),hAPP(nat,nat,suc,U_1665)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1666),U_1665)),
    inference(clausify,[status(thm)],[f_489_2]) ).

fof(f_490_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_400_Suc__leD]) ).

fof(f_490_2,plain,
    ! [U_1668,U_1667] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1668),U_1667))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1668)),U_1667)) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

cnf(f_490_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1668),U_1667))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1668)),U_1667)) ),
    inference(clausify,[status(thm)],[f_490_2]) ).

fof(f_491_1,plain,
    ! [M_3,N] :
      ( M_3 = hAPP(nat,nat,suc,N)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_401_le__SucE]) ).

fof(f_491_2,plain,
    ! [U_1670,U_1669] :
      ( U_1670 = hAPP(nat,nat,suc,U_1669)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1670),U_1669))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1670),hAPP(nat,nat,suc,U_1669))) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

cnf(f_491_3,plain,
    ( U_1670 = hAPP(nat,nat,suc,U_1669)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1670),U_1669))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1670),hAPP(nat,nat,suc,U_1669))) ),
    inference(clausify,[status(thm)],[f_491_2]) ).

fof(f_492_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_402_le__SucI]) ).

fof(f_492_2,plain,
    ! [U_1672,U_1671] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1672),hAPP(nat,nat,suc,U_1671)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1672),U_1671)) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

cnf(f_492_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1672),hAPP(nat,nat,suc,U_1671)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1672),U_1671)) ),
    inference(clausify,[status(thm)],[f_492_2]) ).

fof(f_493_1,plain,
    ! [Na,M] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M))) ) ),
    inference(fof_nnf,[status(thm)],[fact_403_Suc__le__mono]) ).

fof(f_493_2,plain,
    ! [U_1674,U_1673] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1674)),hAPP(nat,nat,suc,U_1673)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1674),U_1673)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1674),U_1673))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1674)),hAPP(nat,nat,suc,U_1673))) ) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

fof(f_493_3,plain,
    ( ! [U_1678,U_1676] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1678)),hAPP(nat,nat,suc,U_1676)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1678),U_1676)) )
    & ! [U_1677,U_1675] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1677),U_1675))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1677)),hAPP(nat,nat,suc,U_1675))) ) ),
    inference(miniscope,[status(thm)],[f_493_2]) ).

cnf(f_493_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1677),U_1675))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1677)),hAPP(nat,nat,suc,U_1675))) ),
    inference(clausify,[status(thm)],[f_493_3]) ).

cnf(f_493_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1678)),hAPP(nat,nat,suc,U_1676)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1678),U_1676)) ),
    inference(clausify,[status(thm)],[f_493_3]) ).

fof(f_494_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,Na)))
        | ( M != hAPP(nat,nat,suc,Na)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) )
      & ( M = hAPP(nat,nat,suc,Na)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_404_le__Suc__eq]) ).

fof(f_494_2,plain,
    ! [U_1680,U_1679] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1680),hAPP(nat,nat,suc,U_1679)))
        | ( U_1680 != hAPP(nat,nat,suc,U_1679)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1680),U_1679)) ) )
      & ( U_1680 = hAPP(nat,nat,suc,U_1679)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1680),U_1679))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1680),hAPP(nat,nat,suc,U_1679))) ) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

fof(f_494_3,plain,
    ( ! [U_1684,U_1682] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1684),hAPP(nat,nat,suc,U_1682)))
        | ( U_1684 != hAPP(nat,nat,suc,U_1682)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1684),U_1682)) ) )
    & ! [U_1683,U_1681] :
        ( U_1683 = hAPP(nat,nat,suc,U_1681)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1683),U_1681))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1683),hAPP(nat,nat,suc,U_1681))) ) ),
    inference(miniscope,[status(thm)],[f_494_2]) ).

cnf(f_494_4,plain,
    ( U_1683 = hAPP(nat,nat,suc,U_1681)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1683),U_1681))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1683),hAPP(nat,nat,suc,U_1681))) ),
    inference(clausify,[status(thm)],[f_494_3]) ).

cnf(f_494_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1684),U_1682))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1684),hAPP(nat,nat,suc,U_1682))) ),
    inference(clausify,[status(thm)],[f_494_3]) ).

cnf(f_494_6,plain,
    ( U_1684 != hAPP(nat,nat,suc,U_1682)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1684),hAPP(nat,nat,suc,U_1682))) ),
    inference(clausify,[status(thm)],[f_494_3]) ).

fof(f_495_1,plain,
    ! [M,Na] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_405_not__less__eq__eq]) ).

fof(f_495_2,plain,
    ! [U_1686,U_1685] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1686),U_1685))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1685)),U_1686)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1685)),U_1686))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1686),U_1685)) ) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

fof(f_495_3,plain,
    ( ! [U_1690,U_1688] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1690),U_1688))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1688)),U_1690)) )
    & ! [U_1689,U_1687] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1687)),U_1689))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1689),U_1687)) ) ),
    inference(miniscope,[status(thm)],[f_495_2]) ).

cnf(f_495_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1687)),U_1689))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1689),U_1687)) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1690),U_1688))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1688)),U_1690)) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

fof(f_496_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N)),
    inference(fof_nnf,[status(thm)],[fact_406_Suc__n__not__le__n]) ).

fof(f_496_2,plain,
    ! [U_1691] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1691)),U_1691)),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

cnf(f_496_3,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1691)),U_1691)),
    inference(clausify,[status(thm)],[f_496_2]) ).

fof(f_497_1,plain,
    ! [N_1] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),N_1)),
    inference(fof_nnf,[status(thm)],[fact_407_inj__Suc]) ).

fof(f_497_2,plain,
    ! [U_1692] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),U_1692)),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

cnf(f_497_3,plain,
    hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),U_1692)),
    inference(clausify,[status(thm)],[f_497_2]) ).

fof(f_498_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | ! [M_1] : Na != hAPP(nat,nat,suc,M_1) )
      & ( ? [M_1] : Na = hAPP(nat,nat,suc,M_1)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_408_gr0__conv__Suc]) ).

fof(f_498_2,plain,
    ! [U_1695] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1695))
        | ! [U_1694] : U_1695 != hAPP(nat,nat,suc,U_1694) )
      & ( ? [U_1693] : U_1695 = hAPP(nat,nat,suc,U_1693)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1695)) ) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

fof(f_498_3,plain,
    ( ! [U_1697] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1697))
        | ! [U_1694] : U_1697 != hAPP(nat,nat,suc,U_1694) )
    & ! [U_1696] :
        ( ? [U_1693] : U_1696 = hAPP(nat,nat,suc,U_1693)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1696)) ) ),
    inference(miniscope,[status(thm)],[f_498_2]) ).

fof(f_498_4,plain,
    ( ! [U_1697] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1697))
        | ! [U_1694] : U_1697 != hAPP(nat,nat,suc,U_1694) )
    & ! [U_1696] :
        ( U_1696 = hAPP(nat,nat,suc,sK92(U_1696))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1696)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_1693,sK92(U_1696))],[f_498_3]) ).

cnf(f_498_5,plain,
    ( U_1696 = hAPP(nat,nat,suc,sK92(U_1696))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1696)) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1697))
    | U_1697 != hAPP(nat,nat,suc,U_1694) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

fof(f_499_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_409_less__Suc0]) ).

fof(f_499_2,plain,
    ! [U_1698] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1698),hAPP(nat,nat,suc,zero_zero(nat))))
        | U_1698 != zero_zero(nat) )
      & ( U_1698 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1698),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ( ! [U_1700] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1700),hAPP(nat,nat,suc,zero_zero(nat))))
        | U_1700 != zero_zero(nat) )
    & ! [U_1699] :
        ( U_1699 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1699),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(miniscope,[status(thm)],[f_499_2]) ).

cnf(f_499_4,plain,
    ( U_1699 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1699),hAPP(nat,nat,suc,zero_zero(nat)))) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

cnf(f_499_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1700),hAPP(nat,nat,suc,zero_zero(nat))))
    | U_1700 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

fof(f_500_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
        | ( ! [J_2] :
              ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),Na))
              | M != hAPP(nat,nat,suc,J_2) )
          & M != zero_zero(nat) ) )
      & ( ? [J_2] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),Na))
            & M = hAPP(nat,nat,suc,J_2) )
        | M = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_410_less__Suc__eq__0__disj]) ).

fof(f_500_2,plain,
    ! [U_1704,U_1703] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1704),hAPP(nat,nat,suc,U_1703)))
        | ( ! [U_1702] :
              ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1702),U_1703))
              | U_1704 != hAPP(nat,nat,suc,U_1702) )
          & U_1704 != zero_zero(nat) ) )
      & ( ? [U_1701] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1701),U_1703))
            & U_1704 = hAPP(nat,nat,suc,U_1701) )
        | U_1704 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1704),hAPP(nat,nat,suc,U_1703))) ) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ( ! [U_1708,U_1706] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1708),hAPP(nat,nat,suc,U_1706)))
        | ( ! [U_1702] :
              ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1702),U_1706))
              | U_1708 != hAPP(nat,nat,suc,U_1702) )
          & U_1708 != zero_zero(nat) ) )
    & ! [U_1707,U_1705] :
        ( ? [U_1701] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1701),U_1705))
            & U_1707 = hAPP(nat,nat,suc,U_1701) )
        | U_1707 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1707),hAPP(nat,nat,suc,U_1705))) ) ),
    inference(miniscope,[status(thm)],[f_500_2]) ).

fof(f_500_4,plain,
    ( ! [U_1708,U_1706] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1708),hAPP(nat,nat,suc,U_1706)))
        | ( ! [U_1702] :
              ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1702),U_1706))
              | U_1708 != hAPP(nat,nat,suc,U_1702) )
          & U_1708 != zero_zero(nat) ) )
    & ! [U_1707,U_1705] :
        ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK93(U_1707,U_1705)),U_1705))
          & U_1707 = hAPP(nat,nat,suc,sK93(U_1707,U_1705)) )
        | U_1707 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1707),hAPP(nat,nat,suc,U_1705))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_1701,sK93(U_1707,U_1705))],[f_500_3]) ).

cnf(f_500_5,plain,
    ( U_1707 = hAPP(nat,nat,suc,sK93(U_1707,U_1705))
    | U_1707 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1707),hAPP(nat,nat,suc,U_1705))) ),
    inference(clausify,[status(thm)],[f_500_4]) ).

cnf(f_500_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK93(U_1707,U_1705)),U_1705))
    | U_1707 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1707),hAPP(nat,nat,suc,U_1705))) ),
    inference(clausify,[status(thm)],[f_500_4]) ).

cnf(f_500_7,plain,
    ( U_1708 != zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1708),hAPP(nat,nat,suc,U_1706))) ),
    inference(clausify,[status(thm)],[f_500_4]) ).

cnf(f_500_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1702),U_1706))
    | U_1708 != hAPP(nat,nat,suc,U_1702)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1708),hAPP(nat,nat,suc,U_1706))) ),
    inference(clausify,[status(thm)],[f_500_4]) ).

fof(f_501_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) = hAPP(nat,nat,suc,zero_zero(nat))
        | ( ( Na != hAPP(nat,nat,suc,zero_zero(nat))
            | M != zero_zero(nat) )
          & ( Na != zero_zero(nat)
            | M != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_411_add__is__1]) ).

fof(f_501_2,plain,
    ! [U_1710,U_1709] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1710),U_1709) = hAPP(nat,nat,suc,zero_zero(nat))
        | ( ( U_1709 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_1710 != zero_zero(nat) )
          & ( U_1709 != zero_zero(nat)
            | U_1710 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( U_1709 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_1710 = zero_zero(nat) )
        | ( U_1709 = zero_zero(nat)
          & U_1710 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1710),U_1709) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

fof(f_501_3,plain,
    ( ! [U_1714,U_1712] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1714),U_1712) = hAPP(nat,nat,suc,zero_zero(nat))
        | ( ( U_1712 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_1714 != zero_zero(nat) )
          & ( U_1712 != zero_zero(nat)
            | U_1714 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
    & ! [U_1713,U_1711] :
        ( ( U_1711 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_1713 = zero_zero(nat) )
        | ( U_1711 = zero_zero(nat)
          & U_1713 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1713),U_1711) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(miniscope,[status(thm)],[f_501_2]) ).

cnf(f_501_4,plain,
    ( U_1713 = zero_zero(nat)
    | U_1713 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1713),U_1711) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_501_3]) ).

cnf(f_501_5,plain,
    ( U_1711 = hAPP(nat,nat,suc,zero_zero(nat))
    | U_1713 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1713),U_1711) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_501_3]) ).

cnf(f_501_6,plain,
    ( U_1713 = zero_zero(nat)
    | U_1711 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1713),U_1711) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_501_3]) ).

cnf(f_501_7,plain,
    ( U_1711 = hAPP(nat,nat,suc,zero_zero(nat))
    | U_1711 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1713),U_1711) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_501_3]) ).

cnf(f_501_8,plain,
    ( U_1712 != zero_zero(nat)
    | U_1714 != hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1714),U_1712) = hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_501_3]) ).

cnf(f_501_9,plain,
    ( U_1712 != hAPP(nat,nat,suc,zero_zero(nat))
    | U_1714 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1714),U_1712) = hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_501_3]) ).

fof(f_502_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na)
        | ( ( Na != hAPP(nat,nat,suc,zero_zero(nat))
            | M != zero_zero(nat) )
          & ( Na != zero_zero(nat)
            | M != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M = 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),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_412_one__is__add]) ).

fof(f_502_2,plain,
    ! [U_1716,U_1715] :
      ( ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1716),U_1715)
        | ( ( U_1715 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_1716 != zero_zero(nat) )
          & ( U_1715 != zero_zero(nat)
            | U_1716 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( U_1715 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_1716 = zero_zero(nat) )
        | ( U_1715 = zero_zero(nat)
          & U_1716 = 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_1716),U_1715) ) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ( ! [U_1720,U_1718] :
        ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1720),U_1718)
        | ( ( U_1718 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_1720 != zero_zero(nat) )
          & ( U_1718 != zero_zero(nat)
            | U_1720 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
    & ! [U_1719,U_1717] :
        ( ( U_1717 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_1719 = zero_zero(nat) )
        | ( U_1717 = zero_zero(nat)
          & U_1719 = 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_1719),U_1717) ) ),
    inference(miniscope,[status(thm)],[f_502_2]) ).

cnf(f_502_4,plain,
    ( U_1719 = zero_zero(nat)
    | U_1719 = 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_1719),U_1717) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

cnf(f_502_5,plain,
    ( U_1717 = hAPP(nat,nat,suc,zero_zero(nat))
    | U_1719 = 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_1719),U_1717) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

cnf(f_502_6,plain,
    ( U_1719 = zero_zero(nat)
    | U_1717 = zero_zero(nat)
    | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1719),U_1717) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

cnf(f_502_7,plain,
    ( U_1717 = hAPP(nat,nat,suc,zero_zero(nat))
    | U_1717 = zero_zero(nat)
    | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1719),U_1717) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

cnf(f_502_8,plain,
    ( U_1718 != zero_zero(nat)
    | U_1720 != 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_1720),U_1718) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

cnf(f_502_9,plain,
    ( U_1718 != hAPP(nat,nat,suc,zero_zero(nat))
    | U_1720 != zero_zero(nat)
    | hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1720),U_1718) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

fof(f_503_1,plain,
    ! [I_2,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),M_3)))),
    inference(fof_nnf,[status(thm)],[fact_413_less__add__Suc1]) ).

fof(f_503_2,plain,
    ! [U_1722,U_1721] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1722),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1722),U_1721)))),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

cnf(f_503_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1722),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1722),U_1721)))),
    inference(clausify,[status(thm)],[f_503_2]) ).

fof(f_504_1,plain,
    ! [I_2,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),I_2)))),
    inference(fof_nnf,[status(thm)],[fact_414_less__add__Suc2]) ).

fof(f_504_2,plain,
    ! [U_1724,U_1723] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1724),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1723),U_1724)))),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

cnf(f_504_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1724),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1723),U_1724)))),
    inference(clausify,[status(thm)],[f_504_2]) ).

fof(f_505_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ! [K_1] : Na != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1)) )
      & ( ? [K_1] : Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_415_less__iff__Suc__add]) ).

fof(f_505_2,plain,
    ! [U_1728,U_1727] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1728),U_1727))
        | ! [U_1726] : U_1727 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1728),U_1726)) )
      & ( ? [U_1725] : U_1727 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1728),U_1725))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1728),U_1727)) ) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ( ! [U_1732,U_1730] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1732),U_1730))
        | ! [U_1726] : U_1730 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1732),U_1726)) )
    & ! [U_1731,U_1729] :
        ( ? [U_1725] : U_1729 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1731),U_1725))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1731),U_1729)) ) ),
    inference(miniscope,[status(thm)],[f_505_2]) ).

fof(f_505_4,plain,
    ( ! [U_1732,U_1730] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1732),U_1730))
        | ! [U_1726] : U_1730 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1732),U_1726)) )
    & ! [U_1731,U_1729] :
        ( U_1729 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1731),sK94(U_1731,U_1729)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1731),U_1729)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_1725,sK94(U_1731,U_1729))],[f_505_3]) ).

cnf(f_505_5,plain,
    ( U_1729 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1731),sK94(U_1731,U_1729)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1731),U_1729)) ),
    inference(clausify,[status(thm)],[f_505_4]) ).

cnf(f_505_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1732),U_1730))
    | U_1730 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1732),U_1726)) ),
    inference(clausify,[status(thm)],[f_505_4]) ).

fof(f_506_1,plain,
    ! [Na,M] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) ) ),
    inference(fof_nnf,[status(thm)],[fact_416_less__eq__Suc__le]) ).

fof(f_506_2,plain,
    ! [U_1734,U_1733] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1734),U_1733))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1734)),U_1733)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1734)),U_1733))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1734),U_1733)) ) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ( ! [U_1738,U_1736] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1738),U_1736))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1738)),U_1736)) )
    & ! [U_1737,U_1735] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1737)),U_1735))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1737),U_1735)) ) ),
    inference(miniscope,[status(thm)],[f_506_2]) ).

cnf(f_506_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1737)),U_1735))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1737),U_1735)) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

cnf(f_506_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1738),U_1736))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1738)),U_1736)) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

fof(f_507_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_417_less__Suc__eq__le]) ).

fof(f_507_2,plain,
    ! [U_1740,U_1739] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1740),hAPP(nat,nat,suc,U_1739)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1740),U_1739)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1740),U_1739))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1740),hAPP(nat,nat,suc,U_1739))) ) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ( ! [U_1744,U_1742] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1744),hAPP(nat,nat,suc,U_1742)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1744),U_1742)) )
    & ! [U_1743,U_1741] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1743),U_1741))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1743),hAPP(nat,nat,suc,U_1741))) ) ),
    inference(miniscope,[status(thm)],[f_507_2]) ).

cnf(f_507_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1743),U_1741))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1743),hAPP(nat,nat,suc,U_1741))) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

cnf(f_507_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1744),hAPP(nat,nat,suc,U_1742)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1744),U_1742)) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

fof(f_508_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_418_Suc__le__eq]) ).

fof(f_508_2,plain,
    ! [U_1746,U_1745] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1746)),U_1745))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1746),U_1745)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1746),U_1745))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1746)),U_1745)) ) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ( ! [U_1750,U_1748] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1750)),U_1748))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1750),U_1748)) )
    & ! [U_1749,U_1747] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1749),U_1747))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1749)),U_1747)) ) ),
    inference(miniscope,[status(thm)],[f_508_2]) ).

cnf(f_508_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1749),U_1747))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1749)),U_1747)) ),
    inference(clausify,[status(thm)],[f_508_3]) ).

cnf(f_508_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1750)),U_1748))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1750),U_1748)) ),
    inference(clausify,[status(thm)],[f_508_3]) ).

fof(f_509_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_419_le__imp__less__Suc]) ).

fof(f_509_2,plain,
    ! [U_1752,U_1751] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1752),hAPP(nat,nat,suc,U_1751)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1752),U_1751)) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

cnf(f_509_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1752),hAPP(nat,nat,suc,U_1751)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1752),U_1751)) ),
    inference(clausify,[status(thm)],[f_509_2]) ).

fof(f_510_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_420_Suc__leI]) ).

fof(f_510_2,plain,
    ! [U_1754,U_1753] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1754)),U_1753))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1754),U_1753)) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

cnf(f_510_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1754)),U_1753))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1754),U_1753)) ),
    inference(clausify,[status(thm)],[f_510_2]) ).

fof(f_511_1,plain,
    ! [M,Na] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M)))
          | Na != M )
        & ( Na = M
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) ),
    inference(fof_nnf,[status(thm)],[fact_421_le__less__Suc__eq]) ).

fof(f_511_2,plain,
    ! [U_1756,U_1755] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1755),hAPP(nat,nat,suc,U_1756)))
          | U_1755 != U_1756 )
        & ( U_1755 = U_1756
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1755),hAPP(nat,nat,suc,U_1756))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1756),U_1755)) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

cnf(f_511_3,plain,
    ( U_1755 = U_1756
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1755),hAPP(nat,nat,suc,U_1756)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1756),U_1755)) ),
    inference(clausify,[status(thm)],[f_511_2]) ).

cnf(f_511_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1755),hAPP(nat,nat,suc,U_1756)))
    | U_1755 != U_1756
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1756),U_1755)) ),
    inference(clausify,[status(thm)],[f_511_2]) ).

fof(f_512_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_422_Suc__le__lessD]) ).

fof(f_512_2,plain,
    ! [U_1758,U_1757] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1758),U_1757))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1758)),U_1757)) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

cnf(f_512_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1758),U_1757))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1758)),U_1757)) ),
    inference(clausify,[status(thm)],[f_512_2]) ).

fof(f_513_1,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(fof_nnf,[status(thm)],[fact_423_One__nat__def]) ).

cnf(f_513_2,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(clausify,[status(thm)],[f_513_1]) ).

fof(f_514_1,plain,
    ! [X_1] : hAPP(nat,fun(nat,bool),ord_less(nat),X_1) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_1)),
    inference(fof_nnf,[status(thm)],[fact_424_less__eq__Suc__le__raw]) ).

fof(f_514_2,plain,
    ! [U_1759] : hAPP(nat,fun(nat,bool),ord_less(nat),U_1759) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1759)),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

cnf(f_514_3,plain,
    hAPP(nat,fun(nat,bool),ord_less(nat),U_1759) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1759)),
    inference(clausify,[status(thm)],[f_514_2]) ).

fof(f_515_1,plain,
    ! [Na] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),Na))) = hAPP(nat,nat,suc,Na),
    inference(fof_nnf,[status(thm)],[fact_425_card__Collect__le__nat]) ).

fof(f_515_2,plain,
    ! [U_1760] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),U_1760))) = hAPP(nat,nat,suc,U_1760),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

cnf(f_515_3,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),U_1760))) = hAPP(nat,nat,suc,U_1760),
    inference(clausify,[status(thm)],[f_515_2]) ).

fof(f_516_1,plain,
    ! [I,M_2] :
      ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I)))))
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_426_card__less__Suc]) ).

fof(f_516_2,plain,
    ! [U_1762,U_1761] :
      ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),U_1761))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1762))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_1761))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_1762)))))
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1761)) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

cnf(f_516_3,plain,
    ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),U_1761))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1762))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_1761))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_1762)))))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1761)) ),
    inference(clausify,[status(thm)],[f_516_2]) ).

fof(f_517_1,plain,
    ! [I,M_2] :
      ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))) != zero_zero(nat)
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_427_card__less]) ).

fof(f_517_2,plain,
    ! [U_1764,U_1763] :
      ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_1763))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_1764))))) != zero_zero(nat)
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1763)) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

cnf(f_517_3,plain,
    ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_1763))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_1764))))) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1763)) ),
    inference(clausify,[status(thm)],[f_517_2]) ).

fof(f_518_1,plain,
    ! [I,M_2] :
      ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I)))))
      | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_428_card__less__Suc2]) ).

fof(f_518_2,plain,
    ! [U_1766,U_1765] :
      ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),U_1765))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1766)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_1765))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_1766)))))
      | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1765)) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

cnf(f_518_3,plain,
    ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),U_1765))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1766)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),U_1765))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,U_1766)))))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1765)) ),
    inference(clausify,[status(thm)],[f_518_2]) ).

fof(f_519_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a)
            | ti(X_a,Aa) != zero_zero(X_a) )
          & ( ti(X_a,Aa) = zero_zero(X_a)
            | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) != zero_zero(X_a) ) )
      | ~ linord219039673up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_429_double__eq__0__iff]) ).

fof(f_519_2,plain,
    ! [U_1768] :
      ( ! [U_1767] :
          ( ( hAPP(U_1768,U_1768,hAPP(U_1768,fun(U_1768,U_1768),plus_plus(U_1768),U_1767),U_1767) = zero_zero(U_1768)
            | ti(U_1768,U_1767) != zero_zero(U_1768) )
          & ( ti(U_1768,U_1767) = zero_zero(U_1768)
            | hAPP(U_1768,U_1768,hAPP(U_1768,fun(U_1768,U_1768),plus_plus(U_1768),U_1767),U_1767) != zero_zero(U_1768) ) )
      | ~ linord219039673up_add(U_1768) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ! [U_1768] :
      ( ( ! [U_1770] :
            ( hAPP(U_1768,U_1768,hAPP(U_1768,fun(U_1768,U_1768),plus_plus(U_1768),U_1770),U_1770) = zero_zero(U_1768)
            | ti(U_1768,U_1770) != zero_zero(U_1768) )
        & ! [U_1769] :
            ( ti(U_1768,U_1769) = zero_zero(U_1768)
            | hAPP(U_1768,U_1768,hAPP(U_1768,fun(U_1768,U_1768),plus_plus(U_1768),U_1769),U_1769) != zero_zero(U_1768) ) )
      | ~ linord219039673up_add(U_1768) ),
    inference(miniscope,[status(thm)],[f_519_2]) ).

cnf(f_519_4,plain,
    ( ti(U_1768,U_1769) = zero_zero(U_1768)
    | hAPP(U_1768,U_1768,hAPP(U_1768,fun(U_1768,U_1768),plus_plus(U_1768),U_1769),U_1769) != zero_zero(U_1768)
    | ~ linord219039673up_add(U_1768) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

cnf(f_519_5,plain,
    ( hAPP(U_1768,U_1768,hAPP(U_1768,fun(U_1768,U_1768),plus_plus(U_1768),U_1770),U_1770) = zero_zero(U_1768)
    | ti(U_1768,U_1770) != zero_zero(U_1768)
    | ~ linord219039673up_add(U_1768) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

fof(f_520_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(nat,fun(nat,bool),ord_less(nat),I_1),J)) )
      | ~ hBOOL(hAPP(nat,bool,Pa,J))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) ),
    inference(fof_nnf,[status(thm)],[fact_430_inc__induct]) ).

fof(f_520_2,plain,
    ! [U_1774,U_1773,U_1772] :
      ( hBOOL(hAPP(nat,bool,U_1774,U_1773))
      | ? [U_1771] :
          ( ~ hBOOL(hAPP(nat,bool,U_1774,U_1771))
          & hBOOL(hAPP(nat,bool,U_1774,hAPP(nat,nat,suc,U_1771)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1771),U_1772)) )
      | ~ hBOOL(hAPP(nat,bool,U_1774,U_1772))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1773),U_1772)) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ! [U_1774,U_1773,U_1772] :
      ( hBOOL(hAPP(nat,bool,U_1774,U_1773))
      | ( ~ hBOOL(hAPP(nat,bool,U_1774,sK95(U_1774,U_1773,U_1772)))
        & hBOOL(hAPP(nat,bool,U_1774,hAPP(nat,nat,suc,sK95(U_1774,U_1773,U_1772))))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK95(U_1774,U_1773,U_1772)),U_1772)) )
      | ~ hBOOL(hAPP(nat,bool,U_1774,U_1772))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1773),U_1772)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_1771,sK95(U_1774,U_1773,U_1772))],[f_520_2]) ).

cnf(f_520_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK95(U_1774,U_1773,U_1772)),U_1772))
    | hBOOL(hAPP(nat,bool,U_1774,U_1773))
    | ~ hBOOL(hAPP(nat,bool,U_1774,U_1772))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1773),U_1772)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_5,plain,
    ( hBOOL(hAPP(nat,bool,U_1774,hAPP(nat,nat,suc,sK95(U_1774,U_1773,U_1772))))
    | hBOOL(hAPP(nat,bool,U_1774,U_1773))
    | ~ hBOOL(hAPP(nat,bool,U_1774,U_1772))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1773),U_1772)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_1774,sK95(U_1774,U_1773,U_1772)))
    | hBOOL(hAPP(nat,bool,U_1774,U_1773))
    | ~ hBOOL(hAPP(nat,bool,U_1774,U_1772))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1773),U_1772)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

fof(f_521_1,plain,
    ! [M_3,N] :
      ( ? [K_1] : N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) ),
    inference(fof_nnf,[status(thm)],[fact_431_less__imp__Suc__add]) ).

fof(f_521_2,plain,
    ! [U_1777,U_1776] :
      ( ? [U_1775] : U_1776 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1777),U_1775))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1777),U_1776)) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ! [U_1777,U_1776] :
      ( U_1776 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1777),sK96(U_1777,U_1776)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1777),U_1776)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_1775,sK96(U_1777,U_1776))],[f_521_2]) ).

cnf(f_521_4,plain,
    ( U_1776 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1777),sK96(U_1777,U_1776)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1777),U_1776)) ),
    inference(clausify,[status(thm)],[f_521_3]) ).

fof(f_522_1,plain,
    ! [N] :
      ( ? [M_1] : N = hAPP(nat,nat,suc,M_1)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_432_gr0__implies__Suc]) ).

fof(f_522_2,plain,
    ! [U_1779] :
      ( ? [U_1778] : U_1779 = hAPP(nat,nat,suc,U_1778)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1779)) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ! [U_1779] :
      ( U_1779 = hAPP(nat,nat,suc,sK97(U_1779))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1779)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_1778,sK97(U_1779))],[f_522_2]) ).

cnf(f_522_4,plain,
    ( U_1779 = hAPP(nat,nat,suc,sK97(U_1779))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1779)) ),
    inference(clausify,[status(thm)],[f_522_3]) ).

fof(f_523_1,plain,
    ! [X_a] :
      ( ! [Na,N_3,F] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,N_3)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_3))
          | ? [N_2] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_433_lift__Suc__mono__le]) ).

fof(f_523_2,plain,
    ! [U_1784] :
      ( ! [U_1783,U_1782,U_1781] :
          ( hBOOL(hAPP(U_1784,bool,hAPP(U_1784,fun(U_1784,bool),ord_less_eq(U_1784),hAPP(nat,U_1784,U_1781,U_1783)),hAPP(nat,U_1784,U_1781,U_1782)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1783),U_1782))
          | ? [U_1780] : ~ hBOOL(hAPP(U_1784,bool,hAPP(U_1784,fun(U_1784,bool),ord_less_eq(U_1784),hAPP(nat,U_1784,U_1781,U_1780)),hAPP(nat,U_1784,U_1781,hAPP(nat,nat,suc,U_1780)))) )
      | ~ order(U_1784) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ! [U_1784] :
      ( ! [U_1783,U_1782,U_1781] :
          ( hBOOL(hAPP(U_1784,bool,hAPP(U_1784,fun(U_1784,bool),ord_less_eq(U_1784),hAPP(nat,U_1784,U_1781,U_1783)),hAPP(nat,U_1784,U_1781,U_1782)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1783),U_1782))
          | ~ hBOOL(hAPP(U_1784,bool,hAPP(U_1784,fun(U_1784,bool),ord_less_eq(U_1784),hAPP(nat,U_1784,U_1781,sK98(U_1784,U_1783,U_1782,U_1781))),hAPP(nat,U_1784,U_1781,hAPP(nat,nat,suc,sK98(U_1784,U_1783,U_1782,U_1781))))) )
      | ~ order(U_1784) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_1780,sK98(U_1784,U_1783,U_1782,U_1781))],[f_523_2]) ).

cnf(f_523_4,plain,
    ( hBOOL(hAPP(U_1784,bool,hAPP(U_1784,fun(U_1784,bool),ord_less_eq(U_1784),hAPP(nat,U_1784,U_1781,U_1783)),hAPP(nat,U_1784,U_1781,U_1782)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1783),U_1782))
    | ~ hBOOL(hAPP(U_1784,bool,hAPP(U_1784,fun(U_1784,bool),ord_less_eq(U_1784),hAPP(nat,U_1784,U_1781,sK98(U_1784,U_1783,U_1782,U_1781))),hAPP(nat,U_1784,U_1781,hAPP(nat,nat,suc,sK98(U_1784,U_1783,U_1782,U_1781)))))
    | ~ order(U_1784) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

fof(f_524_1,plain,
    ! [X_a] :
      ( ! [Na,M,F] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,M)))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) )
            & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,M))) ) )
          | ? [N_2] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_434_lift__Suc__mono__less__iff]) ).

fof(f_524_2,plain,
    ! [U_1789] :
      ( ! [U_1788,U_1787,U_1786] :
          ( ( ( hBOOL(hAPP(U_1789,bool,hAPP(U_1789,fun(U_1789,bool),ord_less(U_1789),hAPP(nat,U_1789,U_1786,U_1788)),hAPP(nat,U_1789,U_1786,U_1787)))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1788),U_1787)) )
            & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1788),U_1787))
              | ~ hBOOL(hAPP(U_1789,bool,hAPP(U_1789,fun(U_1789,bool),ord_less(U_1789),hAPP(nat,U_1789,U_1786,U_1788)),hAPP(nat,U_1789,U_1786,U_1787))) ) )
          | ? [U_1785] : ~ hBOOL(hAPP(U_1789,bool,hAPP(U_1789,fun(U_1789,bool),ord_less(U_1789),hAPP(nat,U_1789,U_1786,U_1785)),hAPP(nat,U_1789,U_1786,hAPP(nat,nat,suc,U_1785)))) )
      | ~ order(U_1789) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ! [U_1789] :
      ( ! [U_1788,U_1787,U_1786] :
          ( ( ( hBOOL(hAPP(U_1789,bool,hAPP(U_1789,fun(U_1789,bool),ord_less(U_1789),hAPP(nat,U_1789,U_1786,U_1788)),hAPP(nat,U_1789,U_1786,U_1787)))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1788),U_1787)) )
            & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1788),U_1787))
              | ~ hBOOL(hAPP(U_1789,bool,hAPP(U_1789,fun(U_1789,bool),ord_less(U_1789),hAPP(nat,U_1789,U_1786,U_1788)),hAPP(nat,U_1789,U_1786,U_1787))) ) )
          | ~ hBOOL(hAPP(U_1789,bool,hAPP(U_1789,fun(U_1789,bool),ord_less(U_1789),hAPP(nat,U_1789,U_1786,sK99(U_1789,U_1788,U_1787,U_1786))),hAPP(nat,U_1789,U_1786,hAPP(nat,nat,suc,sK99(U_1789,U_1788,U_1787,U_1786))))) )
      | ~ order(U_1789) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_1785,sK99(U_1789,U_1788,U_1787,U_1786))],[f_524_2]) ).

cnf(f_524_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1788),U_1787))
    | ~ hBOOL(hAPP(U_1789,bool,hAPP(U_1789,fun(U_1789,bool),ord_less(U_1789),hAPP(nat,U_1789,U_1786,U_1788)),hAPP(nat,U_1789,U_1786,U_1787)))
    | ~ hBOOL(hAPP(U_1789,bool,hAPP(U_1789,fun(U_1789,bool),ord_less(U_1789),hAPP(nat,U_1789,U_1786,sK99(U_1789,U_1788,U_1787,U_1786))),hAPP(nat,U_1789,U_1786,hAPP(nat,nat,suc,sK99(U_1789,U_1788,U_1787,U_1786)))))
    | ~ order(U_1789) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

cnf(f_524_5,plain,
    ( hBOOL(hAPP(U_1789,bool,hAPP(U_1789,fun(U_1789,bool),ord_less(U_1789),hAPP(nat,U_1789,U_1786,U_1788)),hAPP(nat,U_1789,U_1786,U_1787)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1788),U_1787))
    | ~ hBOOL(hAPP(U_1789,bool,hAPP(U_1789,fun(U_1789,bool),ord_less(U_1789),hAPP(nat,U_1789,U_1786,sK99(U_1789,U_1788,U_1787,U_1786))),hAPP(nat,U_1789,U_1786,hAPP(nat,nat,suc,sK99(U_1789,U_1788,U_1787,U_1786)))))
    | ~ order(U_1789) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

fof(f_525_1,plain,
    ! [X_a] :
      ( ! [Na,N_3,F] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,N_3)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_3))
          | ? [N_2] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_435_lift__Suc__mono__less]) ).

fof(f_525_2,plain,
    ! [U_1794] :
      ( ! [U_1793,U_1792,U_1791] :
          ( hBOOL(hAPP(U_1794,bool,hAPP(U_1794,fun(U_1794,bool),ord_less(U_1794),hAPP(nat,U_1794,U_1791,U_1793)),hAPP(nat,U_1794,U_1791,U_1792)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1793),U_1792))
          | ? [U_1790] : ~ hBOOL(hAPP(U_1794,bool,hAPP(U_1794,fun(U_1794,bool),ord_less(U_1794),hAPP(nat,U_1794,U_1791,U_1790)),hAPP(nat,U_1794,U_1791,hAPP(nat,nat,suc,U_1790)))) )
      | ~ order(U_1794) ),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

fof(f_525_3,plain,
    ! [U_1794] :
      ( ! [U_1793,U_1792,U_1791] :
          ( hBOOL(hAPP(U_1794,bool,hAPP(U_1794,fun(U_1794,bool),ord_less(U_1794),hAPP(nat,U_1794,U_1791,U_1793)),hAPP(nat,U_1794,U_1791,U_1792)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1793),U_1792))
          | ~ hBOOL(hAPP(U_1794,bool,hAPP(U_1794,fun(U_1794,bool),ord_less(U_1794),hAPP(nat,U_1794,U_1791,sK100(U_1794,U_1793,U_1792,U_1791))),hAPP(nat,U_1794,U_1791,hAPP(nat,nat,suc,sK100(U_1794,U_1793,U_1792,U_1791))))) )
      | ~ order(U_1794) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_1790,sK100(U_1794,U_1793,U_1792,U_1791))],[f_525_2]) ).

cnf(f_525_4,plain,
    ( hBOOL(hAPP(U_1794,bool,hAPP(U_1794,fun(U_1794,bool),ord_less(U_1794),hAPP(nat,U_1794,U_1791,U_1793)),hAPP(nat,U_1794,U_1791,U_1792)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1793),U_1792))
    | ~ hBOOL(hAPP(U_1794,bool,hAPP(U_1794,fun(U_1794,bool),ord_less(U_1794),hAPP(nat,U_1794,U_1791,sK100(U_1794,U_1793,U_1792,U_1791))),hAPP(nat,U_1794,U_1791,hAPP(nat,nat,suc,sK100(U_1794,U_1793,U_1792,U_1791)))))
    | ~ order(U_1794) ),
    inference(clausify,[status(thm)],[f_525_3]) ).

fof(f_526_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_436_Suc__eq__plus1]) ).

fof(f_526_2,plain,
    ! [U_1795] : hAPP(nat,nat,suc,U_1795) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1795),one_one(nat)),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

cnf(f_526_3,plain,
    hAPP(nat,nat,suc,U_1795) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1795),one_one(nat)),
    inference(clausify,[status(thm)],[f_526_2]) ).

fof(f_527_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_437_Suc__eq__plus1__left]) ).

fof(f_527_2,plain,
    ! [U_1796] : hAPP(nat,nat,suc,U_1796) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_1796),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

cnf(f_527_3,plain,
    hAPP(nat,nat,suc,U_1796) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_1796),
    inference(clausify,[status(thm)],[f_527_2]) ).

fof(f_528_1,plain,
    ! [N,M_4] :
      ( ? [M_1] : M_4 = hAPP(nat,nat,suc,M_1)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M_4)) ),
    inference(fof_nnf,[status(thm)],[fact_438_Suc__le__D]) ).

fof(f_528_2,plain,
    ! [U_1799,U_1798] :
      ( ? [U_1797] : U_1798 = hAPP(nat,nat,suc,U_1797)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1799)),U_1798)) ),
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ! [U_1799,U_1798] :
      ( U_1798 = hAPP(nat,nat,suc,sK101(U_1799,U_1798))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1799)),U_1798)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_1797,sK101(U_1799,U_1798))],[f_528_2]) ).

cnf(f_528_4,plain,
    ( U_1798 = hAPP(nat,nat,suc,sK101(U_1799,U_1798))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1799)),U_1798)) ),
    inference(clausify,[status(thm)],[f_528_3]) ).

fof(f_529_1,plain,
    ! [I_2,K_2] :
      ( ? [J_2] :
          ( K_2 = hAPP(nat,nat,suc,J_2)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) )
      | K_2 = hAPP(nat,nat,suc,I_2)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_2)) ),
    inference(fof_nnf,[status(thm)],[fact_439_lessE]) ).

fof(f_529_2,plain,
    ! [U_1802,U_1801] :
      ( ? [U_1800] :
          ( U_1801 = hAPP(nat,nat,suc,U_1800)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1802),U_1800)) )
      | U_1801 = hAPP(nat,nat,suc,U_1802)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1802),U_1801)) ),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ! [U_1802,U_1801] :
      ( ( U_1801 = hAPP(nat,nat,suc,sK102(U_1802,U_1801))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1802),sK102(U_1802,U_1801))) )
      | U_1801 = hAPP(nat,nat,suc,U_1802)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1802),U_1801)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_1800,sK102(U_1802,U_1801))],[f_529_2]) ).

cnf(f_529_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1802),sK102(U_1802,U_1801)))
    | U_1801 = hAPP(nat,nat,suc,U_1802)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1802),U_1801)) ),
    inference(clausify,[status(thm)],[f_529_3]) ).

cnf(f_529_5,plain,
    ( U_1801 = hAPP(nat,nat,suc,sK102(U_1802,U_1801))
    | U_1801 = hAPP(nat,nat,suc,U_1802)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1802),U_1801)) ),
    inference(clausify,[status(thm)],[f_529_3]) ).

fof(f_530_1,plain,
    ! [I_2,K_2] :
      ( ? [J_2] :
          ( K_2 = hAPP(nat,nat,suc,J_2)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_2)) ),
    inference(fof_nnf,[status(thm)],[fact_440_Suc__lessE]) ).

fof(f_530_2,plain,
    ! [U_1805,U_1804] :
      ( ? [U_1803] :
          ( U_1804 = hAPP(nat,nat,suc,U_1803)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1805),U_1803)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1805)),U_1804)) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ! [U_1805,U_1804] :
      ( ( U_1804 = hAPP(nat,nat,suc,sK103(U_1805,U_1804))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1805),sK103(U_1805,U_1804))) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1805)),U_1804)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_1803,sK103(U_1805,U_1804))],[f_530_2]) ).

cnf(f_530_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1805),sK103(U_1805,U_1804)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1805)),U_1804)) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

cnf(f_530_5,plain,
    ( U_1804 = hAPP(nat,nat,suc,sK103(U_1805,U_1804))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1805)),U_1804)) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

fof(f_531_1,plain,
    ! [N] :
      ( ? [M_1] : N = hAPP(nat,nat,suc,M_1)
      | N = zero_zero(nat) ),
    inference(fof_nnf,[status(thm)],[fact_441_not0__implies__Suc]) ).

fof(f_531_2,plain,
    ! [U_1807] :
      ( ? [U_1806] : U_1807 = hAPP(nat,nat,suc,U_1806)
      | U_1807 = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ! [U_1807] :
      ( U_1807 = hAPP(nat,nat,suc,sK104(U_1807))
      | U_1807 = zero_zero(nat) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_1806,sK104(U_1807))],[f_531_2]) ).

cnf(f_531_4,plain,
    ( U_1807 = hAPP(nat,nat,suc,sK104(U_1807))
    | U_1807 = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

fof(f_532_1,plain,
    ! [Y] :
      ( ? [Nat_2] : Y = hAPP(nat,nat,suc,Nat_2)
      | Y = zero_zero(nat) ),
    inference(fof_nnf,[status(thm)],[fact_442_nat_Oexhaust]) ).

fof(f_532_2,plain,
    ! [U_1809] :
      ( ? [U_1808] : U_1809 = hAPP(nat,nat,suc,U_1808)
      | U_1809 = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ! [U_1809] :
      ( U_1809 = hAPP(nat,nat,suc,sK105(U_1809))
      | U_1809 = zero_zero(nat) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_1808,sK105(U_1809))],[f_532_2]) ).

cnf(f_532_4,plain,
    ( U_1809 = hAPP(nat,nat,suc,sK105(U_1809))
    | U_1809 = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

fof(f_533_1,plain,
    ! [Pa,K] :
      ( hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
      | ? [N_2] :
          ( ~ hBOOL(hAPP(nat,bool,Pa,N_2))
          & hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_2))) )
      | ~ hBOOL(hAPP(nat,bool,Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_443_zero__induct]) ).

fof(f_533_2,plain,
    ! [U_1812,U_1811] :
      ( hBOOL(hAPP(nat,bool,U_1812,zero_zero(nat)))
      | ? [U_1810] :
          ( ~ hBOOL(hAPP(nat,bool,U_1812,U_1810))
          & hBOOL(hAPP(nat,bool,U_1812,hAPP(nat,nat,suc,U_1810))) )
      | ~ hBOOL(hAPP(nat,bool,U_1812,U_1811)) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ! [U_1812] :
      ( ! [U_1811] : ~ hBOOL(hAPP(nat,bool,U_1812,U_1811))
      | hBOOL(hAPP(nat,bool,U_1812,zero_zero(nat)))
      | ? [U_1810] :
          ( ~ hBOOL(hAPP(nat,bool,U_1812,U_1810))
          & hBOOL(hAPP(nat,bool,U_1812,hAPP(nat,nat,suc,U_1810))) ) ),
    inference(miniscope,[status(thm)],[f_533_2]) ).

fof(f_533_4,plain,
    ! [U_1812] :
      ( ! [U_1811] : ~ hBOOL(hAPP(nat,bool,U_1812,U_1811))
      | hBOOL(hAPP(nat,bool,U_1812,zero_zero(nat)))
      | ( ~ hBOOL(hAPP(nat,bool,U_1812,sK106(U_1812)))
        & hBOOL(hAPP(nat,bool,U_1812,hAPP(nat,nat,suc,sK106(U_1812)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_1810,sK106(U_1812))],[f_533_3]) ).

cnf(f_533_5,plain,
    ( hBOOL(hAPP(nat,bool,U_1812,hAPP(nat,nat,suc,sK106(U_1812))))
    | hBOOL(hAPP(nat,bool,U_1812,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,U_1812,U_1811)) ),
    inference(clausify,[status(thm)],[f_533_4]) ).

cnf(f_533_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_1812,sK106(U_1812)))
    | hBOOL(hAPP(nat,bool,U_1812,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,U_1812,U_1811)) ),
    inference(clausify,[status(thm)],[f_533_4]) ).

fof(f_534_1,plain,
    ! [Na,Pa] :
      ( hBOOL(hAPP(nat,bool,Pa,Na))
      | ? [N_2] :
          ( ~ hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_2)))
          & hBOOL(hAPP(nat,bool,Pa,N_2)) )
      | ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ),
    inference(fof_nnf,[status(thm)],[fact_444_nat__induct]) ).

fof(f_534_2,plain,
    ! [U_1815,U_1814] :
      ( hBOOL(hAPP(nat,bool,U_1814,U_1815))
      | ? [U_1813] :
          ( ~ hBOOL(hAPP(nat,bool,U_1814,hAPP(nat,nat,suc,U_1813)))
          & hBOOL(hAPP(nat,bool,U_1814,U_1813)) )
      | ~ hBOOL(hAPP(nat,bool,U_1814,zero_zero(nat))) ),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ! [U_1815,U_1814] :
      ( hBOOL(hAPP(nat,bool,U_1814,U_1815))
      | ( ~ hBOOL(hAPP(nat,bool,U_1814,hAPP(nat,nat,suc,sK107(U_1815,U_1814))))
        & hBOOL(hAPP(nat,bool,U_1814,sK107(U_1815,U_1814))) )
      | ~ hBOOL(hAPP(nat,bool,U_1814,zero_zero(nat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_1813,sK107(U_1815,U_1814))],[f_534_2]) ).

cnf(f_534_4,plain,
    ( hBOOL(hAPP(nat,bool,U_1814,sK107(U_1815,U_1814)))
    | hBOOL(hAPP(nat,bool,U_1814,U_1815))
    | ~ hBOOL(hAPP(nat,bool,U_1814,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

cnf(f_534_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_1814,hAPP(nat,nat,suc,sK107(U_1815,U_1814))))
    | hBOOL(hAPP(nat,bool,U_1814,U_1815))
    | ~ hBOOL(hAPP(nat,bool,U_1814,zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

fof(f_535_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2) = ti(X_a,A_2)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_445_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).

fof(f_535_2,plain,
    ! [U_1817] :
      ( ! [U_1816] : hAPP(U_1817,U_1817,hAPP(U_1817,fun(U_1817,U_1817),plus_plus(U_1817),zero_zero(U_1817)),U_1816) = ti(U_1817,U_1816)
      | ~ comm_semiring_1(U_1817) ),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

cnf(f_535_3,plain,
    ( hAPP(U_1817,U_1817,hAPP(U_1817,fun(U_1817,U_1817),plus_plus(U_1817),zero_zero(U_1817)),U_1816) = ti(U_1817,U_1816)
    | ~ comm_semiring_1(U_1817) ),
    inference(clausify,[status(thm)],[f_535_2]) ).

fof(f_536_1,plain,
    ! [X_a] :
      ( ! [A_2,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_446_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).

fof(f_536_2,plain,
    ! [U_1820] :
      ( ! [U_1819,U_1818] : hAPP(U_1820,U_1820,hAPP(U_1820,fun(U_1820,U_1820),plus_plus(U_1820),U_1819),U_1818) = hAPP(U_1820,U_1820,hAPP(U_1820,fun(U_1820,U_1820),plus_plus(U_1820),U_1818),U_1819)
      | ~ comm_semiring_1(U_1820) ),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

cnf(f_536_3,plain,
    ( hAPP(U_1820,U_1820,hAPP(U_1820,fun(U_1820,U_1820),plus_plus(U_1820),U_1819),U_1818) = hAPP(U_1820,U_1820,hAPP(U_1820,fun(U_1820,U_1820),plus_plus(U_1820),U_1818),U_1819)
    | ~ comm_semiring_1(U_1820) ),
    inference(clausify,[status(thm)],[f_536_2]) ).

fof(f_537_1,plain,
    ! [X_a] :
      ( ! [A_2,C_1,D] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),D))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_447_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).

fof(f_537_2,plain,
    ! [U_1824] :
      ( ! [U_1823,U_1822,U_1821] : hAPP(U_1824,U_1824,hAPP(U_1824,fun(U_1824,U_1824),plus_plus(U_1824),U_1823),hAPP(U_1824,U_1824,hAPP(U_1824,fun(U_1824,U_1824),plus_plus(U_1824),U_1822),U_1821)) = hAPP(U_1824,U_1824,hAPP(U_1824,fun(U_1824,U_1824),plus_plus(U_1824),U_1822),hAPP(U_1824,U_1824,hAPP(U_1824,fun(U_1824,U_1824),plus_plus(U_1824),U_1823),U_1821))
      | ~ comm_semiring_1(U_1824) ),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

cnf(f_537_3,plain,
    ( hAPP(U_1824,U_1824,hAPP(U_1824,fun(U_1824,U_1824),plus_plus(U_1824),U_1823),hAPP(U_1824,U_1824,hAPP(U_1824,fun(U_1824,U_1824),plus_plus(U_1824),U_1822),U_1821)) = hAPP(U_1824,U_1824,hAPP(U_1824,fun(U_1824,U_1824),plus_plus(U_1824),U_1822),hAPP(U_1824,U_1824,hAPP(U_1824,fun(U_1824,U_1824),plus_plus(U_1824),U_1823),U_1821))
    | ~ comm_semiring_1(U_1824) ),
    inference(clausify,[status(thm)],[f_537_2]) ).

fof(f_538_1,plain,
    ! [X_a] :
      ( ! [A_2,C_1,D] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),D)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_448_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).

fof(f_538_2,plain,
    ! [U_1828] :
      ( ! [U_1827,U_1826,U_1825] : hAPP(U_1828,U_1828,hAPP(U_1828,fun(U_1828,U_1828),plus_plus(U_1828),U_1827),hAPP(U_1828,U_1828,hAPP(U_1828,fun(U_1828,U_1828),plus_plus(U_1828),U_1826),U_1825)) = hAPP(U_1828,U_1828,hAPP(U_1828,fun(U_1828,U_1828),plus_plus(U_1828),hAPP(U_1828,U_1828,hAPP(U_1828,fun(U_1828,U_1828),plus_plus(U_1828),U_1827),U_1826)),U_1825)
      | ~ comm_semiring_1(U_1828) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

cnf(f_538_3,plain,
    ( hAPP(U_1828,U_1828,hAPP(U_1828,fun(U_1828,U_1828),plus_plus(U_1828),U_1827),hAPP(U_1828,U_1828,hAPP(U_1828,fun(U_1828,U_1828),plus_plus(U_1828),U_1826),U_1825)) = hAPP(U_1828,U_1828,hAPP(U_1828,fun(U_1828,U_1828),plus_plus(U_1828),hAPP(U_1828,U_1828,hAPP(U_1828,fun(U_1828,U_1828),plus_plus(U_1828),U_1827),U_1826)),U_1825)
    | ~ comm_semiring_1(U_1828) ),
    inference(clausify,[status(thm)],[f_538_2]) ).

fof(f_539_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_449_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).

fof(f_539_2,plain,
    ! [U_1832] :
      ( ! [U_1831,U_1830,U_1829] : hAPP(U_1832,U_1832,hAPP(U_1832,fun(U_1832,U_1832),plus_plus(U_1832),hAPP(U_1832,U_1832,hAPP(U_1832,fun(U_1832,U_1832),plus_plus(U_1832),U_1831),U_1830)),U_1829) = hAPP(U_1832,U_1832,hAPP(U_1832,fun(U_1832,U_1832),plus_plus(U_1832),U_1831),hAPP(U_1832,U_1832,hAPP(U_1832,fun(U_1832,U_1832),plus_plus(U_1832),U_1830),U_1829))
      | ~ comm_semiring_1(U_1832) ),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

cnf(f_539_3,plain,
    ( hAPP(U_1832,U_1832,hAPP(U_1832,fun(U_1832,U_1832),plus_plus(U_1832),hAPP(U_1832,U_1832,hAPP(U_1832,fun(U_1832,U_1832),plus_plus(U_1832),U_1831),U_1830)),U_1829) = hAPP(U_1832,U_1832,hAPP(U_1832,fun(U_1832,U_1832),plus_plus(U_1832),U_1831),hAPP(U_1832,U_1832,hAPP(U_1832,fun(U_1832,U_1832),plus_plus(U_1832),U_1830),U_1829))
    | ~ comm_semiring_1(U_1832) ),
    inference(clausify,[status(thm)],[f_539_2]) ).

fof(f_540_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),B_1)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_450_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).

fof(f_540_2,plain,
    ! [U_1836] :
      ( ! [U_1835,U_1834,U_1833] : hAPP(U_1836,U_1836,hAPP(U_1836,fun(U_1836,U_1836),plus_plus(U_1836),hAPP(U_1836,U_1836,hAPP(U_1836,fun(U_1836,U_1836),plus_plus(U_1836),U_1835),U_1834)),U_1833) = hAPP(U_1836,U_1836,hAPP(U_1836,fun(U_1836,U_1836),plus_plus(U_1836),hAPP(U_1836,U_1836,hAPP(U_1836,fun(U_1836,U_1836),plus_plus(U_1836),U_1835),U_1833)),U_1834)
      | ~ comm_semiring_1(U_1836) ),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

cnf(f_540_3,plain,
    ( hAPP(U_1836,U_1836,hAPP(U_1836,fun(U_1836,U_1836),plus_plus(U_1836),hAPP(U_1836,U_1836,hAPP(U_1836,fun(U_1836,U_1836),plus_plus(U_1836),U_1835),U_1834)),U_1833) = hAPP(U_1836,U_1836,hAPP(U_1836,fun(U_1836,U_1836),plus_plus(U_1836),hAPP(U_1836,U_1836,hAPP(U_1836,fun(U_1836,U_1836),plus_plus(U_1836),U_1835),U_1833)),U_1834)
    | ~ comm_semiring_1(U_1836) ),
    inference(clausify,[status(thm)],[f_540_2]) ).

fof(f_541_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1,D] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_451_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).

fof(f_541_2,plain,
    ! [U_1841] :
      ( ! [U_1840,U_1839,U_1838,U_1837] : hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),U_1840),U_1839)),hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),U_1838),U_1837)) = hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),U_1840),U_1838)),hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),U_1839),U_1837))
      | ~ comm_semiring_1(U_1841) ),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

cnf(f_541_3,plain,
    ( hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),U_1840),U_1839)),hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),U_1838),U_1837)) = hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),U_1840),U_1838)),hAPP(U_1841,U_1841,hAPP(U_1841,fun(U_1841,U_1841),plus_plus(U_1841),U_1839),U_1837))
    | ~ comm_semiring_1(U_1841) ),
    inference(clausify,[status(thm)],[f_541_2]) ).

fof(f_542_1,plain,
    ! [X_a] :
      ( ! [Ba,Aa] :
          ( ( ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)
            | ti(X_a,Aa) != zero_zero(X_a) )
          & ( ti(X_a,Aa) = zero_zero(X_a)
            | ti(X_a,Ba) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) ) )
      | ~ semiri456707255roduct(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_452_add__0__iff]) ).

fof(f_542_2,plain,
    ! [U_1844] :
      ( ! [U_1843,U_1842] :
          ( ( ti(U_1844,U_1843) = hAPP(U_1844,U_1844,hAPP(U_1844,fun(U_1844,U_1844),plus_plus(U_1844),U_1843),U_1842)
            | ti(U_1844,U_1842) != zero_zero(U_1844) )
          & ( ti(U_1844,U_1842) = zero_zero(U_1844)
            | ti(U_1844,U_1843) != hAPP(U_1844,U_1844,hAPP(U_1844,fun(U_1844,U_1844),plus_plus(U_1844),U_1843),U_1842) ) )
      | ~ semiri456707255roduct(U_1844) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ! [U_1844] :
      ( ( ! [U_1848,U_1846] :
            ( ti(U_1844,U_1848) = hAPP(U_1844,U_1844,hAPP(U_1844,fun(U_1844,U_1844),plus_plus(U_1844),U_1848),U_1846)
            | ti(U_1844,U_1846) != zero_zero(U_1844) )
        & ! [U_1847,U_1845] :
            ( ti(U_1844,U_1845) = zero_zero(U_1844)
            | ti(U_1844,U_1847) != hAPP(U_1844,U_1844,hAPP(U_1844,fun(U_1844,U_1844),plus_plus(U_1844),U_1847),U_1845) ) )
      | ~ semiri456707255roduct(U_1844) ),
    inference(miniscope,[status(thm)],[f_542_2]) ).

cnf(f_542_4,plain,
    ( ti(U_1844,U_1845) = zero_zero(U_1844)
    | ti(U_1844,U_1847) != hAPP(U_1844,U_1844,hAPP(U_1844,fun(U_1844,U_1844),plus_plus(U_1844),U_1847),U_1845)
    | ~ semiri456707255roduct(U_1844) ),
    inference(clausify,[status(thm)],[f_542_3]) ).

cnf(f_542_5,plain,
    ( ti(U_1844,U_1848) = hAPP(U_1844,U_1844,hAPP(U_1844,fun(U_1844,U_1844),plus_plus(U_1844),U_1848),U_1846)
    | ti(U_1844,U_1846) != zero_zero(U_1844)
    | ~ semiri456707255roduct(U_1844) ),
    inference(clausify,[status(thm)],[f_542_3]) ).

fof(f_543_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a)) = ti(X_a,A_2)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_453_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).

fof(f_543_2,plain,
    ! [U_1850] :
      ( ! [U_1849] : hAPP(U_1850,U_1850,hAPP(U_1850,fun(U_1850,U_1850),plus_plus(U_1850),U_1849),zero_zero(U_1850)) = ti(U_1850,U_1849)
      | ~ comm_semiring_1(U_1850) ),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

cnf(f_543_3,plain,
    ( hAPP(U_1850,U_1850,hAPP(U_1850,fun(U_1850,U_1850),plus_plus(U_1850),U_1849),zero_zero(U_1850)) = ti(U_1850,U_1849)
    | ~ comm_semiring_1(U_1850) ),
    inference(clausify,[status(thm)],[f_543_2]) ).

fof(f_544_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
          | ? [E_1] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E_1)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E_1)) ) )
      | ~ linordered_field(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_454_field__le__epsilon]) ).

fof(f_544_2,plain,
    ! [U_1854] :
      ( ! [U_1853,U_1852] :
          ( hBOOL(hAPP(U_1854,bool,hAPP(U_1854,fun(U_1854,bool),ord_less_eq(U_1854),U_1853),U_1852))
          | ? [U_1851] :
              ( ~ hBOOL(hAPP(U_1854,bool,hAPP(U_1854,fun(U_1854,bool),ord_less_eq(U_1854),U_1853),hAPP(U_1854,U_1854,hAPP(U_1854,fun(U_1854,U_1854),plus_plus(U_1854),U_1852),U_1851)))
              & hBOOL(hAPP(U_1854,bool,hAPP(U_1854,fun(U_1854,bool),ord_less(U_1854),zero_zero(U_1854)),U_1851)) ) )
      | ~ linordered_field(U_1854) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ! [U_1854] :
      ( ! [U_1853,U_1852] :
          ( hBOOL(hAPP(U_1854,bool,hAPP(U_1854,fun(U_1854,bool),ord_less_eq(U_1854),U_1853),U_1852))
          | ( ~ hBOOL(hAPP(U_1854,bool,hAPP(U_1854,fun(U_1854,bool),ord_less_eq(U_1854),U_1853),hAPP(U_1854,U_1854,hAPP(U_1854,fun(U_1854,U_1854),plus_plus(U_1854),U_1852),sK108(U_1854,U_1853,U_1852))))
            & hBOOL(hAPP(U_1854,bool,hAPP(U_1854,fun(U_1854,bool),ord_less(U_1854),zero_zero(U_1854)),sK108(U_1854,U_1853,U_1852))) ) )
      | ~ linordered_field(U_1854) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_1851,sK108(U_1854,U_1853,U_1852))],[f_544_2]) ).

cnf(f_544_4,plain,
    ( hBOOL(hAPP(U_1854,bool,hAPP(U_1854,fun(U_1854,bool),ord_less(U_1854),zero_zero(U_1854)),sK108(U_1854,U_1853,U_1852)))
    | hBOOL(hAPP(U_1854,bool,hAPP(U_1854,fun(U_1854,bool),ord_less_eq(U_1854),U_1853),U_1852))
    | ~ linordered_field(U_1854) ),
    inference(clausify,[status(thm)],[f_544_3]) ).

cnf(f_544_5,plain,
    ( ~ hBOOL(hAPP(U_1854,bool,hAPP(U_1854,fun(U_1854,bool),ord_less_eq(U_1854),U_1853),hAPP(U_1854,U_1854,hAPP(U_1854,fun(U_1854,U_1854),plus_plus(U_1854),U_1852),sK108(U_1854,U_1853,U_1852))))
    | hBOOL(hAPP(U_1854,bool,hAPP(U_1854,fun(U_1854,bool),ord_less_eq(U_1854),U_1853),U_1852))
    | ~ linordered_field(U_1854) ),
    inference(clausify,[status(thm)],[f_544_3]) ).

fof(f_545_1,plain,
    ! [X_a,A_1] :
      ( ( hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = zero_zero(nat)
        | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      & ( hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_a,bool),nat,hAPP(nat,fun(fun(X_a,bool),nat),hAPP(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat))),finite_fold_image(nat,X_a),plus_plus(nat)),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),zero_zero(nat)),A_1)
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_455_card__def]) ).

fof(f_545_2,plain,
    ! [U_1856,U_1855] :
      ( ( hAPP(fun(U_1856,bool),nat,finite_card(U_1856),U_1855) = zero_zero(nat)
        | hBOOL(hAPP(fun(U_1856,bool),bool,finite_finite_1(U_1856),U_1855)) )
      & ( hAPP(fun(U_1856,bool),nat,finite_card(U_1856),U_1855) = hAPP(fun(U_1856,bool),nat,hAPP(nat,fun(fun(U_1856,bool),nat),hAPP(fun(U_1856,nat),fun(nat,fun(fun(U_1856,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_1856,nat),fun(nat,fun(fun(U_1856,bool),nat))),finite_fold_image(nat,U_1856),plus_plus(nat)),hAPP(nat,fun(U_1856,nat),combk(nat,U_1856),one_one(nat))),zero_zero(nat)),U_1855)
        | ~ hBOOL(hAPP(fun(U_1856,bool),bool,finite_finite_1(U_1856),U_1855)) ) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ( ! [U_1860,U_1858] :
        ( hAPP(fun(U_1860,bool),nat,finite_card(U_1860),U_1858) = zero_zero(nat)
        | hBOOL(hAPP(fun(U_1860,bool),bool,finite_finite_1(U_1860),U_1858)) )
    & ! [U_1859,U_1857] :
        ( hAPP(fun(U_1859,bool),nat,finite_card(U_1859),U_1857) = hAPP(fun(U_1859,bool),nat,hAPP(nat,fun(fun(U_1859,bool),nat),hAPP(fun(U_1859,nat),fun(nat,fun(fun(U_1859,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_1859,nat),fun(nat,fun(fun(U_1859,bool),nat))),finite_fold_image(nat,U_1859),plus_plus(nat)),hAPP(nat,fun(U_1859,nat),combk(nat,U_1859),one_one(nat))),zero_zero(nat)),U_1857)
        | ~ hBOOL(hAPP(fun(U_1859,bool),bool,finite_finite_1(U_1859),U_1857)) ) ),
    inference(miniscope,[status(thm)],[f_545_2]) ).

cnf(f_545_4,plain,
    ( hAPP(fun(U_1859,bool),nat,finite_card(U_1859),U_1857) = hAPP(fun(U_1859,bool),nat,hAPP(nat,fun(fun(U_1859,bool),nat),hAPP(fun(U_1859,nat),fun(nat,fun(fun(U_1859,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_1859,nat),fun(nat,fun(fun(U_1859,bool),nat))),finite_fold_image(nat,U_1859),plus_plus(nat)),hAPP(nat,fun(U_1859,nat),combk(nat,U_1859),one_one(nat))),zero_zero(nat)),U_1857)
    | ~ hBOOL(hAPP(fun(U_1859,bool),bool,finite_finite_1(U_1859),U_1857)) ),
    inference(clausify,[status(thm)],[f_545_3]) ).

cnf(f_545_5,plain,
    ( hAPP(fun(U_1860,bool),nat,finite_card(U_1860),U_1858) = zero_zero(nat)
    | hBOOL(hAPP(fun(U_1860,bool),bool,finite_finite_1(U_1860),U_1858)) ),
    inference(clausify,[status(thm)],[f_545_3]) ).

fof(f_546_1,plain,
    ! [X_a,A_1] :
      ( hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_a,bool),nat,hAPP(nat,fun(fun(X_a,bool),nat),hAPP(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat))),finite_fold_image(nat,X_a),plus_plus(nat)),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),zero_zero(nat)),A_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_456_card_Oeq__fold__g]) ).

fof(f_546_2,plain,
    ! [U_1862,U_1861] :
      ( hAPP(fun(U_1862,bool),nat,finite_card(U_1862),U_1861) = hAPP(fun(U_1862,bool),nat,hAPP(nat,fun(fun(U_1862,bool),nat),hAPP(fun(U_1862,nat),fun(nat,fun(fun(U_1862,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_1862,nat),fun(nat,fun(fun(U_1862,bool),nat))),finite_fold_image(nat,U_1862),plus_plus(nat)),hAPP(nat,fun(U_1862,nat),combk(nat,U_1862),one_one(nat))),zero_zero(nat)),U_1861)
      | ~ hBOOL(hAPP(fun(U_1862,bool),bool,finite_finite_1(U_1862),U_1861)) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

cnf(f_546_3,plain,
    ( hAPP(fun(U_1862,bool),nat,finite_card(U_1862),U_1861) = hAPP(fun(U_1862,bool),nat,hAPP(nat,fun(fun(U_1862,bool),nat),hAPP(fun(U_1862,nat),fun(nat,fun(fun(U_1862,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_1862,nat),fun(nat,fun(fun(U_1862,bool),nat))),finite_fold_image(nat,U_1862),plus_plus(nat)),hAPP(nat,fun(U_1862,nat),combk(nat,U_1862),one_one(nat))),zero_zero(nat)),U_1861)
    | ~ hBOOL(hAPP(fun(U_1862,bool),bool,finite_finite_1(U_1862),U_1861)) ),
    inference(clausify,[status(thm)],[f_546_2]) ).

fof(f_547_1,plain,
    hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(fof_nnf,[status(thm)],[fact_457_surjh]) ).

cnf(f_547_2,plain,
    hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(clausify,[status(thm)],[f_547_1]) ).

fof(f_548_1,plain,
    ! [X_a,X_b,A_1,Ba,F,X_2] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
      | ti(X_a,Ba) != hAPP(X_b,X_a,F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_458_image__eqI]) ).

fof(f_548_2,plain,
    ! [U_1868,U_1867,U_1866,U_1865,U_1864,U_1863] :
      ( hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(U_1868,fun(fun(U_1868,bool),bool),member(U_1868),U_1865),hAPP(fun(U_1867,bool),fun(U_1868,bool),hAPP(fun(U_1867,U_1868),fun(fun(U_1867,bool),fun(U_1868,bool)),image(U_1867,U_1868),U_1864),U_1866)))
      | ~ hBOOL(hAPP(fun(U_1867,bool),bool,hAPP(U_1867,fun(fun(U_1867,bool),bool),member(U_1867),U_1863),U_1866))
      | ti(U_1868,U_1865) != hAPP(U_1867,U_1868,U_1864,U_1863) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

cnf(f_548_3,plain,
    ( hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(U_1868,fun(fun(U_1868,bool),bool),member(U_1868),U_1865),hAPP(fun(U_1867,bool),fun(U_1868,bool),hAPP(fun(U_1867,U_1868),fun(fun(U_1867,bool),fun(U_1868,bool)),image(U_1867,U_1868),U_1864),U_1866)))
    | ~ hBOOL(hAPP(fun(U_1867,bool),bool,hAPP(U_1867,fun(fun(U_1867,bool),bool),member(U_1867),U_1863),U_1866))
    | ti(U_1868,U_1865) != hAPP(U_1867,U_1868,U_1864,U_1863) ),
    inference(clausify,[status(thm)],[f_548_2]) ).

fof(f_549_1,plain,
    ! [X_b,X_a,Ha,Fa] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),Ha),Fa)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_459_finite__imageI]) ).

fof(f_549_2,plain,
    ! [U_1872,U_1871,U_1870,U_1869] :
      ( hBOOL(hAPP(fun(U_1872,bool),bool,finite_finite_1(U_1872),hAPP(fun(U_1871,bool),fun(U_1872,bool),hAPP(fun(U_1871,U_1872),fun(fun(U_1871,bool),fun(U_1872,bool)),image(U_1871,U_1872),U_1870),U_1869)))
      | ~ hBOOL(hAPP(fun(U_1871,bool),bool,finite_finite_1(U_1871),U_1869)) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

cnf(f_549_3,plain,
    ( hBOOL(hAPP(fun(U_1872,bool),bool,finite_finite_1(U_1872),hAPP(fun(U_1871,bool),fun(U_1872,bool),hAPP(fun(U_1871,U_1872),fun(fun(U_1871,bool),fun(U_1872,bool)),image(U_1871,U_1872),U_1870),U_1869)))
    | ~ hBOOL(hAPP(fun(U_1871,bool),bool,finite_finite_1(U_1871),U_1869)) ),
    inference(clausify,[status(thm)],[f_549_2]) ).

fof(f_550_1,plain,
    ! [L,U] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),U))),
    inference(fof_nnf,[status(thm)],[fact_460_finite__atLeastLessThan]) ).

fof(f_550_2,plain,
    ! [U_1874,U_1873] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_1874),U_1873))),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

cnf(f_550_3,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_1874),U_1873))),
    inference(clausify,[status(thm)],[f_550_2]) ).

fof(f_551_1,plain,
    ? [H] :
      ( hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),H),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))
      & hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),H),top_top(fun(arrow_1998540521e_indi,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_461__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123]) ).

fof(f_551_2,plain,
    ? [U_1875] :
      ( hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),U_1875),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))
      & hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),U_1875),top_top(fun(arrow_1998540521e_indi,bool)))) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

fof(f_551_3,plain,
    ( hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),sK109),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))
    & hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),sK109),top_top(fun(arrow_1998540521e_indi,bool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_1875,sK109)],[f_551_2]) ).

cnf(f_551_4,plain,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),sK109),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(clausify,[status(thm)],[f_551_3]) ).

cnf(f_551_5,plain,
    hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),sK109),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(clausify,[status(thm)],[f_551_3]) ).

fof(f_552_1,plain,
    ! [X_b,X_a,F,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_462_image__mono]) ).

fof(f_552_2,plain,
    ! [U_1880,U_1879,U_1878,U_1877,U_1876] :
      ( hBOOL(hAPP(fun(U_1880,bool),bool,hAPP(fun(U_1880,bool),fun(fun(U_1880,bool),bool),ord_less_eq(fun(U_1880,bool)),hAPP(fun(U_1879,bool),fun(U_1880,bool),hAPP(fun(U_1879,U_1880),fun(fun(U_1879,bool),fun(U_1880,bool)),image(U_1879,U_1880),U_1878),U_1877)),hAPP(fun(U_1879,bool),fun(U_1880,bool),hAPP(fun(U_1879,U_1880),fun(fun(U_1879,bool),fun(U_1880,bool)),image(U_1879,U_1880),U_1878),U_1876)))
      | ~ hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(fun(U_1879,bool),fun(fun(U_1879,bool),bool),ord_less_eq(fun(U_1879,bool)),U_1877),U_1876)) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

cnf(f_552_3,plain,
    ( hBOOL(hAPP(fun(U_1880,bool),bool,hAPP(fun(U_1880,bool),fun(fun(U_1880,bool),bool),ord_less_eq(fun(U_1880,bool)),hAPP(fun(U_1879,bool),fun(U_1880,bool),hAPP(fun(U_1879,U_1880),fun(fun(U_1879,bool),fun(U_1880,bool)),image(U_1879,U_1880),U_1878),U_1877)),hAPP(fun(U_1879,bool),fun(U_1880,bool),hAPP(fun(U_1879,U_1880),fun(fun(U_1879,bool),fun(U_1880,bool)),image(U_1879,U_1880),U_1878),U_1876)))
    | ~ hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(fun(U_1879,bool),fun(fun(U_1879,bool),bool),ord_less_eq(fun(U_1879,bool)),U_1877),U_1876)) ),
    inference(clausify,[status(thm)],[f_552_2]) ).

fof(f_553_1,plain,
    ! [X_a,X_b,B,F,A_1] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
        | ! [AA] :
            ( ti(fun(X_a,bool),B) != hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA)
            | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_1)) ) )
      & ( ? [AA] :
            ( ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA)
            & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_1)) )
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_463_subset__image__iff]) ).

fof(f_553_2,plain,
    ! [U_1887,U_1886,U_1885,U_1884,U_1883] :
      ( ( hBOOL(hAPP(fun(U_1887,bool),bool,hAPP(fun(U_1887,bool),fun(fun(U_1887,bool),bool),ord_less_eq(fun(U_1887,bool)),U_1885),hAPP(fun(U_1886,bool),fun(U_1887,bool),hAPP(fun(U_1886,U_1887),fun(fun(U_1886,bool),fun(U_1887,bool)),image(U_1886,U_1887),U_1884),U_1883)))
        | ! [U_1882] :
            ( ti(fun(U_1887,bool),U_1885) != hAPP(fun(U_1886,bool),fun(U_1887,bool),hAPP(fun(U_1886,U_1887),fun(fun(U_1886,bool),fun(U_1887,bool)),image(U_1886,U_1887),U_1884),U_1882)
            | ~ hBOOL(hAPP(fun(U_1886,bool),bool,hAPP(fun(U_1886,bool),fun(fun(U_1886,bool),bool),ord_less_eq(fun(U_1886,bool)),U_1882),U_1883)) ) )
      & ( ? [U_1881] :
            ( ti(fun(U_1887,bool),U_1885) = hAPP(fun(U_1886,bool),fun(U_1887,bool),hAPP(fun(U_1886,U_1887),fun(fun(U_1886,bool),fun(U_1887,bool)),image(U_1886,U_1887),U_1884),U_1881)
            & hBOOL(hAPP(fun(U_1886,bool),bool,hAPP(fun(U_1886,bool),fun(fun(U_1886,bool),bool),ord_less_eq(fun(U_1886,bool)),U_1881),U_1883)) )
        | ~ hBOOL(hAPP(fun(U_1887,bool),bool,hAPP(fun(U_1887,bool),fun(fun(U_1887,bool),bool),ord_less_eq(fun(U_1887,bool)),U_1885),hAPP(fun(U_1886,bool),fun(U_1887,bool),hAPP(fun(U_1886,U_1887),fun(fun(U_1886,bool),fun(U_1887,bool)),image(U_1886,U_1887),U_1884),U_1883))) ) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

fof(f_553_3,plain,
    ( ! [U_1897,U_1895,U_1893,U_1891,U_1889] :
        ( hBOOL(hAPP(fun(U_1897,bool),bool,hAPP(fun(U_1897,bool),fun(fun(U_1897,bool),bool),ord_less_eq(fun(U_1897,bool)),U_1893),hAPP(fun(U_1895,bool),fun(U_1897,bool),hAPP(fun(U_1895,U_1897),fun(fun(U_1895,bool),fun(U_1897,bool)),image(U_1895,U_1897),U_1891),U_1889)))
        | ! [U_1882] :
            ( ti(fun(U_1897,bool),U_1893) != hAPP(fun(U_1895,bool),fun(U_1897,bool),hAPP(fun(U_1895,U_1897),fun(fun(U_1895,bool),fun(U_1897,bool)),image(U_1895,U_1897),U_1891),U_1882)
            | ~ hBOOL(hAPP(fun(U_1895,bool),bool,hAPP(fun(U_1895,bool),fun(fun(U_1895,bool),bool),ord_less_eq(fun(U_1895,bool)),U_1882),U_1889)) ) )
    & ! [U_1896,U_1894,U_1892,U_1890,U_1888] :
        ( ? [U_1881] :
            ( ti(fun(U_1896,bool),U_1892) = hAPP(fun(U_1894,bool),fun(U_1896,bool),hAPP(fun(U_1894,U_1896),fun(fun(U_1894,bool),fun(U_1896,bool)),image(U_1894,U_1896),U_1890),U_1881)
            & hBOOL(hAPP(fun(U_1894,bool),bool,hAPP(fun(U_1894,bool),fun(fun(U_1894,bool),bool),ord_less_eq(fun(U_1894,bool)),U_1881),U_1888)) )
        | ~ hBOOL(hAPP(fun(U_1896,bool),bool,hAPP(fun(U_1896,bool),fun(fun(U_1896,bool),bool),ord_less_eq(fun(U_1896,bool)),U_1892),hAPP(fun(U_1894,bool),fun(U_1896,bool),hAPP(fun(U_1894,U_1896),fun(fun(U_1894,bool),fun(U_1896,bool)),image(U_1894,U_1896),U_1890),U_1888))) ) ),
    inference(miniscope,[status(thm)],[f_553_2]) ).

fof(f_553_4,plain,
    ( ! [U_1897,U_1895,U_1893,U_1891,U_1889] :
        ( hBOOL(hAPP(fun(U_1897,bool),bool,hAPP(fun(U_1897,bool),fun(fun(U_1897,bool),bool),ord_less_eq(fun(U_1897,bool)),U_1893),hAPP(fun(U_1895,bool),fun(U_1897,bool),hAPP(fun(U_1895,U_1897),fun(fun(U_1895,bool),fun(U_1897,bool)),image(U_1895,U_1897),U_1891),U_1889)))
        | ! [U_1882] :
            ( ti(fun(U_1897,bool),U_1893) != hAPP(fun(U_1895,bool),fun(U_1897,bool),hAPP(fun(U_1895,U_1897),fun(fun(U_1895,bool),fun(U_1897,bool)),image(U_1895,U_1897),U_1891),U_1882)
            | ~ hBOOL(hAPP(fun(U_1895,bool),bool,hAPP(fun(U_1895,bool),fun(fun(U_1895,bool),bool),ord_less_eq(fun(U_1895,bool)),U_1882),U_1889)) ) )
    & ! [U_1896,U_1894,U_1892,U_1890,U_1888] :
        ( ( ti(fun(U_1896,bool),U_1892) = hAPP(fun(U_1894,bool),fun(U_1896,bool),hAPP(fun(U_1894,U_1896),fun(fun(U_1894,bool),fun(U_1896,bool)),image(U_1894,U_1896),U_1890),sK110(U_1896,U_1894,U_1892,U_1890,U_1888))
          & hBOOL(hAPP(fun(U_1894,bool),bool,hAPP(fun(U_1894,bool),fun(fun(U_1894,bool),bool),ord_less_eq(fun(U_1894,bool)),sK110(U_1896,U_1894,U_1892,U_1890,U_1888)),U_1888)) )
        | ~ hBOOL(hAPP(fun(U_1896,bool),bool,hAPP(fun(U_1896,bool),fun(fun(U_1896,bool),bool),ord_less_eq(fun(U_1896,bool)),U_1892),hAPP(fun(U_1894,bool),fun(U_1896,bool),hAPP(fun(U_1894,U_1896),fun(fun(U_1894,bool),fun(U_1896,bool)),image(U_1894,U_1896),U_1890),U_1888))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_1881,sK110(U_1896,U_1894,U_1892,U_1890,U_1888))],[f_553_3]) ).

cnf(f_553_5,plain,
    ( hBOOL(hAPP(fun(U_1894,bool),bool,hAPP(fun(U_1894,bool),fun(fun(U_1894,bool),bool),ord_less_eq(fun(U_1894,bool)),sK110(U_1896,U_1894,U_1892,U_1890,U_1888)),U_1888))
    | ~ hBOOL(hAPP(fun(U_1896,bool),bool,hAPP(fun(U_1896,bool),fun(fun(U_1896,bool),bool),ord_less_eq(fun(U_1896,bool)),U_1892),hAPP(fun(U_1894,bool),fun(U_1896,bool),hAPP(fun(U_1894,U_1896),fun(fun(U_1894,bool),fun(U_1896,bool)),image(U_1894,U_1896),U_1890),U_1888))) ),
    inference(clausify,[status(thm)],[f_553_4]) ).

cnf(f_553_6,plain,
    ( ti(fun(U_1896,bool),U_1892) = hAPP(fun(U_1894,bool),fun(U_1896,bool),hAPP(fun(U_1894,U_1896),fun(fun(U_1894,bool),fun(U_1896,bool)),image(U_1894,U_1896),U_1890),sK110(U_1896,U_1894,U_1892,U_1890,U_1888))
    | ~ hBOOL(hAPP(fun(U_1896,bool),bool,hAPP(fun(U_1896,bool),fun(fun(U_1896,bool),bool),ord_less_eq(fun(U_1896,bool)),U_1892),hAPP(fun(U_1894,bool),fun(U_1896,bool),hAPP(fun(U_1894,U_1896),fun(fun(U_1894,bool),fun(U_1896,bool)),image(U_1894,U_1896),U_1890),U_1888))) ),
    inference(clausify,[status(thm)],[f_553_4]) ).

cnf(f_553_7,plain,
    ( hBOOL(hAPP(fun(U_1897,bool),bool,hAPP(fun(U_1897,bool),fun(fun(U_1897,bool),bool),ord_less_eq(fun(U_1897,bool)),U_1893),hAPP(fun(U_1895,bool),fun(U_1897,bool),hAPP(fun(U_1895,U_1897),fun(fun(U_1895,bool),fun(U_1897,bool)),image(U_1895,U_1897),U_1891),U_1889)))
    | ti(fun(U_1897,bool),U_1893) != hAPP(fun(U_1895,bool),fun(U_1897,bool),hAPP(fun(U_1895,U_1897),fun(fun(U_1895,bool),fun(U_1897,bool)),image(U_1895,U_1897),U_1891),U_1882)
    | ~ hBOOL(hAPP(fun(U_1895,bool),bool,hAPP(fun(U_1895,bool),fun(fun(U_1895,bool),bool),ord_less_eq(fun(U_1895,bool)),U_1882),U_1889)) ),
    inference(clausify,[status(thm)],[f_553_4]) ).

fof(f_554_1,plain,
    ! [X_a,X_b,F,X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))))),
    inference(fof_nnf,[status(thm)],[fact_464_rangeI]) ).

fof(f_554_2,plain,
    ! [U_1901,U_1900,U_1899,U_1898] : hBOOL(hAPP(fun(U_1901,bool),bool,hAPP(U_1901,fun(fun(U_1901,bool),bool),member(U_1901),hAPP(U_1900,U_1901,U_1899,U_1898)),hAPP(fun(U_1900,bool),fun(U_1901,bool),hAPP(fun(U_1900,U_1901),fun(fun(U_1900,bool),fun(U_1901,bool)),image(U_1900,U_1901),U_1899),top_top(fun(U_1900,bool))))),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

cnf(f_554_3,plain,
    hBOOL(hAPP(fun(U_1901,bool),bool,hAPP(U_1901,fun(fun(U_1901,bool),bool),member(U_1901),hAPP(U_1900,U_1901,U_1899,U_1898)),hAPP(fun(U_1900,bool),fun(U_1901,bool),hAPP(fun(U_1900,U_1901),fun(fun(U_1900,bool),fun(U_1901,bool)),image(U_1900,U_1901),U_1899),top_top(fun(U_1900,bool))))),
    inference(clausify,[status(thm)],[f_554_2]) ).

fof(f_555_1,plain,
    ! [X_a,X_b,Ba,F,X_2] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool)))))
      | ti(X_a,Ba) != hAPP(X_b,X_a,F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_465_range__eqI]) ).

fof(f_555_2,plain,
    ! [U_1906,U_1905,U_1904,U_1903,U_1902] :
      ( hBOOL(hAPP(fun(U_1906,bool),bool,hAPP(U_1906,fun(fun(U_1906,bool),bool),member(U_1906),U_1904),hAPP(fun(U_1905,bool),fun(U_1906,bool),hAPP(fun(U_1905,U_1906),fun(fun(U_1905,bool),fun(U_1906,bool)),image(U_1905,U_1906),U_1903),top_top(fun(U_1905,bool)))))
      | ti(U_1906,U_1904) != hAPP(U_1905,U_1906,U_1903,U_1902) ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ! [U_1906,U_1905,U_1904,U_1903] :
      ( ! [U_1902] : ti(U_1906,U_1904) != hAPP(U_1905,U_1906,U_1903,U_1902)
      | hBOOL(hAPP(fun(U_1906,bool),bool,hAPP(U_1906,fun(fun(U_1906,bool),bool),member(U_1906),U_1904),hAPP(fun(U_1905,bool),fun(U_1906,bool),hAPP(fun(U_1905,U_1906),fun(fun(U_1905,bool),fun(U_1906,bool)),image(U_1905,U_1906),U_1903),top_top(fun(U_1905,bool))))) ),
    inference(miniscope,[status(thm)],[f_555_2]) ).

cnf(f_555_4,plain,
    ( ti(U_1906,U_1904) != hAPP(U_1905,U_1906,U_1903,U_1902)
    | hBOOL(hAPP(fun(U_1906,bool),bool,hAPP(U_1906,fun(fun(U_1906,bool),bool),member(U_1906),U_1904),hAPP(fun(U_1905,bool),fun(U_1906,bool),hAPP(fun(U_1905,U_1906),fun(fun(U_1905,bool),fun(U_1906,bool)),image(U_1905,U_1906),U_1903),top_top(fun(U_1905,bool))))) ),
    inference(clausify,[status(thm)],[f_555_3]) ).

fof(f_556_1,plain,
    ! [X_a,Y_3] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_3) = ti(fun(X_a,bool),Y_3),
    inference(fof_nnf,[status(thm)],[fact_466_image__ident]) ).

fof(f_556_2,plain,
    ! [U_1908,U_1907] : hAPP(fun(U_1908,bool),fun(U_1908,bool),hAPP(fun(U_1908,U_1908),fun(fun(U_1908,bool),fun(U_1908,bool)),image(U_1908,U_1908),combi(U_1908)),U_1907) = ti(fun(U_1908,bool),U_1907),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

cnf(f_556_3,plain,
    hAPP(fun(U_1908,bool),fun(U_1908,bool),hAPP(fun(U_1908,U_1908),fun(fun(U_1908,bool),fun(U_1908,bool)),image(U_1908,U_1908),combi(U_1908)),U_1907) = ti(fun(U_1908,bool),U_1907),
    inference(clausify,[status(thm)],[f_556_2]) ).

fof(f_557_1,plain,
    ! [X_b,X_a,X_c,F,G,A_1] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),G),A_1)) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G)),A_1),
    inference(fof_nnf,[status(thm)],[fact_467_image__image]) ).

fof(f_557_2,plain,
    ! [U_1914,U_1913,U_1912,U_1911,U_1910,U_1909] : hAPP(fun(U_1914,bool),fun(U_1913,bool),hAPP(fun(U_1914,U_1913),fun(fun(U_1914,bool),fun(U_1913,bool)),image(U_1914,U_1913),U_1911),hAPP(fun(U_1912,bool),fun(U_1914,bool),hAPP(fun(U_1912,U_1914),fun(fun(U_1912,bool),fun(U_1914,bool)),image(U_1912,U_1914),U_1910),U_1909)) = hAPP(fun(U_1912,bool),fun(U_1913,bool),hAPP(fun(U_1912,U_1913),fun(fun(U_1912,bool),fun(U_1913,bool)),image(U_1912,U_1913),hAPP(fun(U_1912,U_1914),fun(U_1912,U_1913),hAPP(fun(U_1914,U_1913),fun(fun(U_1912,U_1914),fun(U_1912,U_1913)),combb(U_1914,U_1913,U_1912),U_1911),U_1910)),U_1909),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

cnf(f_557_3,plain,
    hAPP(fun(U_1914,bool),fun(U_1913,bool),hAPP(fun(U_1914,U_1913),fun(fun(U_1914,bool),fun(U_1913,bool)),image(U_1914,U_1913),U_1911),hAPP(fun(U_1912,bool),fun(U_1914,bool),hAPP(fun(U_1912,U_1914),fun(fun(U_1912,bool),fun(U_1914,bool)),image(U_1912,U_1914),U_1910),U_1909)) = hAPP(fun(U_1912,bool),fun(U_1913,bool),hAPP(fun(U_1912,U_1913),fun(fun(U_1912,bool),fun(U_1913,bool)),image(U_1912,U_1913),hAPP(fun(U_1912,U_1914),fun(U_1912,U_1913),hAPP(fun(U_1914,U_1913),fun(fun(U_1912,U_1914),fun(U_1912,U_1913)),combb(U_1914,U_1913,U_1912),U_1911),U_1910)),U_1909),
    inference(clausify,[status(thm)],[f_557_2]) ).

fof(f_558_1,plain,
    ! [X_a,X_b,Z_1,F,A_1] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
        | ! [X_1] :
            ( ti(X_a,Z_1) != hAPP(X_b,X_a,F,X_1)
            | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) ) )
      & ( ? [X_1] :
            ( ti(X_a,Z_1) = hAPP(X_b,X_a,F,X_1)
            & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) )
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_468_image__iff]) ).

fof(f_558_2,plain,
    ! [U_1921,U_1920,U_1919,U_1918,U_1917] :
      ( ( hBOOL(hAPP(fun(U_1921,bool),bool,hAPP(U_1921,fun(fun(U_1921,bool),bool),member(U_1921),U_1919),hAPP(fun(U_1920,bool),fun(U_1921,bool),hAPP(fun(U_1920,U_1921),fun(fun(U_1920,bool),fun(U_1921,bool)),image(U_1920,U_1921),U_1918),U_1917)))
        | ! [U_1916] :
            ( ti(U_1921,U_1919) != hAPP(U_1920,U_1921,U_1918,U_1916)
            | ~ hBOOL(hAPP(fun(U_1920,bool),bool,hAPP(U_1920,fun(fun(U_1920,bool),bool),member(U_1920),U_1916),U_1917)) ) )
      & ( ? [U_1915] :
            ( ti(U_1921,U_1919) = hAPP(U_1920,U_1921,U_1918,U_1915)
            & hBOOL(hAPP(fun(U_1920,bool),bool,hAPP(U_1920,fun(fun(U_1920,bool),bool),member(U_1920),U_1915),U_1917)) )
        | ~ hBOOL(hAPP(fun(U_1921,bool),bool,hAPP(U_1921,fun(fun(U_1921,bool),bool),member(U_1921),U_1919),hAPP(fun(U_1920,bool),fun(U_1921,bool),hAPP(fun(U_1920,U_1921),fun(fun(U_1920,bool),fun(U_1921,bool)),image(U_1920,U_1921),U_1918),U_1917))) ) ),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

fof(f_558_3,plain,
    ( ! [U_1931,U_1929,U_1927,U_1925,U_1923] :
        ( hBOOL(hAPP(fun(U_1931,bool),bool,hAPP(U_1931,fun(fun(U_1931,bool),bool),member(U_1931),U_1927),hAPP(fun(U_1929,bool),fun(U_1931,bool),hAPP(fun(U_1929,U_1931),fun(fun(U_1929,bool),fun(U_1931,bool)),image(U_1929,U_1931),U_1925),U_1923)))
        | ! [U_1916] :
            ( ti(U_1931,U_1927) != hAPP(U_1929,U_1931,U_1925,U_1916)
            | ~ hBOOL(hAPP(fun(U_1929,bool),bool,hAPP(U_1929,fun(fun(U_1929,bool),bool),member(U_1929),U_1916),U_1923)) ) )
    & ! [U_1930,U_1928,U_1926,U_1924,U_1922] :
        ( ? [U_1915] :
            ( ti(U_1930,U_1926) = hAPP(U_1928,U_1930,U_1924,U_1915)
            & hBOOL(hAPP(fun(U_1928,bool),bool,hAPP(U_1928,fun(fun(U_1928,bool),bool),member(U_1928),U_1915),U_1922)) )
        | ~ hBOOL(hAPP(fun(U_1930,bool),bool,hAPP(U_1930,fun(fun(U_1930,bool),bool),member(U_1930),U_1926),hAPP(fun(U_1928,bool),fun(U_1930,bool),hAPP(fun(U_1928,U_1930),fun(fun(U_1928,bool),fun(U_1930,bool)),image(U_1928,U_1930),U_1924),U_1922))) ) ),
    inference(miniscope,[status(thm)],[f_558_2]) ).

fof(f_558_4,plain,
    ( ! [U_1931,U_1929,U_1927,U_1925,U_1923] :
        ( hBOOL(hAPP(fun(U_1931,bool),bool,hAPP(U_1931,fun(fun(U_1931,bool),bool),member(U_1931),U_1927),hAPP(fun(U_1929,bool),fun(U_1931,bool),hAPP(fun(U_1929,U_1931),fun(fun(U_1929,bool),fun(U_1931,bool)),image(U_1929,U_1931),U_1925),U_1923)))
        | ! [U_1916] :
            ( ti(U_1931,U_1927) != hAPP(U_1929,U_1931,U_1925,U_1916)
            | ~ hBOOL(hAPP(fun(U_1929,bool),bool,hAPP(U_1929,fun(fun(U_1929,bool),bool),member(U_1929),U_1916),U_1923)) ) )
    & ! [U_1930,U_1928,U_1926,U_1924,U_1922] :
        ( ( ti(U_1930,U_1926) = hAPP(U_1928,U_1930,U_1924,sK111(U_1930,U_1928,U_1926,U_1924,U_1922))
          & hBOOL(hAPP(fun(U_1928,bool),bool,hAPP(U_1928,fun(fun(U_1928,bool),bool),member(U_1928),sK111(U_1930,U_1928,U_1926,U_1924,U_1922)),U_1922)) )
        | ~ hBOOL(hAPP(fun(U_1930,bool),bool,hAPP(U_1930,fun(fun(U_1930,bool),bool),member(U_1930),U_1926),hAPP(fun(U_1928,bool),fun(U_1930,bool),hAPP(fun(U_1928,U_1930),fun(fun(U_1928,bool),fun(U_1930,bool)),image(U_1928,U_1930),U_1924),U_1922))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_1915,sK111(U_1930,U_1928,U_1926,U_1924,U_1922))],[f_558_3]) ).

cnf(f_558_5,plain,
    ( hBOOL(hAPP(fun(U_1928,bool),bool,hAPP(U_1928,fun(fun(U_1928,bool),bool),member(U_1928),sK111(U_1930,U_1928,U_1926,U_1924,U_1922)),U_1922))
    | ~ hBOOL(hAPP(fun(U_1930,bool),bool,hAPP(U_1930,fun(fun(U_1930,bool),bool),member(U_1930),U_1926),hAPP(fun(U_1928,bool),fun(U_1930,bool),hAPP(fun(U_1928,U_1930),fun(fun(U_1928,bool),fun(U_1930,bool)),image(U_1928,U_1930),U_1924),U_1922))) ),
    inference(clausify,[status(thm)],[f_558_4]) ).

cnf(f_558_6,plain,
    ( ti(U_1930,U_1926) = hAPP(U_1928,U_1930,U_1924,sK111(U_1930,U_1928,U_1926,U_1924,U_1922))
    | ~ hBOOL(hAPP(fun(U_1930,bool),bool,hAPP(U_1930,fun(fun(U_1930,bool),bool),member(U_1930),U_1926),hAPP(fun(U_1928,bool),fun(U_1930,bool),hAPP(fun(U_1928,U_1930),fun(fun(U_1928,bool),fun(U_1930,bool)),image(U_1928,U_1930),U_1924),U_1922))) ),
    inference(clausify,[status(thm)],[f_558_4]) ).

cnf(f_558_7,plain,
    ( hBOOL(hAPP(fun(U_1931,bool),bool,hAPP(U_1931,fun(fun(U_1931,bool),bool),member(U_1931),U_1927),hAPP(fun(U_1929,bool),fun(U_1931,bool),hAPP(fun(U_1929,U_1931),fun(fun(U_1929,bool),fun(U_1931,bool)),image(U_1929,U_1931),U_1925),U_1923)))
    | ti(U_1931,U_1927) != hAPP(U_1929,U_1931,U_1925,U_1916)
    | ~ hBOOL(hAPP(fun(U_1929,bool),bool,hAPP(U_1929,fun(fun(U_1929,bool),bool),member(U_1929),U_1916),U_1923)) ),
    inference(clausify,[status(thm)],[f_558_4]) ).

fof(f_559_1,plain,
    ! [X_b,X_a,F,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_469_imageI]) ).

fof(f_559_2,plain,
    ! [U_1936,U_1935,U_1934,U_1933,U_1932] :
      ( hBOOL(hAPP(fun(U_1936,bool),bool,hAPP(U_1936,fun(fun(U_1936,bool),bool),member(U_1936),hAPP(U_1935,U_1936,U_1934,U_1933)),hAPP(fun(U_1935,bool),fun(U_1936,bool),hAPP(fun(U_1935,U_1936),fun(fun(U_1935,bool),fun(U_1936,bool)),image(U_1935,U_1936),U_1934),U_1932)))
      | ~ hBOOL(hAPP(fun(U_1935,bool),bool,hAPP(U_1935,fun(fun(U_1935,bool),bool),member(U_1935),U_1933),U_1932)) ),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

cnf(f_559_3,plain,
    ( hBOOL(hAPP(fun(U_1936,bool),bool,hAPP(U_1936,fun(fun(U_1936,bool),bool),member(U_1936),hAPP(U_1935,U_1936,U_1934,U_1933)),hAPP(fun(U_1935,bool),fun(U_1936,bool),hAPP(fun(U_1935,U_1936),fun(fun(U_1935,bool),fun(U_1936,bool)),image(U_1935,U_1936),U_1934),U_1932)))
    | ~ hBOOL(hAPP(fun(U_1935,bool),bool,hAPP(U_1935,fun(fun(U_1935,bool),bool),member(U_1935),U_1933),U_1932)) ),
    inference(clausify,[status(thm)],[f_559_2]) ).

fof(f_560_1,plain,
    ! [X_b,X_a,Ba,F,X_2,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      | ti(X_b,Ba) != hAPP(X_a,X_b,F,X_2)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_470_rev__image__eqI]) ).

fof(f_560_2,plain,
    ! [U_1942,U_1941,U_1940,U_1939,U_1938,U_1937] :
      ( hBOOL(hAPP(fun(U_1942,bool),bool,hAPP(U_1942,fun(fun(U_1942,bool),bool),member(U_1942),U_1940),hAPP(fun(U_1941,bool),fun(U_1942,bool),hAPP(fun(U_1941,U_1942),fun(fun(U_1941,bool),fun(U_1942,bool)),image(U_1941,U_1942),U_1939),U_1937)))
      | ti(U_1942,U_1940) != hAPP(U_1941,U_1942,U_1939,U_1938)
      | ~ hBOOL(hAPP(fun(U_1941,bool),bool,hAPP(U_1941,fun(fun(U_1941,bool),bool),member(U_1941),U_1938),U_1937)) ),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

cnf(f_560_3,plain,
    ( hBOOL(hAPP(fun(U_1942,bool),bool,hAPP(U_1942,fun(fun(U_1942,bool),bool),member(U_1942),U_1940),hAPP(fun(U_1941,bool),fun(U_1942,bool),hAPP(fun(U_1941,U_1942),fun(fun(U_1941,bool),fun(U_1942,bool)),image(U_1941,U_1942),U_1939),U_1937)))
    | ti(U_1942,U_1940) != hAPP(U_1941,U_1942,U_1939,U_1938)
    | ~ hBOOL(hAPP(fun(U_1941,bool),bool,hAPP(U_1941,fun(fun(U_1941,bool),bool),member(U_1941),U_1938),U_1937)) ),
    inference(clausify,[status(thm)],[f_560_2]) ).

fof(f_561_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ti(X_a,Ba) = ti(X_a,Da)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Da))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
          | hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) != hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_471_atLeastLessThan__inj_I2_J]) ).

fof(f_561_2,plain,
    ! [U_1947] :
      ( ! [U_1946,U_1945,U_1944,U_1943] :
          ( ti(U_1947,U_1945) = ti(U_1947,U_1943)
          | ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),U_1943))
          | ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1946),U_1945))
          | hAPP(U_1947,fun(U_1947,bool),hAPP(U_1947,fun(U_1947,fun(U_1947,bool)),ord_atLeastLessThan(U_1947),U_1946),U_1945) != hAPP(U_1947,fun(U_1947,bool),hAPP(U_1947,fun(U_1947,fun(U_1947,bool)),ord_atLeastLessThan(U_1947),U_1944),U_1943) )
      | ~ linorder(U_1947) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

cnf(f_561_3,plain,
    ( ti(U_1947,U_1945) = ti(U_1947,U_1943)
    | ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1944),U_1943))
    | ~ hBOOL(hAPP(U_1947,bool,hAPP(U_1947,fun(U_1947,bool),ord_less(U_1947),U_1946),U_1945))
    | hAPP(U_1947,fun(U_1947,bool),hAPP(U_1947,fun(U_1947,fun(U_1947,bool)),ord_atLeastLessThan(U_1947),U_1946),U_1945) != hAPP(U_1947,fun(U_1947,bool),hAPP(U_1947,fun(U_1947,fun(U_1947,bool)),ord_atLeastLessThan(U_1947),U_1944),U_1943)
    | ~ linorder(U_1947) ),
    inference(clausify,[status(thm)],[f_561_2]) ).

fof(f_562_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ti(X_a,Aa) = ti(X_a,Ca)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Da))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
          | hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) != hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_472_atLeastLessThan__inj_I1_J]) ).

fof(f_562_2,plain,
    ! [U_1952] :
      ( ! [U_1951,U_1950,U_1949,U_1948] :
          ( ti(U_1952,U_1951) = ti(U_1952,U_1949)
          | ~ hBOOL(hAPP(U_1952,bool,hAPP(U_1952,fun(U_1952,bool),ord_less(U_1952),U_1949),U_1948))
          | ~ hBOOL(hAPP(U_1952,bool,hAPP(U_1952,fun(U_1952,bool),ord_less(U_1952),U_1951),U_1950))
          | hAPP(U_1952,fun(U_1952,bool),hAPP(U_1952,fun(U_1952,fun(U_1952,bool)),ord_atLeastLessThan(U_1952),U_1951),U_1950) != hAPP(U_1952,fun(U_1952,bool),hAPP(U_1952,fun(U_1952,fun(U_1952,bool)),ord_atLeastLessThan(U_1952),U_1949),U_1948) )
      | ~ linorder(U_1952) ),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

cnf(f_562_3,plain,
    ( ti(U_1952,U_1951) = ti(U_1952,U_1949)
    | ~ hBOOL(hAPP(U_1952,bool,hAPP(U_1952,fun(U_1952,bool),ord_less(U_1952),U_1949),U_1948))
    | ~ hBOOL(hAPP(U_1952,bool,hAPP(U_1952,fun(U_1952,bool),ord_less(U_1952),U_1951),U_1950))
    | hAPP(U_1952,fun(U_1952,bool),hAPP(U_1952,fun(U_1952,fun(U_1952,bool)),ord_atLeastLessThan(U_1952),U_1951),U_1950) != hAPP(U_1952,fun(U_1952,bool),hAPP(U_1952,fun(U_1952,fun(U_1952,bool)),ord_atLeastLessThan(U_1952),U_1949),U_1948)
    | ~ linorder(U_1952) ),
    inference(clausify,[status(thm)],[f_562_2]) ).

fof(f_563_1,plain,
    ! [X_a] :
      ( ! [Ca,Da,Aa,Ba] :
          ( ( ( hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)
              | ti(X_a,Ba) != ti(X_a,Da)
              | ti(X_a,Aa) != ti(X_a,Ca) )
            & ( ( ti(X_a,Ba) = ti(X_a,Da)
                & ti(X_a,Aa) = ti(X_a,Ca) )
              | hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) != hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da) ) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Da))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_473_atLeastLessThan__eq__iff]) ).

fof(f_563_2,plain,
    ! [U_1957] :
      ( ! [U_1956,U_1955,U_1954,U_1953] :
          ( ( ( hAPP(U_1957,fun(U_1957,bool),hAPP(U_1957,fun(U_1957,fun(U_1957,bool)),ord_atLeastLessThan(U_1957),U_1954),U_1953) = hAPP(U_1957,fun(U_1957,bool),hAPP(U_1957,fun(U_1957,fun(U_1957,bool)),ord_atLeastLessThan(U_1957),U_1956),U_1955)
              | ti(U_1957,U_1953) != ti(U_1957,U_1955)
              | ti(U_1957,U_1954) != ti(U_1957,U_1956) )
            & ( ( ti(U_1957,U_1953) = ti(U_1957,U_1955)
                & ti(U_1957,U_1954) = ti(U_1957,U_1956) )
              | hAPP(U_1957,fun(U_1957,bool),hAPP(U_1957,fun(U_1957,fun(U_1957,bool)),ord_atLeastLessThan(U_1957),U_1954),U_1953) != hAPP(U_1957,fun(U_1957,bool),hAPP(U_1957,fun(U_1957,fun(U_1957,bool)),ord_atLeastLessThan(U_1957),U_1956),U_1955) ) )
          | ~ hBOOL(hAPP(U_1957,bool,hAPP(U_1957,fun(U_1957,bool),ord_less(U_1957),U_1956),U_1955))
          | ~ hBOOL(hAPP(U_1957,bool,hAPP(U_1957,fun(U_1957,bool),ord_less(U_1957),U_1954),U_1953)) )
      | ~ linorder(U_1957) ),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

cnf(f_563_3,plain,
    ( ti(U_1957,U_1954) = ti(U_1957,U_1956)
    | hAPP(U_1957,fun(U_1957,bool),hAPP(U_1957,fun(U_1957,fun(U_1957,bool)),ord_atLeastLessThan(U_1957),U_1954),U_1953) != hAPP(U_1957,fun(U_1957,bool),hAPP(U_1957,fun(U_1957,fun(U_1957,bool)),ord_atLeastLessThan(U_1957),U_1956),U_1955)
    | ~ hBOOL(hAPP(U_1957,bool,hAPP(U_1957,fun(U_1957,bool),ord_less(U_1957),U_1956),U_1955))
    | ~ hBOOL(hAPP(U_1957,bool,hAPP(U_1957,fun(U_1957,bool),ord_less(U_1957),U_1954),U_1953))
    | ~ linorder(U_1957) ),
    inference(clausify,[status(thm)],[f_563_2]) ).

cnf(f_563_4,plain,
    ( ti(U_1957,U_1953) = ti(U_1957,U_1955)
    | hAPP(U_1957,fun(U_1957,bool),hAPP(U_1957,fun(U_1957,fun(U_1957,bool)),ord_atLeastLessThan(U_1957),U_1954),U_1953) != hAPP(U_1957,fun(U_1957,bool),hAPP(U_1957,fun(U_1957,fun(U_1957,bool)),ord_atLeastLessThan(U_1957),U_1956),U_1955)
    | ~ hBOOL(hAPP(U_1957,bool,hAPP(U_1957,fun(U_1957,bool),ord_less(U_1957),U_1956),U_1955))
    | ~ hBOOL(hAPP(U_1957,bool,hAPP(U_1957,fun(U_1957,bool),ord_less(U_1957),U_1954),U_1953))
    | ~ linorder(U_1957) ),
    inference(clausify,[status(thm)],[f_563_2]) ).

cnf(f_563_5,plain,
    ( hAPP(U_1957,fun(U_1957,bool),hAPP(U_1957,fun(U_1957,fun(U_1957,bool)),ord_atLeastLessThan(U_1957),U_1954),U_1953) = hAPP(U_1957,fun(U_1957,bool),hAPP(U_1957,fun(U_1957,fun(U_1957,bool)),ord_atLeastLessThan(U_1957),U_1956),U_1955)
    | ti(U_1957,U_1953) != ti(U_1957,U_1955)
    | ti(U_1957,U_1954) != ti(U_1957,U_1956)
    | ~ hBOOL(hAPP(U_1957,bool,hAPP(U_1957,fun(U_1957,bool),ord_less(U_1957),U_1956),U_1955))
    | ~ hBOOL(hAPP(U_1957,bool,hAPP(U_1957,fun(U_1957,bool),ord_less(U_1957),U_1954),U_1953))
    | ~ linorder(U_1957) ),
    inference(clausify,[status(thm)],[f_563_2]) ).

fof(f_564_1,plain,
    ! [X_a,X_b,Y_1,F,A_1] :
      ( hAPP(X_b,X_a,F,hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F),Y_1)) = ti(X_a,Y_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_474_f__inv__into__f]) ).

fof(f_564_2,plain,
    ! [U_1962,U_1961,U_1960,U_1959,U_1958] :
      ( hAPP(U_1961,U_1962,U_1959,hAPP(U_1962,U_1961,hAPP(fun(U_1961,U_1962),fun(U_1962,U_1961),hAPP(fun(U_1961,bool),fun(fun(U_1961,U_1962),fun(U_1962,U_1961)),hilbert_inv_into(U_1961,U_1962),U_1958),U_1959),U_1960)) = ti(U_1962,U_1960)
      | ~ hBOOL(hAPP(fun(U_1962,bool),bool,hAPP(U_1962,fun(fun(U_1962,bool),bool),member(U_1962),U_1960),hAPP(fun(U_1961,bool),fun(U_1962,bool),hAPP(fun(U_1961,U_1962),fun(fun(U_1961,bool),fun(U_1962,bool)),image(U_1961,U_1962),U_1959),U_1958))) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

cnf(f_564_3,plain,
    ( hAPP(U_1961,U_1962,U_1959,hAPP(U_1962,U_1961,hAPP(fun(U_1961,U_1962),fun(U_1962,U_1961),hAPP(fun(U_1961,bool),fun(fun(U_1961,U_1962),fun(U_1962,U_1961)),hilbert_inv_into(U_1961,U_1962),U_1958),U_1959),U_1960)) = ti(U_1962,U_1960)
    | ~ hBOOL(hAPP(fun(U_1962,bool),bool,hAPP(U_1962,fun(fun(U_1962,bool),bool),member(U_1962),U_1960),hAPP(fun(U_1961,bool),fun(U_1962,bool),hAPP(fun(U_1961,U_1962),fun(fun(U_1961,bool),fun(U_1962,bool)),image(U_1961,U_1962),U_1959),U_1958))) ),
    inference(clausify,[status(thm)],[f_564_2]) ).

fof(f_565_1,plain,
    ! [X_a,X_b,X_2,F,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F),X_2)),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_475_inv__into__into]) ).

fof(f_565_2,plain,
    ! [U_1967,U_1966,U_1965,U_1964,U_1963] :
      ( hBOOL(hAPP(fun(U_1966,bool),bool,hAPP(U_1966,fun(fun(U_1966,bool),bool),member(U_1966),hAPP(U_1967,U_1966,hAPP(fun(U_1966,U_1967),fun(U_1967,U_1966),hAPP(fun(U_1966,bool),fun(fun(U_1966,U_1967),fun(U_1967,U_1966)),hilbert_inv_into(U_1966,U_1967),U_1963),U_1964),U_1965)),U_1963))
      | ~ hBOOL(hAPP(fun(U_1967,bool),bool,hAPP(U_1967,fun(fun(U_1967,bool),bool),member(U_1967),U_1965),hAPP(fun(U_1966,bool),fun(U_1967,bool),hAPP(fun(U_1966,U_1967),fun(fun(U_1966,bool),fun(U_1967,bool)),image(U_1966,U_1967),U_1964),U_1963))) ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

cnf(f_565_3,plain,
    ( hBOOL(hAPP(fun(U_1966,bool),bool,hAPP(U_1966,fun(fun(U_1966,bool),bool),member(U_1966),hAPP(U_1967,U_1966,hAPP(fun(U_1966,U_1967),fun(U_1967,U_1966),hAPP(fun(U_1966,bool),fun(fun(U_1966,U_1967),fun(U_1967,U_1966)),hilbert_inv_into(U_1966,U_1967),U_1963),U_1964),U_1965)),U_1963))
    | ~ hBOOL(hAPP(fun(U_1967,bool),bool,hAPP(U_1967,fun(fun(U_1967,bool),bool),member(U_1967),U_1965),hAPP(fun(U_1966,bool),fun(U_1967,bool),hAPP(fun(U_1966,U_1967),fun(fun(U_1966,bool),fun(U_1967,bool)),image(U_1966,U_1967),U_1964),U_1963))) ),
    inference(clausify,[status(thm)],[f_565_2]) ).

fof(f_566_1,plain,
    ! [X_b,X_a,A_1,F,X_2,Y_1] :
      ( ti(X_b,X_2) = ti(X_b,Y_1)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      | hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),X_2) != hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),Y_1) ),
    inference(fof_nnf,[status(thm)],[fact_476_inv__into__injective]) ).

fof(f_566_2,plain,
    ! [U_1973,U_1972,U_1971,U_1970,U_1969,U_1968] :
      ( ti(U_1973,U_1969) = ti(U_1973,U_1968)
      | ~ hBOOL(hAPP(fun(U_1973,bool),bool,hAPP(U_1973,fun(fun(U_1973,bool),bool),member(U_1973),U_1968),hAPP(fun(U_1972,bool),fun(U_1973,bool),hAPP(fun(U_1972,U_1973),fun(fun(U_1972,bool),fun(U_1973,bool)),image(U_1972,U_1973),U_1970),U_1971)))
      | ~ hBOOL(hAPP(fun(U_1973,bool),bool,hAPP(U_1973,fun(fun(U_1973,bool),bool),member(U_1973),U_1969),hAPP(fun(U_1972,bool),fun(U_1973,bool),hAPP(fun(U_1972,U_1973),fun(fun(U_1972,bool),fun(U_1973,bool)),image(U_1972,U_1973),U_1970),U_1971)))
      | hAPP(U_1973,U_1972,hAPP(fun(U_1972,U_1973),fun(U_1973,U_1972),hAPP(fun(U_1972,bool),fun(fun(U_1972,U_1973),fun(U_1973,U_1972)),hilbert_inv_into(U_1972,U_1973),U_1971),U_1970),U_1969) != hAPP(U_1973,U_1972,hAPP(fun(U_1972,U_1973),fun(U_1973,U_1972),hAPP(fun(U_1972,bool),fun(fun(U_1972,U_1973),fun(U_1973,U_1972)),hilbert_inv_into(U_1972,U_1973),U_1971),U_1970),U_1968) ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

cnf(f_566_3,plain,
    ( ti(U_1973,U_1969) = ti(U_1973,U_1968)
    | ~ hBOOL(hAPP(fun(U_1973,bool),bool,hAPP(U_1973,fun(fun(U_1973,bool),bool),member(U_1973),U_1968),hAPP(fun(U_1972,bool),fun(U_1973,bool),hAPP(fun(U_1972,U_1973),fun(fun(U_1972,bool),fun(U_1973,bool)),image(U_1972,U_1973),U_1970),U_1971)))
    | ~ hBOOL(hAPP(fun(U_1973,bool),bool,hAPP(U_1973,fun(fun(U_1973,bool),bool),member(U_1973),U_1969),hAPP(fun(U_1972,bool),fun(U_1973,bool),hAPP(fun(U_1972,U_1973),fun(fun(U_1972,bool),fun(U_1973,bool)),image(U_1972,U_1973),U_1970),U_1971)))
    | hAPP(U_1973,U_1972,hAPP(fun(U_1972,U_1973),fun(U_1973,U_1972),hAPP(fun(U_1972,bool),fun(fun(U_1972,U_1973),fun(U_1973,U_1972)),hilbert_inv_into(U_1972,U_1973),U_1971),U_1970),U_1969) != hAPP(U_1973,U_1972,hAPP(fun(U_1972,U_1973),fun(U_1973,U_1972),hAPP(fun(U_1972,bool),fun(fun(U_1972,U_1973),fun(U_1973,U_1972)),hilbert_inv_into(U_1972,U_1973),U_1971),U_1970),U_1968) ),
    inference(clausify,[status(thm)],[f_566_2]) ).

fof(f_567_1,plain,
    ! [X_b,X_a,X_c,F,G] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,X_c),fun(X_b,X_a),hAPP(fun(X_c,X_a),fun(fun(X_b,X_c),fun(X_b,X_a)),combb(X_c,X_a,X_b),F),G)),top_top(fun(X_b,bool))) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),F),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),top_top(fun(X_b,bool)))),
    inference(fof_nnf,[status(thm)],[fact_477_range__composition]) ).

fof(f_567_2,plain,
    ! [U_1978,U_1977,U_1976,U_1975,U_1974] : hAPP(fun(U_1978,bool),fun(U_1977,bool),hAPP(fun(U_1978,U_1977),fun(fun(U_1978,bool),fun(U_1977,bool)),image(U_1978,U_1977),hAPP(fun(U_1978,U_1976),fun(U_1978,U_1977),hAPP(fun(U_1976,U_1977),fun(fun(U_1978,U_1976),fun(U_1978,U_1977)),combb(U_1976,U_1977,U_1978),U_1975),U_1974)),top_top(fun(U_1978,bool))) = hAPP(fun(U_1976,bool),fun(U_1977,bool),hAPP(fun(U_1976,U_1977),fun(fun(U_1976,bool),fun(U_1977,bool)),image(U_1976,U_1977),U_1975),hAPP(fun(U_1978,bool),fun(U_1976,bool),hAPP(fun(U_1978,U_1976),fun(fun(U_1978,bool),fun(U_1976,bool)),image(U_1978,U_1976),U_1974),top_top(fun(U_1978,bool)))),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

cnf(f_567_3,plain,
    hAPP(fun(U_1978,bool),fun(U_1977,bool),hAPP(fun(U_1978,U_1977),fun(fun(U_1978,bool),fun(U_1977,bool)),image(U_1978,U_1977),hAPP(fun(U_1978,U_1976),fun(U_1978,U_1977),hAPP(fun(U_1976,U_1977),fun(fun(U_1978,U_1976),fun(U_1978,U_1977)),combb(U_1976,U_1977,U_1978),U_1975),U_1974)),top_top(fun(U_1978,bool))) = hAPP(fun(U_1976,bool),fun(U_1977,bool),hAPP(fun(U_1976,U_1977),fun(fun(U_1976,bool),fun(U_1977,bool)),image(U_1976,U_1977),U_1975),hAPP(fun(U_1978,bool),fun(U_1976,bool),hAPP(fun(U_1978,U_1976),fun(fun(U_1978,bool),fun(U_1976,bool)),image(U_1978,U_1976),U_1974),top_top(fun(U_1978,bool)))),
    inference(clausify,[status(thm)],[f_567_2]) ).

fof(f_568_1,plain,
    ! [X_b,X_a,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_478_finite__surj]) ).

fof(f_568_2,plain,
    ! [U_1983,U_1982,U_1981,U_1980,U_1979] :
      ( hBOOL(hAPP(fun(U_1983,bool),bool,finite_finite_1(U_1983),U_1981))
      | ~ hBOOL(hAPP(fun(U_1983,bool),bool,hAPP(fun(U_1983,bool),fun(fun(U_1983,bool),bool),ord_less_eq(fun(U_1983,bool)),U_1981),hAPP(fun(U_1982,bool),fun(U_1983,bool),hAPP(fun(U_1982,U_1983),fun(fun(U_1982,bool),fun(U_1983,bool)),image(U_1982,U_1983),U_1980),U_1979)))
      | ~ hBOOL(hAPP(fun(U_1982,bool),bool,finite_finite_1(U_1982),U_1979)) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

cnf(f_568_3,plain,
    ( hBOOL(hAPP(fun(U_1983,bool),bool,finite_finite_1(U_1983),U_1981))
    | ~ hBOOL(hAPP(fun(U_1983,bool),bool,hAPP(fun(U_1983,bool),fun(fun(U_1983,bool),bool),ord_less_eq(fun(U_1983,bool)),U_1981),hAPP(fun(U_1982,bool),fun(U_1983,bool),hAPP(fun(U_1982,U_1983),fun(fun(U_1982,bool),fun(U_1983,bool)),image(U_1982,U_1983),U_1980),U_1979)))
    | ~ hBOOL(hAPP(fun(U_1982,bool),bool,finite_finite_1(U_1982),U_1979)) ),
    inference(clausify,[status(thm)],[f_568_2]) ).

fof(f_569_1,plain,
    ! [X_a,X_b,F,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),F),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_479_finite__imageD]) ).

fof(f_569_2,plain,
    ! [U_1987,U_1986,U_1985,U_1984] :
      ( hBOOL(hAPP(fun(U_1986,bool),bool,finite_finite_1(U_1986),U_1984))
      | ~ hBOOL(hAPP(fun(U_1986,bool),bool,hAPP(fun(U_1986,U_1987),fun(fun(U_1986,bool),bool),inj_on(U_1986,U_1987),U_1985),U_1984))
      | ~ hBOOL(hAPP(fun(U_1987,bool),bool,finite_finite_1(U_1987),hAPP(fun(U_1986,bool),fun(U_1987,bool),hAPP(fun(U_1986,U_1987),fun(fun(U_1986,bool),fun(U_1987,bool)),image(U_1986,U_1987),U_1985),U_1984))) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

cnf(f_569_3,plain,
    ( hBOOL(hAPP(fun(U_1986,bool),bool,finite_finite_1(U_1986),U_1984))
    | ~ hBOOL(hAPP(fun(U_1986,bool),bool,hAPP(fun(U_1986,U_1987),fun(fun(U_1986,bool),bool),inj_on(U_1986,U_1987),U_1985),U_1984))
    | ~ hBOOL(hAPP(fun(U_1987,bool),bool,finite_finite_1(U_1987),hAPP(fun(U_1986,bool),fun(U_1987,bool),hAPP(fun(U_1986,U_1987),fun(fun(U_1986,bool),fun(U_1987,bool)),image(U_1986,U_1987),U_1985),U_1984))) ),
    inference(clausify,[status(thm)],[f_569_2]) ).

fof(f_570_1,plain,
    ! [X_a,X_b,Ba,F] :
      ( ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),top_top(fun(X_a,bool)))))
          | ! [X_1] :
              ( ? [Y_2] :
                  ( ti(X_a,Y_2) != ti(X_a,X_1)
                  & ti(X_b,Ba) = hAPP(X_a,X_b,F,Y_2) )
              | ti(X_b,Ba) != hAPP(X_a,X_b,F,X_1) ) )
        & ( ? [X_1] :
              ( ! [Y_2] :
                  ( ti(X_a,Y_2) = ti(X_a,X_1)
                  | ti(X_b,Ba) != hAPP(X_a,X_b,F,Y_2) )
              & ti(X_b,Ba) = hAPP(X_a,X_b,F,X_1) )
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),top_top(fun(X_a,bool))))) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_480_range__ex1__eq]) ).

fof(f_570_2,plain,
    ! [U_1995,U_1994,U_1993,U_1992] :
      ( ( ( hBOOL(hAPP(fun(U_1994,bool),bool,hAPP(U_1994,fun(fun(U_1994,bool),bool),member(U_1994),U_1993),hAPP(fun(U_1995,bool),fun(U_1994,bool),hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),fun(U_1994,bool)),image(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))))
          | ! [U_1991] :
              ( ? [U_1990] :
                  ( ti(U_1995,U_1990) != ti(U_1995,U_1991)
                  & ti(U_1994,U_1993) = hAPP(U_1995,U_1994,U_1992,U_1990) )
              | ti(U_1994,U_1993) != hAPP(U_1995,U_1994,U_1992,U_1991) ) )
        & ( ? [U_1989] :
              ( ! [U_1988] :
                  ( ti(U_1995,U_1988) = ti(U_1995,U_1989)
                  | ti(U_1994,U_1993) != hAPP(U_1995,U_1994,U_1992,U_1988) )
              & ti(U_1994,U_1993) = hAPP(U_1995,U_1994,U_1992,U_1989) )
          | ~ hBOOL(hAPP(fun(U_1994,bool),bool,hAPP(U_1994,fun(fun(U_1994,bool),bool),member(U_1994),U_1993),hAPP(fun(U_1995,bool),fun(U_1994,bool),hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),fun(U_1994,bool)),image(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool))))) ) )
      | ~ hBOOL(hAPP(fun(U_1995,bool),bool,hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),bool),inj_on(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

fof(f_570_3,plain,
    ! [U_1995,U_1994,U_1993,U_1992] :
      ( ( ( hBOOL(hAPP(fun(U_1994,bool),bool,hAPP(U_1994,fun(fun(U_1994,bool),bool),member(U_1994),U_1993),hAPP(fun(U_1995,bool),fun(U_1994,bool),hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),fun(U_1994,bool)),image(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))))
          | ! [U_1991] :
              ( ? [U_1990] :
                  ( ti(U_1995,U_1990) != ti(U_1995,U_1991)
                  & ti(U_1994,U_1993) = hAPP(U_1995,U_1994,U_1992,U_1990) )
              | ti(U_1994,U_1993) != hAPP(U_1995,U_1994,U_1992,U_1991) ) )
        & ( ( ! [U_1988] :
                ( ti(U_1995,U_1988) = ti(U_1995,sK112(U_1995,U_1994,U_1993,U_1992))
                | ti(U_1994,U_1993) != hAPP(U_1995,U_1994,U_1992,U_1988) )
            & ti(U_1994,U_1993) = hAPP(U_1995,U_1994,U_1992,sK112(U_1995,U_1994,U_1993,U_1992)) )
          | ~ hBOOL(hAPP(fun(U_1994,bool),bool,hAPP(U_1994,fun(fun(U_1994,bool),bool),member(U_1994),U_1993),hAPP(fun(U_1995,bool),fun(U_1994,bool),hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),fun(U_1994,bool)),image(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool))))) ) )
      | ~ hBOOL(hAPP(fun(U_1995,bool),bool,hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),bool),inj_on(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_1989,sK112(U_1995,U_1994,U_1993,U_1992))],[f_570_2]) ).

fof(f_570_4,plain,
    ! [U_1995,U_1994,U_1993,U_1992] :
      ( ( ( hBOOL(hAPP(fun(U_1994,bool),bool,hAPP(U_1994,fun(fun(U_1994,bool),bool),member(U_1994),U_1993),hAPP(fun(U_1995,bool),fun(U_1994,bool),hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),fun(U_1994,bool)),image(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))))
          | ! [U_1991] :
              ( ( ti(U_1995,sK113(U_1995,U_1994,U_1993,U_1992,U_1991)) != ti(U_1995,U_1991)
                & ti(U_1994,U_1993) = hAPP(U_1995,U_1994,U_1992,sK113(U_1995,U_1994,U_1993,U_1992,U_1991)) )
              | ti(U_1994,U_1993) != hAPP(U_1995,U_1994,U_1992,U_1991) ) )
        & ( ( ! [U_1988] :
                ( ti(U_1995,U_1988) = ti(U_1995,sK112(U_1995,U_1994,U_1993,U_1992))
                | ti(U_1994,U_1993) != hAPP(U_1995,U_1994,U_1992,U_1988) )
            & ti(U_1994,U_1993) = hAPP(U_1995,U_1994,U_1992,sK112(U_1995,U_1994,U_1993,U_1992)) )
          | ~ hBOOL(hAPP(fun(U_1994,bool),bool,hAPP(U_1994,fun(fun(U_1994,bool),bool),member(U_1994),U_1993),hAPP(fun(U_1995,bool),fun(U_1994,bool),hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),fun(U_1994,bool)),image(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool))))) ) )
      | ~ hBOOL(hAPP(fun(U_1995,bool),bool,hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),bool),inj_on(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_1990,sK113(U_1995,U_1994,U_1993,U_1992,U_1991))],[f_570_3]) ).

cnf(f_570_5,plain,
    ( ti(U_1994,U_1993) = hAPP(U_1995,U_1994,U_1992,sK112(U_1995,U_1994,U_1993,U_1992))
    | ~ hBOOL(hAPP(fun(U_1994,bool),bool,hAPP(U_1994,fun(fun(U_1994,bool),bool),member(U_1994),U_1993),hAPP(fun(U_1995,bool),fun(U_1994,bool),hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),fun(U_1994,bool)),image(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))))
    | ~ hBOOL(hAPP(fun(U_1995,bool),bool,hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),bool),inj_on(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_6,plain,
    ( ti(U_1995,U_1988) = ti(U_1995,sK112(U_1995,U_1994,U_1993,U_1992))
    | ti(U_1994,U_1993) != hAPP(U_1995,U_1994,U_1992,U_1988)
    | ~ hBOOL(hAPP(fun(U_1994,bool),bool,hAPP(U_1994,fun(fun(U_1994,bool),bool),member(U_1994),U_1993),hAPP(fun(U_1995,bool),fun(U_1994,bool),hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),fun(U_1994,bool)),image(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))))
    | ~ hBOOL(hAPP(fun(U_1995,bool),bool,hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),bool),inj_on(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_7,plain,
    ( ti(U_1994,U_1993) = hAPP(U_1995,U_1994,U_1992,sK113(U_1995,U_1994,U_1993,U_1992,U_1991))
    | ti(U_1994,U_1993) != hAPP(U_1995,U_1994,U_1992,U_1991)
    | hBOOL(hAPP(fun(U_1994,bool),bool,hAPP(U_1994,fun(fun(U_1994,bool),bool),member(U_1994),U_1993),hAPP(fun(U_1995,bool),fun(U_1994,bool),hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),fun(U_1994,bool)),image(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))))
    | ~ hBOOL(hAPP(fun(U_1995,bool),bool,hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),bool),inj_on(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_8,plain,
    ( ti(U_1995,sK113(U_1995,U_1994,U_1993,U_1992,U_1991)) != ti(U_1995,U_1991)
    | ti(U_1994,U_1993) != hAPP(U_1995,U_1994,U_1992,U_1991)
    | hBOOL(hAPP(fun(U_1994,bool),bool,hAPP(U_1994,fun(fun(U_1994,bool),bool),member(U_1994),U_1993),hAPP(fun(U_1995,bool),fun(U_1994,bool),hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),fun(U_1994,bool)),image(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))))
    | ~ hBOOL(hAPP(fun(U_1995,bool),bool,hAPP(fun(U_1995,U_1994),fun(fun(U_1995,bool),bool),inj_on(U_1995,U_1994),U_1992),top_top(fun(U_1995,bool)))) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

fof(f_571_1,plain,
    ! [X_a,X_b,Aa,A_1,F] :
      ( ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,Aa)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),A_1)) )
        & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),A_1))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,Aa)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_481_inj__image__mem__iff]) ).

fof(f_571_2,plain,
    ! [U_2000,U_1999,U_1998,U_1997,U_1996] :
      ( ( ( hBOOL(hAPP(fun(U_1999,bool),bool,hAPP(U_1999,fun(fun(U_1999,bool),bool),member(U_1999),hAPP(U_2000,U_1999,U_1996,U_1998)),hAPP(fun(U_2000,bool),fun(U_1999,bool),hAPP(fun(U_2000,U_1999),fun(fun(U_2000,bool),fun(U_1999,bool)),image(U_2000,U_1999),U_1996),U_1997)))
          | ~ hBOOL(hAPP(fun(U_2000,bool),bool,hAPP(U_2000,fun(fun(U_2000,bool),bool),member(U_2000),U_1998),U_1997)) )
        & ( hBOOL(hAPP(fun(U_2000,bool),bool,hAPP(U_2000,fun(fun(U_2000,bool),bool),member(U_2000),U_1998),U_1997))
          | ~ hBOOL(hAPP(fun(U_1999,bool),bool,hAPP(U_1999,fun(fun(U_1999,bool),bool),member(U_1999),hAPP(U_2000,U_1999,U_1996,U_1998)),hAPP(fun(U_2000,bool),fun(U_1999,bool),hAPP(fun(U_2000,U_1999),fun(fun(U_2000,bool),fun(U_1999,bool)),image(U_2000,U_1999),U_1996),U_1997))) ) )
      | ~ hBOOL(hAPP(fun(U_2000,bool),bool,hAPP(fun(U_2000,U_1999),fun(fun(U_2000,bool),bool),inj_on(U_2000,U_1999),U_1996),top_top(fun(U_2000,bool)))) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

cnf(f_571_3,plain,
    ( hBOOL(hAPP(fun(U_2000,bool),bool,hAPP(U_2000,fun(fun(U_2000,bool),bool),member(U_2000),U_1998),U_1997))
    | ~ hBOOL(hAPP(fun(U_1999,bool),bool,hAPP(U_1999,fun(fun(U_1999,bool),bool),member(U_1999),hAPP(U_2000,U_1999,U_1996,U_1998)),hAPP(fun(U_2000,bool),fun(U_1999,bool),hAPP(fun(U_2000,U_1999),fun(fun(U_2000,bool),fun(U_1999,bool)),image(U_2000,U_1999),U_1996),U_1997)))
    | ~ hBOOL(hAPP(fun(U_2000,bool),bool,hAPP(fun(U_2000,U_1999),fun(fun(U_2000,bool),bool),inj_on(U_2000,U_1999),U_1996),top_top(fun(U_2000,bool)))) ),
    inference(clausify,[status(thm)],[f_571_2]) ).

cnf(f_571_4,plain,
    ( hBOOL(hAPP(fun(U_1999,bool),bool,hAPP(U_1999,fun(fun(U_1999,bool),bool),member(U_1999),hAPP(U_2000,U_1999,U_1996,U_1998)),hAPP(fun(U_2000,bool),fun(U_1999,bool),hAPP(fun(U_2000,U_1999),fun(fun(U_2000,bool),fun(U_1999,bool)),image(U_2000,U_1999),U_1996),U_1997)))
    | ~ hBOOL(hAPP(fun(U_2000,bool),bool,hAPP(U_2000,fun(fun(U_2000,bool),bool),member(U_2000),U_1998),U_1997))
    | ~ hBOOL(hAPP(fun(U_2000,bool),bool,hAPP(fun(U_2000,U_1999),fun(fun(U_2000,bool),bool),inj_on(U_2000,U_1999),U_1996),top_top(fun(U_2000,bool)))) ),
    inference(clausify,[status(thm)],[f_571_2]) ).

fof(f_572_1,plain,
    ! [X_a,X_b,A_1,B,F] :
      ( ( ( hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)
          | ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) )
        & ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
          | hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) != hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_482_inj__image__eq__iff]) ).

fof(f_572_2,plain,
    ! [U_2005,U_2004,U_2003,U_2002,U_2001] :
      ( ( ( hAPP(fun(U_2005,bool),fun(U_2004,bool),hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),fun(U_2004,bool)),image(U_2005,U_2004),U_2001),U_2003) = hAPP(fun(U_2005,bool),fun(U_2004,bool),hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),fun(U_2004,bool)),image(U_2005,U_2004),U_2001),U_2002)
          | ti(fun(U_2005,bool),U_2003) != ti(fun(U_2005,bool),U_2002) )
        & ( ti(fun(U_2005,bool),U_2003) = ti(fun(U_2005,bool),U_2002)
          | hAPP(fun(U_2005,bool),fun(U_2004,bool),hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),fun(U_2004,bool)),image(U_2005,U_2004),U_2001),U_2003) != hAPP(fun(U_2005,bool),fun(U_2004,bool),hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),fun(U_2004,bool)),image(U_2005,U_2004),U_2001),U_2002) ) )
      | ~ hBOOL(hAPP(fun(U_2005,bool),bool,hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),bool),inj_on(U_2005,U_2004),U_2001),top_top(fun(U_2005,bool)))) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

cnf(f_572_3,plain,
    ( ti(fun(U_2005,bool),U_2003) = ti(fun(U_2005,bool),U_2002)
    | hAPP(fun(U_2005,bool),fun(U_2004,bool),hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),fun(U_2004,bool)),image(U_2005,U_2004),U_2001),U_2003) != hAPP(fun(U_2005,bool),fun(U_2004,bool),hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),fun(U_2004,bool)),image(U_2005,U_2004),U_2001),U_2002)
    | ~ hBOOL(hAPP(fun(U_2005,bool),bool,hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),bool),inj_on(U_2005,U_2004),U_2001),top_top(fun(U_2005,bool)))) ),
    inference(clausify,[status(thm)],[f_572_2]) ).

cnf(f_572_4,plain,
    ( hAPP(fun(U_2005,bool),fun(U_2004,bool),hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),fun(U_2004,bool)),image(U_2005,U_2004),U_2001),U_2003) = hAPP(fun(U_2005,bool),fun(U_2004,bool),hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),fun(U_2004,bool)),image(U_2005,U_2004),U_2001),U_2002)
    | ti(fun(U_2005,bool),U_2003) != ti(fun(U_2005,bool),U_2002)
    | ~ hBOOL(hAPP(fun(U_2005,bool),bool,hAPP(fun(U_2005,U_2004),fun(fun(U_2005,bool),bool),inj_on(U_2005,U_2004),U_2001),top_top(fun(U_2005,bool)))) ),
    inference(clausify,[status(thm)],[f_572_2]) ).

fof(f_573_1,plain,
    ! [X_a,X_b,F,A_1] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_483_card__image]) ).

fof(f_573_2,plain,
    ! [U_2009,U_2008,U_2007,U_2006] :
      ( hAPP(fun(U_2008,bool),nat,finite_card(U_2008),hAPP(fun(U_2009,bool),fun(U_2008,bool),hAPP(fun(U_2009,U_2008),fun(fun(U_2009,bool),fun(U_2008,bool)),image(U_2009,U_2008),U_2007),U_2006)) = hAPP(fun(U_2009,bool),nat,finite_card(U_2009),U_2006)
      | ~ hBOOL(hAPP(fun(U_2009,bool),bool,hAPP(fun(U_2009,U_2008),fun(fun(U_2009,bool),bool),inj_on(U_2009,U_2008),U_2007),U_2006)) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

cnf(f_573_3,plain,
    ( hAPP(fun(U_2008,bool),nat,finite_card(U_2008),hAPP(fun(U_2009,bool),fun(U_2008,bool),hAPP(fun(U_2009,U_2008),fun(fun(U_2009,bool),fun(U_2008,bool)),image(U_2009,U_2008),U_2007),U_2006)) = hAPP(fun(U_2009,bool),nat,finite_card(U_2009),U_2006)
    | ~ hBOOL(hAPP(fun(U_2009,bool),bool,hAPP(fun(U_2009,U_2008),fun(fun(U_2009,bool),bool),inj_on(U_2009,U_2008),U_2007),U_2006)) ),
    inference(clausify,[status(thm)],[f_573_2]) ).

fof(f_574_1,plain,
    ! [X_b,X_a,B_2,F,A_1,A_3] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F)),B_2)) = ti(fun(X_a,bool),B_2)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3))
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) != ti(fun(X_a,bool),A_3) ),
    inference(fof_nnf,[status(thm)],[fact_484_image__inv__into__cancel]) ).

fof(f_574_2,plain,
    ! [U_2015,U_2014,U_2013,U_2012,U_2011,U_2010] :
      ( hAPP(fun(U_2015,bool),fun(U_2014,bool),hAPP(fun(U_2015,U_2014),fun(fun(U_2015,bool),fun(U_2014,bool)),image(U_2015,U_2014),U_2012),hAPP(fun(U_2014,bool),fun(U_2015,bool),hAPP(fun(U_2014,U_2015),fun(fun(U_2014,bool),fun(U_2015,bool)),image(U_2014,U_2015),hAPP(fun(U_2015,U_2014),fun(U_2014,U_2015),hAPP(fun(U_2015,bool),fun(fun(U_2015,U_2014),fun(U_2014,U_2015)),hilbert_inv_into(U_2015,U_2014),U_2011),U_2012)),U_2013)) = ti(fun(U_2014,bool),U_2013)
      | ~ hBOOL(hAPP(fun(U_2014,bool),bool,hAPP(fun(U_2014,bool),fun(fun(U_2014,bool),bool),ord_less_eq(fun(U_2014,bool)),U_2013),U_2010))
      | hAPP(fun(U_2015,bool),fun(U_2014,bool),hAPP(fun(U_2015,U_2014),fun(fun(U_2015,bool),fun(U_2014,bool)),image(U_2015,U_2014),U_2012),U_2011) != ti(fun(U_2014,bool),U_2010) ),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

cnf(f_574_3,plain,
    ( hAPP(fun(U_2015,bool),fun(U_2014,bool),hAPP(fun(U_2015,U_2014),fun(fun(U_2015,bool),fun(U_2014,bool)),image(U_2015,U_2014),U_2012),hAPP(fun(U_2014,bool),fun(U_2015,bool),hAPP(fun(U_2014,U_2015),fun(fun(U_2014,bool),fun(U_2015,bool)),image(U_2014,U_2015),hAPP(fun(U_2015,U_2014),fun(U_2014,U_2015),hAPP(fun(U_2015,bool),fun(fun(U_2015,U_2014),fun(U_2014,U_2015)),hilbert_inv_into(U_2015,U_2014),U_2011),U_2012)),U_2013)) = ti(fun(U_2014,bool),U_2013)
    | ~ hBOOL(hAPP(fun(U_2014,bool),bool,hAPP(fun(U_2014,bool),fun(fun(U_2014,bool),bool),ord_less_eq(fun(U_2014,bool)),U_2013),U_2010))
    | hAPP(fun(U_2015,bool),fun(U_2014,bool),hAPP(fun(U_2015,U_2014),fun(fun(U_2015,bool),fun(U_2014,bool)),image(U_2015,U_2014),U_2012),U_2011) != ti(fun(U_2014,bool),U_2010) ),
    inference(clausify,[status(thm)],[f_574_2]) ).

fof(f_575_1,plain,
    ! [X_b,X_a,A_1,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F)),A_1)) = ti(fun(X_a,bool),A_1)
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) != top_top(fun(X_a,bool)) ),
    inference(fof_nnf,[status(thm)],[fact_485_image__surj__f__inv__f]) ).

fof(f_575_2,plain,
    ! [U_2019,U_2018,U_2017,U_2016] :
      ( hAPP(fun(U_2019,bool),fun(U_2018,bool),hAPP(fun(U_2019,U_2018),fun(fun(U_2019,bool),fun(U_2018,bool)),image(U_2019,U_2018),U_2016),hAPP(fun(U_2018,bool),fun(U_2019,bool),hAPP(fun(U_2018,U_2019),fun(fun(U_2018,bool),fun(U_2019,bool)),image(U_2018,U_2019),hAPP(fun(U_2019,U_2018),fun(U_2018,U_2019),hAPP(fun(U_2019,bool),fun(fun(U_2019,U_2018),fun(U_2018,U_2019)),hilbert_inv_into(U_2019,U_2018),top_top(fun(U_2019,bool))),U_2016)),U_2017)) = ti(fun(U_2018,bool),U_2017)
      | hAPP(fun(U_2019,bool),fun(U_2018,bool),hAPP(fun(U_2019,U_2018),fun(fun(U_2019,bool),fun(U_2018,bool)),image(U_2019,U_2018),U_2016),top_top(fun(U_2019,bool))) != top_top(fun(U_2018,bool)) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

cnf(f_575_3,plain,
    ( hAPP(fun(U_2019,bool),fun(U_2018,bool),hAPP(fun(U_2019,U_2018),fun(fun(U_2019,bool),fun(U_2018,bool)),image(U_2019,U_2018),U_2016),hAPP(fun(U_2018,bool),fun(U_2019,bool),hAPP(fun(U_2018,U_2019),fun(fun(U_2018,bool),fun(U_2019,bool)),image(U_2018,U_2019),hAPP(fun(U_2019,U_2018),fun(U_2018,U_2019),hAPP(fun(U_2019,bool),fun(fun(U_2019,U_2018),fun(U_2018,U_2019)),hilbert_inv_into(U_2019,U_2018),top_top(fun(U_2019,bool))),U_2016)),U_2017)) = ti(fun(U_2018,bool),U_2017)
    | hAPP(fun(U_2019,bool),fun(U_2018,bool),hAPP(fun(U_2019,U_2018),fun(fun(U_2019,bool),fun(U_2018,bool)),image(U_2019,U_2018),U_2016),top_top(fun(U_2019,bool))) != top_top(fun(U_2018,bool)) ),
    inference(clausify,[status(thm)],[f_575_2]) ).

fof(f_576_1,plain,
    ! [X_b,X_a,Y_1,F] :
      ( hAPP(X_b,X_a,F,hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F),Y_1)) = ti(X_a,Y_1)
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) != top_top(fun(X_a,bool)) ),
    inference(fof_nnf,[status(thm)],[fact_486_surj__f__inv__f]) ).

fof(f_576_2,plain,
    ! [U_2023,U_2022,U_2021,U_2020] :
      ( hAPP(U_2023,U_2022,U_2020,hAPP(U_2022,U_2023,hAPP(fun(U_2023,U_2022),fun(U_2022,U_2023),hAPP(fun(U_2023,bool),fun(fun(U_2023,U_2022),fun(U_2022,U_2023)),hilbert_inv_into(U_2023,U_2022),top_top(fun(U_2023,bool))),U_2020),U_2021)) = ti(U_2022,U_2021)
      | hAPP(fun(U_2023,bool),fun(U_2022,bool),hAPP(fun(U_2023,U_2022),fun(fun(U_2023,bool),fun(U_2022,bool)),image(U_2023,U_2022),U_2020),top_top(fun(U_2023,bool))) != top_top(fun(U_2022,bool)) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

cnf(f_576_3,plain,
    ( hAPP(U_2023,U_2022,U_2020,hAPP(U_2022,U_2023,hAPP(fun(U_2023,U_2022),fun(U_2022,U_2023),hAPP(fun(U_2023,bool),fun(fun(U_2023,U_2022),fun(U_2022,U_2023)),hilbert_inv_into(U_2023,U_2022),top_top(fun(U_2023,bool))),U_2020),U_2021)) = ti(U_2022,U_2021)
    | hAPP(fun(U_2023,bool),fun(U_2022,bool),hAPP(fun(U_2023,U_2022),fun(fun(U_2023,bool),fun(U_2022,bool)),image(U_2023,U_2022),U_2020),top_top(fun(U_2023,bool))) != top_top(fun(U_2022,bool)) ),
    inference(clausify,[status(thm)],[f_576_2]) ).

fof(f_577_1,plain,
    ! [X_b,X_a,F] :
      ( ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
        | ? [X_1] : hAPP(X_b,X_a,F,hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F),X_1)) != ti(X_a,X_1) )
      & ( ! [X_1] : hAPP(X_b,X_a,F,hAPP(X_a,X_b,hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F),X_1)) = ti(X_a,X_1)
        | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) != top_top(fun(X_a,bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_487_surj__iff__all]) ).

fof(f_577_2,plain,
    ! [U_2028,U_2027,U_2026] :
      ( ( hAPP(fun(U_2028,bool),fun(U_2027,bool),hAPP(fun(U_2028,U_2027),fun(fun(U_2028,bool),fun(U_2027,bool)),image(U_2028,U_2027),U_2026),top_top(fun(U_2028,bool))) = top_top(fun(U_2027,bool))
        | ? [U_2025] : hAPP(U_2028,U_2027,U_2026,hAPP(U_2027,U_2028,hAPP(fun(U_2028,U_2027),fun(U_2027,U_2028),hAPP(fun(U_2028,bool),fun(fun(U_2028,U_2027),fun(U_2027,U_2028)),hilbert_inv_into(U_2028,U_2027),top_top(fun(U_2028,bool))),U_2026),U_2025)) != ti(U_2027,U_2025) )
      & ( ! [U_2024] : hAPP(U_2028,U_2027,U_2026,hAPP(U_2027,U_2028,hAPP(fun(U_2028,U_2027),fun(U_2027,U_2028),hAPP(fun(U_2028,bool),fun(fun(U_2028,U_2027),fun(U_2027,U_2028)),hilbert_inv_into(U_2028,U_2027),top_top(fun(U_2028,bool))),U_2026),U_2024)) = ti(U_2027,U_2024)
        | hAPP(fun(U_2028,bool),fun(U_2027,bool),hAPP(fun(U_2028,U_2027),fun(fun(U_2028,bool),fun(U_2027,bool)),image(U_2028,U_2027),U_2026),top_top(fun(U_2028,bool))) != top_top(fun(U_2027,bool)) ) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

fof(f_577_3,plain,
    ( ! [U_2034,U_2032,U_2030] :
        ( hAPP(fun(U_2034,bool),fun(U_2032,bool),hAPP(fun(U_2034,U_2032),fun(fun(U_2034,bool),fun(U_2032,bool)),image(U_2034,U_2032),U_2030),top_top(fun(U_2034,bool))) = top_top(fun(U_2032,bool))
        | ? [U_2025] : hAPP(U_2034,U_2032,U_2030,hAPP(U_2032,U_2034,hAPP(fun(U_2034,U_2032),fun(U_2032,U_2034),hAPP(fun(U_2034,bool),fun(fun(U_2034,U_2032),fun(U_2032,U_2034)),hilbert_inv_into(U_2034,U_2032),top_top(fun(U_2034,bool))),U_2030),U_2025)) != ti(U_2032,U_2025) )
    & ! [U_2033,U_2031,U_2029] :
        ( ! [U_2024] : hAPP(U_2033,U_2031,U_2029,hAPP(U_2031,U_2033,hAPP(fun(U_2033,U_2031),fun(U_2031,U_2033),hAPP(fun(U_2033,bool),fun(fun(U_2033,U_2031),fun(U_2031,U_2033)),hilbert_inv_into(U_2033,U_2031),top_top(fun(U_2033,bool))),U_2029),U_2024)) = ti(U_2031,U_2024)
        | hAPP(fun(U_2033,bool),fun(U_2031,bool),hAPP(fun(U_2033,U_2031),fun(fun(U_2033,bool),fun(U_2031,bool)),image(U_2033,U_2031),U_2029),top_top(fun(U_2033,bool))) != top_top(fun(U_2031,bool)) ) ),
    inference(miniscope,[status(thm)],[f_577_2]) ).

fof(f_577_4,plain,
    ( ! [U_2034,U_2032,U_2030] :
        ( hAPP(fun(U_2034,bool),fun(U_2032,bool),hAPP(fun(U_2034,U_2032),fun(fun(U_2034,bool),fun(U_2032,bool)),image(U_2034,U_2032),U_2030),top_top(fun(U_2034,bool))) = top_top(fun(U_2032,bool))
        | hAPP(U_2034,U_2032,U_2030,hAPP(U_2032,U_2034,hAPP(fun(U_2034,U_2032),fun(U_2032,U_2034),hAPP(fun(U_2034,bool),fun(fun(U_2034,U_2032),fun(U_2032,U_2034)),hilbert_inv_into(U_2034,U_2032),top_top(fun(U_2034,bool))),U_2030),sK114(U_2034,U_2032,U_2030))) != ti(U_2032,sK114(U_2034,U_2032,U_2030)) )
    & ! [U_2033,U_2031,U_2029] :
        ( ! [U_2024] : hAPP(U_2033,U_2031,U_2029,hAPP(U_2031,U_2033,hAPP(fun(U_2033,U_2031),fun(U_2031,U_2033),hAPP(fun(U_2033,bool),fun(fun(U_2033,U_2031),fun(U_2031,U_2033)),hilbert_inv_into(U_2033,U_2031),top_top(fun(U_2033,bool))),U_2029),U_2024)) = ti(U_2031,U_2024)
        | hAPP(fun(U_2033,bool),fun(U_2031,bool),hAPP(fun(U_2033,U_2031),fun(fun(U_2033,bool),fun(U_2031,bool)),image(U_2033,U_2031),U_2029),top_top(fun(U_2033,bool))) != top_top(fun(U_2031,bool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_2025,sK114(U_2034,U_2032,U_2030))],[f_577_3]) ).

cnf(f_577_5,plain,
    ( hAPP(U_2033,U_2031,U_2029,hAPP(U_2031,U_2033,hAPP(fun(U_2033,U_2031),fun(U_2031,U_2033),hAPP(fun(U_2033,bool),fun(fun(U_2033,U_2031),fun(U_2031,U_2033)),hilbert_inv_into(U_2033,U_2031),top_top(fun(U_2033,bool))),U_2029),U_2024)) = ti(U_2031,U_2024)
    | hAPP(fun(U_2033,bool),fun(U_2031,bool),hAPP(fun(U_2033,U_2031),fun(fun(U_2033,bool),fun(U_2031,bool)),image(U_2033,U_2031),U_2029),top_top(fun(U_2033,bool))) != top_top(fun(U_2031,bool)) ),
    inference(clausify,[status(thm)],[f_577_4]) ).

cnf(f_577_6,plain,
    ( hAPP(fun(U_2034,bool),fun(U_2032,bool),hAPP(fun(U_2034,U_2032),fun(fun(U_2034,bool),fun(U_2032,bool)),image(U_2034,U_2032),U_2030),top_top(fun(U_2034,bool))) = top_top(fun(U_2032,bool))
    | hAPP(U_2034,U_2032,U_2030,hAPP(U_2032,U_2034,hAPP(fun(U_2034,U_2032),fun(U_2032,U_2034),hAPP(fun(U_2034,bool),fun(fun(U_2034,U_2032),fun(U_2032,U_2034)),hilbert_inv_into(U_2034,U_2032),top_top(fun(U_2034,bool))),U_2030),sK114(U_2034,U_2032,U_2030))) != ti(U_2032,sK114(U_2034,U_2032,U_2030)) ),
    inference(clausify,[status(thm)],[f_577_4]) ).

fof(f_578_1,plain,
    ! [X_a,X_b,A_1,F,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B)) ),
    inference(fof_nnf,[status(thm)],[fact_488_inj__on__strict__subset]) ).

fof(f_578_2,plain,
    ! [U_2039,U_2038,U_2037,U_2036,U_2035] :
      ( hBOOL(hAPP(fun(U_2038,bool),bool,hAPP(fun(U_2038,bool),fun(fun(U_2038,bool),bool),ord_less(fun(U_2038,bool)),hAPP(fun(U_2039,bool),fun(U_2038,bool),hAPP(fun(U_2039,U_2038),fun(fun(U_2039,bool),fun(U_2038,bool)),image(U_2039,U_2038),U_2036),U_2037)),hAPP(fun(U_2039,bool),fun(U_2038,bool),hAPP(fun(U_2039,U_2038),fun(fun(U_2039,bool),fun(U_2038,bool)),image(U_2039,U_2038),U_2036),U_2035)))
      | ~ hBOOL(hAPP(fun(U_2039,bool),bool,hAPP(fun(U_2039,bool),fun(fun(U_2039,bool),bool),ord_less(fun(U_2039,bool)),U_2037),U_2035))
      | ~ hBOOL(hAPP(fun(U_2039,bool),bool,hAPP(fun(U_2039,U_2038),fun(fun(U_2039,bool),bool),inj_on(U_2039,U_2038),U_2036),U_2035)) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

cnf(f_578_3,plain,
    ( hBOOL(hAPP(fun(U_2038,bool),bool,hAPP(fun(U_2038,bool),fun(fun(U_2038,bool),bool),ord_less(fun(U_2038,bool)),hAPP(fun(U_2039,bool),fun(U_2038,bool),hAPP(fun(U_2039,U_2038),fun(fun(U_2039,bool),fun(U_2038,bool)),image(U_2039,U_2038),U_2036),U_2037)),hAPP(fun(U_2039,bool),fun(U_2038,bool),hAPP(fun(U_2039,U_2038),fun(fun(U_2039,bool),fun(U_2038,bool)),image(U_2039,U_2038),U_2036),U_2035)))
    | ~ hBOOL(hAPP(fun(U_2039,bool),bool,hAPP(fun(U_2039,bool),fun(fun(U_2039,bool),bool),ord_less(fun(U_2039,bool)),U_2037),U_2035))
    | ~ hBOOL(hAPP(fun(U_2039,bool),bool,hAPP(fun(U_2039,U_2038),fun(fun(U_2039,bool),bool),inj_on(U_2039,U_2038),U_2036),U_2035)) ),
    inference(clausify,[status(thm)],[f_578_2]) ).

fof(f_579_1,plain,
    ! [A_1,K] :
      ( A_1 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_1)))
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_1))))) ),
    inference(fof_nnf,[status(thm)],[fact_489_subset__card__intvl__is__intvl]) ).

fof(f_579_2,plain,
    ! [U_2041,U_2040] :
      ( U_2041 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_2040),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2040),hAPP(fun(nat,bool),nat,finite_card(nat),U_2041)))
      | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_2041),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_2040),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2040),hAPP(fun(nat,bool),nat,finite_card(nat),U_2041))))) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

cnf(f_579_3,plain,
    ( U_2041 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_2040),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2040),hAPP(fun(nat,bool),nat,finite_card(nat),U_2041)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_2041),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_2040),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2040),hAPP(fun(nat,bool),nat,finite_card(nat),U_2041))))) ),
    inference(clausify,[status(thm)],[f_579_2]) ).

fof(f_580_1,plain,
    ! [X_c,X_a,X_b,F,G] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),combb(X_a,X_c,X_b),F),G)),top_top(fun(X_b,bool)))))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),top_top(fun(X_b,bool))))) ),
    inference(fof_nnf,[status(thm)],[fact_490_finite__range__imageI]) ).

fof(f_580_2,plain,
    ! [U_2046,U_2045,U_2044,U_2043,U_2042] :
      ( hBOOL(hAPP(fun(U_2046,bool),bool,finite_finite_1(U_2046),hAPP(fun(U_2044,bool),fun(U_2046,bool),hAPP(fun(U_2044,U_2046),fun(fun(U_2044,bool),fun(U_2046,bool)),image(U_2044,U_2046),hAPP(fun(U_2044,U_2045),fun(U_2044,U_2046),hAPP(fun(U_2045,U_2046),fun(fun(U_2044,U_2045),fun(U_2044,U_2046)),combb(U_2045,U_2046,U_2044),U_2043),U_2042)),top_top(fun(U_2044,bool)))))
      | ~ hBOOL(hAPP(fun(U_2045,bool),bool,finite_finite_1(U_2045),hAPP(fun(U_2044,bool),fun(U_2045,bool),hAPP(fun(U_2044,U_2045),fun(fun(U_2044,bool),fun(U_2045,bool)),image(U_2044,U_2045),U_2042),top_top(fun(U_2044,bool))))) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

cnf(f_580_3,plain,
    ( hBOOL(hAPP(fun(U_2046,bool),bool,finite_finite_1(U_2046),hAPP(fun(U_2044,bool),fun(U_2046,bool),hAPP(fun(U_2044,U_2046),fun(fun(U_2044,bool),fun(U_2046,bool)),image(U_2044,U_2046),hAPP(fun(U_2044,U_2045),fun(U_2044,U_2046),hAPP(fun(U_2045,U_2046),fun(fun(U_2044,U_2045),fun(U_2044,U_2046)),combb(U_2045,U_2046,U_2044),U_2043),U_2042)),top_top(fun(U_2044,bool)))))
    | ~ hBOOL(hAPP(fun(U_2045,bool),bool,finite_finite_1(U_2045),hAPP(fun(U_2044,bool),fun(U_2045,bool),hAPP(fun(U_2044,U_2045),fun(fun(U_2044,bool),fun(U_2045,bool)),image(U_2044,U_2045),U_2042),top_top(fun(U_2044,bool))))) ),
    inference(clausify,[status(thm)],[f_580_2]) ).

fof(f_581_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
            & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da))) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_491_atLeastLessThan__subset__iff]) ).

fof(f_581_2,plain,
    ! [U_2051] :
      ( ! [U_2050,U_2049,U_2048,U_2047] :
          ( ( hBOOL(hAPP(U_2051,bool,hAPP(U_2051,fun(U_2051,bool),ord_less_eq(U_2051),U_2049),U_2047))
            & hBOOL(hAPP(U_2051,bool,hAPP(U_2051,fun(U_2051,bool),ord_less_eq(U_2051),U_2048),U_2050)) )
          | hBOOL(hAPP(U_2051,bool,hAPP(U_2051,fun(U_2051,bool),ord_less_eq(U_2051),U_2049),U_2050))
          | ~ hBOOL(hAPP(fun(U_2051,bool),bool,hAPP(fun(U_2051,bool),fun(fun(U_2051,bool),bool),ord_less_eq(fun(U_2051,bool)),hAPP(U_2051,fun(U_2051,bool),hAPP(U_2051,fun(U_2051,fun(U_2051,bool)),ord_atLeastLessThan(U_2051),U_2050),U_2049)),hAPP(U_2051,fun(U_2051,bool),hAPP(U_2051,fun(U_2051,fun(U_2051,bool)),ord_atLeastLessThan(U_2051),U_2048),U_2047))) )
      | ~ linorder(U_2051) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

cnf(f_581_3,plain,
    ( hBOOL(hAPP(U_2051,bool,hAPP(U_2051,fun(U_2051,bool),ord_less_eq(U_2051),U_2048),U_2050))
    | hBOOL(hAPP(U_2051,bool,hAPP(U_2051,fun(U_2051,bool),ord_less_eq(U_2051),U_2049),U_2050))
    | ~ hBOOL(hAPP(fun(U_2051,bool),bool,hAPP(fun(U_2051,bool),fun(fun(U_2051,bool),bool),ord_less_eq(fun(U_2051,bool)),hAPP(U_2051,fun(U_2051,bool),hAPP(U_2051,fun(U_2051,fun(U_2051,bool)),ord_atLeastLessThan(U_2051),U_2050),U_2049)),hAPP(U_2051,fun(U_2051,bool),hAPP(U_2051,fun(U_2051,fun(U_2051,bool)),ord_atLeastLessThan(U_2051),U_2048),U_2047)))
    | ~ linorder(U_2051) ),
    inference(clausify,[status(thm)],[f_581_2]) ).

cnf(f_581_4,plain,
    ( hBOOL(hAPP(U_2051,bool,hAPP(U_2051,fun(U_2051,bool),ord_less_eq(U_2051),U_2049),U_2047))
    | hBOOL(hAPP(U_2051,bool,hAPP(U_2051,fun(U_2051,bool),ord_less_eq(U_2051),U_2049),U_2050))
    | ~ hBOOL(hAPP(fun(U_2051,bool),bool,hAPP(fun(U_2051,bool),fun(fun(U_2051,bool),bool),ord_less_eq(fun(U_2051,bool)),hAPP(U_2051,fun(U_2051,bool),hAPP(U_2051,fun(U_2051,fun(U_2051,bool)),ord_atLeastLessThan(U_2051),U_2050),U_2049)),hAPP(U_2051,fun(U_2051,bool),hAPP(U_2051,fun(U_2051,fun(U_2051,bool)),ord_atLeastLessThan(U_2051),U_2048),U_2047)))
    | ~ linorder(U_2051) ),
    inference(clausify,[status(thm)],[f_581_2]) ).

fof(f_582_1,plain,
    ! [X_a,X_b,F,A_1,B] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
    inference(fof_nnf,[status(thm)],[fact_492_funcset__image]) ).

fof(f_582_2,plain,
    ! [U_2056,U_2055,U_2054,U_2053,U_2052] :
      ( hBOOL(hAPP(fun(U_2055,bool),bool,hAPP(fun(U_2055,bool),fun(fun(U_2055,bool),bool),ord_less_eq(fun(U_2055,bool)),hAPP(fun(U_2056,bool),fun(U_2055,bool),hAPP(fun(U_2056,U_2055),fun(fun(U_2056,bool),fun(U_2055,bool)),image(U_2056,U_2055),U_2054),U_2053)),U_2052))
      | ~ hBOOL(hAPP(fun(fun(U_2056,U_2055),bool),bool,hAPP(fun(U_2056,U_2055),fun(fun(fun(U_2056,U_2055),bool),bool),member(fun(U_2056,U_2055)),U_2054),hAPP(fun(U_2056,fun(U_2055,bool)),fun(fun(U_2056,U_2055),bool),hAPP(fun(U_2056,bool),fun(fun(U_2056,fun(U_2055,bool)),fun(fun(U_2056,U_2055),bool)),pi(U_2056,U_2055),U_2053),hAPP(fun(U_2055,bool),fun(U_2056,fun(U_2055,bool)),combk(fun(U_2055,bool),U_2056),U_2052)))) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

cnf(f_582_3,plain,
    ( hBOOL(hAPP(fun(U_2055,bool),bool,hAPP(fun(U_2055,bool),fun(fun(U_2055,bool),bool),ord_less_eq(fun(U_2055,bool)),hAPP(fun(U_2056,bool),fun(U_2055,bool),hAPP(fun(U_2056,U_2055),fun(fun(U_2056,bool),fun(U_2055,bool)),image(U_2056,U_2055),U_2054),U_2053)),U_2052))
    | ~ hBOOL(hAPP(fun(fun(U_2056,U_2055),bool),bool,hAPP(fun(U_2056,U_2055),fun(fun(fun(U_2056,U_2055),bool),bool),member(fun(U_2056,U_2055)),U_2054),hAPP(fun(U_2056,fun(U_2055,bool)),fun(fun(U_2056,U_2055),bool),hAPP(fun(U_2056,bool),fun(fun(U_2056,fun(U_2055,bool)),fun(fun(U_2056,U_2055),bool)),pi(U_2056,U_2055),U_2053),hAPP(fun(U_2055,bool),fun(U_2056,fun(U_2055,bool)),combk(fun(U_2055,bool),U_2056),U_2052)))) ),
    inference(clausify,[status(thm)],[f_582_2]) ).

fof(f_583_1,plain,
    ! [X_a,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_493_finite__surj__inj]) ).

fof(f_583_2,plain,
    ! [U_2059,U_2058,U_2057] :
      ( hBOOL(hAPP(fun(U_2059,bool),bool,hAPP(fun(U_2059,U_2059),fun(fun(U_2059,bool),bool),inj_on(U_2059,U_2059),U_2058),U_2057))
      | ~ hBOOL(hAPP(fun(U_2059,bool),bool,hAPP(fun(U_2059,bool),fun(fun(U_2059,bool),bool),ord_less_eq(fun(U_2059,bool)),U_2057),hAPP(fun(U_2059,bool),fun(U_2059,bool),hAPP(fun(U_2059,U_2059),fun(fun(U_2059,bool),fun(U_2059,bool)),image(U_2059,U_2059),U_2058),U_2057)))
      | ~ hBOOL(hAPP(fun(U_2059,bool),bool,finite_finite_1(U_2059),U_2057)) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

cnf(f_583_3,plain,
    ( hBOOL(hAPP(fun(U_2059,bool),bool,hAPP(fun(U_2059,U_2059),fun(fun(U_2059,bool),bool),inj_on(U_2059,U_2059),U_2058),U_2057))
    | ~ hBOOL(hAPP(fun(U_2059,bool),bool,hAPP(fun(U_2059,bool),fun(fun(U_2059,bool),bool),ord_less_eq(fun(U_2059,bool)),U_2057),hAPP(fun(U_2059,bool),fun(U_2059,bool),hAPP(fun(U_2059,U_2059),fun(fun(U_2059,bool),fun(U_2059,bool)),image(U_2059,U_2059),U_2058),U_2057)))
    | ~ hBOOL(hAPP(fun(U_2059,bool),bool,finite_finite_1(U_2059),U_2057)) ),
    inference(clausify,[status(thm)],[f_583_2]) ).

fof(f_584_1,plain,
    ! [X_a,F,A_1] :
      ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1) = ti(fun(X_a,bool),A_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1)),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_494_endo__inj__surj]) ).

fof(f_584_2,plain,
    ! [U_2062,U_2061,U_2060] :
      ( hAPP(fun(U_2062,bool),fun(U_2062,bool),hAPP(fun(U_2062,U_2062),fun(fun(U_2062,bool),fun(U_2062,bool)),image(U_2062,U_2062),U_2061),U_2060) = ti(fun(U_2062,bool),U_2060)
      | ~ hBOOL(hAPP(fun(U_2062,bool),bool,hAPP(fun(U_2062,U_2062),fun(fun(U_2062,bool),bool),inj_on(U_2062,U_2062),U_2061),U_2060))
      | ~ hBOOL(hAPP(fun(U_2062,bool),bool,hAPP(fun(U_2062,bool),fun(fun(U_2062,bool),bool),ord_less_eq(fun(U_2062,bool)),hAPP(fun(U_2062,bool),fun(U_2062,bool),hAPP(fun(U_2062,U_2062),fun(fun(U_2062,bool),fun(U_2062,bool)),image(U_2062,U_2062),U_2061),U_2060)),U_2060))
      | ~ hBOOL(hAPP(fun(U_2062,bool),bool,finite_finite_1(U_2062),U_2060)) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

cnf(f_584_3,plain,
    ( hAPP(fun(U_2062,bool),fun(U_2062,bool),hAPP(fun(U_2062,U_2062),fun(fun(U_2062,bool),fun(U_2062,bool)),image(U_2062,U_2062),U_2061),U_2060) = ti(fun(U_2062,bool),U_2060)
    | ~ hBOOL(hAPP(fun(U_2062,bool),bool,hAPP(fun(U_2062,U_2062),fun(fun(U_2062,bool),bool),inj_on(U_2062,U_2062),U_2061),U_2060))
    | ~ hBOOL(hAPP(fun(U_2062,bool),bool,hAPP(fun(U_2062,bool),fun(fun(U_2062,bool),bool),ord_less_eq(fun(U_2062,bool)),hAPP(fun(U_2062,bool),fun(U_2062,bool),hAPP(fun(U_2062,U_2062),fun(fun(U_2062,bool),fun(U_2062,bool)),image(U_2062,U_2062),U_2061),U_2060)),U_2060))
    | ~ hBOOL(hAPP(fun(U_2062,bool),bool,finite_finite_1(U_2062),U_2060)) ),
    inference(clausify,[status(thm)],[f_584_2]) ).

fof(f_585_1,plain,
    ! [X_a,F] :
      ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),top_top(fun(X_a,bool))) = top_top(fun(X_a,bool))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),top_top(fun(X_a,bool))))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_495_finite__UNIV__inj__surj]) ).

fof(f_585_2,plain,
    ! [U_2064,U_2063] :
      ( hAPP(fun(U_2064,bool),fun(U_2064,bool),hAPP(fun(U_2064,U_2064),fun(fun(U_2064,bool),fun(U_2064,bool)),image(U_2064,U_2064),U_2063),top_top(fun(U_2064,bool))) = top_top(fun(U_2064,bool))
      | ~ hBOOL(hAPP(fun(U_2064,bool),bool,hAPP(fun(U_2064,U_2064),fun(fun(U_2064,bool),bool),inj_on(U_2064,U_2064),U_2063),top_top(fun(U_2064,bool))))
      | ~ hBOOL(hAPP(fun(U_2064,bool),bool,finite_finite_1(U_2064),top_top(fun(U_2064,bool)))) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ! [U_2064] :
      ( ! [U_2063] :
          ( hAPP(fun(U_2064,bool),fun(U_2064,bool),hAPP(fun(U_2064,U_2064),fun(fun(U_2064,bool),fun(U_2064,bool)),image(U_2064,U_2064),U_2063),top_top(fun(U_2064,bool))) = top_top(fun(U_2064,bool))
          | ~ hBOOL(hAPP(fun(U_2064,bool),bool,hAPP(fun(U_2064,U_2064),fun(fun(U_2064,bool),bool),inj_on(U_2064,U_2064),U_2063),top_top(fun(U_2064,bool)))) )
      | ~ hBOOL(hAPP(fun(U_2064,bool),bool,finite_finite_1(U_2064),top_top(fun(U_2064,bool)))) ),
    inference(miniscope,[status(thm)],[f_585_2]) ).

cnf(f_585_4,plain,
    ( hAPP(fun(U_2064,bool),fun(U_2064,bool),hAPP(fun(U_2064,U_2064),fun(fun(U_2064,bool),fun(U_2064,bool)),image(U_2064,U_2064),U_2063),top_top(fun(U_2064,bool))) = top_top(fun(U_2064,bool))
    | ~ hBOOL(hAPP(fun(U_2064,bool),bool,hAPP(fun(U_2064,U_2064),fun(fun(U_2064,bool),bool),inj_on(U_2064,U_2064),U_2063),top_top(fun(U_2064,bool))))
    | ~ hBOOL(hAPP(fun(U_2064,bool),bool,finite_finite_1(U_2064),top_top(fun(U_2064,bool)))) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

fof(f_586_1,plain,
    ! [X_a,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),top_top(fun(X_a,bool))))
      | hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),top_top(fun(X_a,bool))) != top_top(fun(X_a,bool))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_496_finite__UNIV__surj__inj]) ).

fof(f_586_2,plain,
    ! [U_2066,U_2065] :
      ( hBOOL(hAPP(fun(U_2066,bool),bool,hAPP(fun(U_2066,U_2066),fun(fun(U_2066,bool),bool),inj_on(U_2066,U_2066),U_2065),top_top(fun(U_2066,bool))))
      | hAPP(fun(U_2066,bool),fun(U_2066,bool),hAPP(fun(U_2066,U_2066),fun(fun(U_2066,bool),fun(U_2066,bool)),image(U_2066,U_2066),U_2065),top_top(fun(U_2066,bool))) != top_top(fun(U_2066,bool))
      | ~ hBOOL(hAPP(fun(U_2066,bool),bool,finite_finite_1(U_2066),top_top(fun(U_2066,bool)))) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ! [U_2066] :
      ( ! [U_2065] :
          ( hBOOL(hAPP(fun(U_2066,bool),bool,hAPP(fun(U_2066,U_2066),fun(fun(U_2066,bool),bool),inj_on(U_2066,U_2066),U_2065),top_top(fun(U_2066,bool))))
          | hAPP(fun(U_2066,bool),fun(U_2066,bool),hAPP(fun(U_2066,U_2066),fun(fun(U_2066,bool),fun(U_2066,bool)),image(U_2066,U_2066),U_2065),top_top(fun(U_2066,bool))) != top_top(fun(U_2066,bool)) )
      | ~ hBOOL(hAPP(fun(U_2066,bool),bool,finite_finite_1(U_2066),top_top(fun(U_2066,bool)))) ),
    inference(miniscope,[status(thm)],[f_586_2]) ).

cnf(f_586_4,plain,
    ( hBOOL(hAPP(fun(U_2066,bool),bool,hAPP(fun(U_2066,U_2066),fun(fun(U_2066,bool),bool),inj_on(U_2066,U_2066),U_2065),top_top(fun(U_2066,bool))))
    | hAPP(fun(U_2066,bool),fun(U_2066,bool),hAPP(fun(U_2066,U_2066),fun(fun(U_2066,bool),fun(U_2066,bool)),image(U_2066,U_2066),U_2065),top_top(fun(U_2066,bool))) != top_top(fun(U_2066,bool))
    | ~ hBOOL(hAPP(fun(U_2066,bool),bool,finite_finite_1(U_2066),top_top(fun(U_2066,bool)))) ),
    inference(clausify,[status(thm)],[f_586_3]) ).

fof(f_587_1,plain,
    ! [X_a,X_b,A_1,B,F] :
      ( ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) )
        & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B))) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_497_inj__image__subset__iff]) ).

fof(f_587_2,plain,
    ! [U_2071,U_2070,U_2069,U_2068,U_2067] :
      ( ( ( hBOOL(hAPP(fun(U_2070,bool),bool,hAPP(fun(U_2070,bool),fun(fun(U_2070,bool),bool),ord_less_eq(fun(U_2070,bool)),hAPP(fun(U_2071,bool),fun(U_2070,bool),hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),fun(U_2070,bool)),image(U_2071,U_2070),U_2067),U_2069)),hAPP(fun(U_2071,bool),fun(U_2070,bool),hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),fun(U_2070,bool)),image(U_2071,U_2070),U_2067),U_2068)))
          | ~ hBOOL(hAPP(fun(U_2071,bool),bool,hAPP(fun(U_2071,bool),fun(fun(U_2071,bool),bool),ord_less_eq(fun(U_2071,bool)),U_2069),U_2068)) )
        & ( hBOOL(hAPP(fun(U_2071,bool),bool,hAPP(fun(U_2071,bool),fun(fun(U_2071,bool),bool),ord_less_eq(fun(U_2071,bool)),U_2069),U_2068))
          | ~ hBOOL(hAPP(fun(U_2070,bool),bool,hAPP(fun(U_2070,bool),fun(fun(U_2070,bool),bool),ord_less_eq(fun(U_2070,bool)),hAPP(fun(U_2071,bool),fun(U_2070,bool),hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),fun(U_2070,bool)),image(U_2071,U_2070),U_2067),U_2069)),hAPP(fun(U_2071,bool),fun(U_2070,bool),hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),fun(U_2070,bool)),image(U_2071,U_2070),U_2067),U_2068))) ) )
      | ~ hBOOL(hAPP(fun(U_2071,bool),bool,hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),bool),inj_on(U_2071,U_2070),U_2067),top_top(fun(U_2071,bool)))) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

cnf(f_587_3,plain,
    ( hBOOL(hAPP(fun(U_2071,bool),bool,hAPP(fun(U_2071,bool),fun(fun(U_2071,bool),bool),ord_less_eq(fun(U_2071,bool)),U_2069),U_2068))
    | ~ hBOOL(hAPP(fun(U_2070,bool),bool,hAPP(fun(U_2070,bool),fun(fun(U_2070,bool),bool),ord_less_eq(fun(U_2070,bool)),hAPP(fun(U_2071,bool),fun(U_2070,bool),hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),fun(U_2070,bool)),image(U_2071,U_2070),U_2067),U_2069)),hAPP(fun(U_2071,bool),fun(U_2070,bool),hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),fun(U_2070,bool)),image(U_2071,U_2070),U_2067),U_2068)))
    | ~ hBOOL(hAPP(fun(U_2071,bool),bool,hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),bool),inj_on(U_2071,U_2070),U_2067),top_top(fun(U_2071,bool)))) ),
    inference(clausify,[status(thm)],[f_587_2]) ).

cnf(f_587_4,plain,
    ( hBOOL(hAPP(fun(U_2070,bool),bool,hAPP(fun(U_2070,bool),fun(fun(U_2070,bool),bool),ord_less_eq(fun(U_2070,bool)),hAPP(fun(U_2071,bool),fun(U_2070,bool),hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),fun(U_2070,bool)),image(U_2071,U_2070),U_2067),U_2069)),hAPP(fun(U_2071,bool),fun(U_2070,bool),hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),fun(U_2070,bool)),image(U_2071,U_2070),U_2067),U_2068)))
    | ~ hBOOL(hAPP(fun(U_2071,bool),bool,hAPP(fun(U_2071,bool),fun(fun(U_2071,bool),bool),ord_less_eq(fun(U_2071,bool)),U_2069),U_2068))
    | ~ hBOOL(hAPP(fun(U_2071,bool),bool,hAPP(fun(U_2071,U_2070),fun(fun(U_2071,bool),bool),inj_on(U_2071,U_2070),U_2067),top_top(fun(U_2071,bool)))) ),
    inference(clausify,[status(thm)],[f_587_2]) ).

fof(f_588_1,plain,
    ! [X_b,X_a,F,A_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_498_card__image__le]) ).

fof(f_588_2,plain,
    ! [U_2075,U_2074,U_2073,U_2072] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2075,bool),nat,finite_card(U_2075),hAPP(fun(U_2074,bool),fun(U_2075,bool),hAPP(fun(U_2074,U_2075),fun(fun(U_2074,bool),fun(U_2075,bool)),image(U_2074,U_2075),U_2073),U_2072))),hAPP(fun(U_2074,bool),nat,finite_card(U_2074),U_2072)))
      | ~ hBOOL(hAPP(fun(U_2074,bool),bool,finite_finite_1(U_2074),U_2072)) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

cnf(f_588_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2075,bool),nat,finite_card(U_2075),hAPP(fun(U_2074,bool),fun(U_2075,bool),hAPP(fun(U_2074,U_2075),fun(fun(U_2074,bool),fun(U_2075,bool)),image(U_2074,U_2075),U_2073),U_2072))),hAPP(fun(U_2074,bool),nat,finite_card(U_2074),U_2072)))
    | ~ hBOOL(hAPP(fun(U_2074,bool),bool,finite_finite_1(U_2074),U_2072)) ),
    inference(clausify,[status(thm)],[f_588_2]) ).

fof(f_589_1,plain,
    ! [X_b,X_a,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
      | hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) != hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_499_eq__card__imp__inj__on]) ).

fof(f_589_2,plain,
    ! [U_2079,U_2078,U_2077,U_2076] :
      ( hBOOL(hAPP(fun(U_2078,bool),bool,hAPP(fun(U_2078,U_2079),fun(fun(U_2078,bool),bool),inj_on(U_2078,U_2079),U_2077),U_2076))
      | hAPP(fun(U_2079,bool),nat,finite_card(U_2079),hAPP(fun(U_2078,bool),fun(U_2079,bool),hAPP(fun(U_2078,U_2079),fun(fun(U_2078,bool),fun(U_2079,bool)),image(U_2078,U_2079),U_2077),U_2076)) != hAPP(fun(U_2078,bool),nat,finite_card(U_2078),U_2076)
      | ~ hBOOL(hAPP(fun(U_2078,bool),bool,finite_finite_1(U_2078),U_2076)) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

cnf(f_589_3,plain,
    ( hBOOL(hAPP(fun(U_2078,bool),bool,hAPP(fun(U_2078,U_2079),fun(fun(U_2078,bool),bool),inj_on(U_2078,U_2079),U_2077),U_2076))
    | hAPP(fun(U_2079,bool),nat,finite_card(U_2079),hAPP(fun(U_2078,bool),fun(U_2079,bool),hAPP(fun(U_2078,U_2079),fun(fun(U_2078,bool),fun(U_2079,bool)),image(U_2078,U_2079),U_2077),U_2076)) != hAPP(fun(U_2078,bool),nat,finite_card(U_2078),U_2076)
    | ~ hBOOL(hAPP(fun(U_2078,bool),bool,finite_finite_1(U_2078),U_2076)) ),
    inference(clausify,[status(thm)],[f_589_2]) ).

fof(f_590_1,plain,
    ! [X_b,X_a,F,A_1] :
      ( ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
          | hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) != hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) )
        & ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_500_inj__on__iff__eq__card]) ).

fof(f_590_2,plain,
    ! [U_2083,U_2082,U_2081,U_2080] :
      ( ( ( hBOOL(hAPP(fun(U_2082,bool),bool,hAPP(fun(U_2082,U_2083),fun(fun(U_2082,bool),bool),inj_on(U_2082,U_2083),U_2081),U_2080))
          | hAPP(fun(U_2083,bool),nat,finite_card(U_2083),hAPP(fun(U_2082,bool),fun(U_2083,bool),hAPP(fun(U_2082,U_2083),fun(fun(U_2082,bool),fun(U_2083,bool)),image(U_2082,U_2083),U_2081),U_2080)) != hAPP(fun(U_2082,bool),nat,finite_card(U_2082),U_2080) )
        & ( hAPP(fun(U_2083,bool),nat,finite_card(U_2083),hAPP(fun(U_2082,bool),fun(U_2083,bool),hAPP(fun(U_2082,U_2083),fun(fun(U_2082,bool),fun(U_2083,bool)),image(U_2082,U_2083),U_2081),U_2080)) = hAPP(fun(U_2082,bool),nat,finite_card(U_2082),U_2080)
          | ~ hBOOL(hAPP(fun(U_2082,bool),bool,hAPP(fun(U_2082,U_2083),fun(fun(U_2082,bool),bool),inj_on(U_2082,U_2083),U_2081),U_2080)) ) )
      | ~ hBOOL(hAPP(fun(U_2082,bool),bool,finite_finite_1(U_2082),U_2080)) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

cnf(f_590_3,plain,
    ( hAPP(fun(U_2083,bool),nat,finite_card(U_2083),hAPP(fun(U_2082,bool),fun(U_2083,bool),hAPP(fun(U_2082,U_2083),fun(fun(U_2082,bool),fun(U_2083,bool)),image(U_2082,U_2083),U_2081),U_2080)) = hAPP(fun(U_2082,bool),nat,finite_card(U_2082),U_2080)
    | ~ hBOOL(hAPP(fun(U_2082,bool),bool,hAPP(fun(U_2082,U_2083),fun(fun(U_2082,bool),bool),inj_on(U_2082,U_2083),U_2081),U_2080))
    | ~ hBOOL(hAPP(fun(U_2082,bool),bool,finite_finite_1(U_2082),U_2080)) ),
    inference(clausify,[status(thm)],[f_590_2]) ).

cnf(f_590_4,plain,
    ( hBOOL(hAPP(fun(U_2082,bool),bool,hAPP(fun(U_2082,U_2083),fun(fun(U_2082,bool),bool),inj_on(U_2082,U_2083),U_2081),U_2080))
    | hAPP(fun(U_2083,bool),nat,finite_card(U_2083),hAPP(fun(U_2082,bool),fun(U_2083,bool),hAPP(fun(U_2082,U_2083),fun(fun(U_2082,bool),fun(U_2083,bool)),image(U_2082,U_2083),U_2081),U_2080)) != hAPP(fun(U_2082,bool),nat,finite_card(U_2082),U_2080)
    | ~ hBOOL(hAPP(fun(U_2082,bool),bool,finite_finite_1(U_2082),U_2080)) ),
    inference(clausify,[status(thm)],[f_590_2]) ).

fof(f_591_1,plain,
    ! [X_a,X_b,F,A_1] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),F),A_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_501_pigeonhole]) ).

fof(f_591_2,plain,
    ! [U_2087,U_2086,U_2085,U_2084] :
      ( ~ hBOOL(hAPP(fun(U_2086,bool),bool,hAPP(fun(U_2086,U_2087),fun(fun(U_2086,bool),bool),inj_on(U_2086,U_2087),U_2085),U_2084))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_2087,bool),nat,finite_card(U_2087),hAPP(fun(U_2086,bool),fun(U_2087,bool),hAPP(fun(U_2086,U_2087),fun(fun(U_2086,bool),fun(U_2087,bool)),image(U_2086,U_2087),U_2085),U_2084))),hAPP(fun(U_2086,bool),nat,finite_card(U_2086),U_2084))) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

cnf(f_591_3,plain,
    ( ~ hBOOL(hAPP(fun(U_2086,bool),bool,hAPP(fun(U_2086,U_2087),fun(fun(U_2086,bool),bool),inj_on(U_2086,U_2087),U_2085),U_2084))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_2087,bool),nat,finite_card(U_2087),hAPP(fun(U_2086,bool),fun(U_2087,bool),hAPP(fun(U_2086,U_2087),fun(fun(U_2086,bool),fun(U_2087,bool)),image(U_2086,U_2087),U_2085),U_2084))),hAPP(fun(U_2086,bool),nat,finite_card(U_2086),U_2084))) ),
    inference(clausify,[status(thm)],[f_591_2]) ).

fof(f_592_1,plain,
    ! [X_a,X_b,S,F,A_1] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),S)) = ti(fun(X_a,bool),S)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_502_inv__into__image__cancel]) ).

fof(f_592_2,plain,
    ! [U_2092,U_2091,U_2090,U_2089,U_2088] :
      ( hAPP(fun(U_2091,bool),fun(U_2092,bool),hAPP(fun(U_2091,U_2092),fun(fun(U_2091,bool),fun(U_2092,bool)),image(U_2091,U_2092),hAPP(fun(U_2092,U_2091),fun(U_2091,U_2092),hAPP(fun(U_2092,bool),fun(fun(U_2092,U_2091),fun(U_2091,U_2092)),hilbert_inv_into(U_2092,U_2091),U_2088),U_2089)),hAPP(fun(U_2092,bool),fun(U_2091,bool),hAPP(fun(U_2092,U_2091),fun(fun(U_2092,bool),fun(U_2091,bool)),image(U_2092,U_2091),U_2089),U_2090)) = ti(fun(U_2092,bool),U_2090)
      | ~ hBOOL(hAPP(fun(U_2092,bool),bool,hAPP(fun(U_2092,bool),fun(fun(U_2092,bool),bool),ord_less_eq(fun(U_2092,bool)),U_2090),U_2088))
      | ~ hBOOL(hAPP(fun(U_2092,bool),bool,hAPP(fun(U_2092,U_2091),fun(fun(U_2092,bool),bool),inj_on(U_2092,U_2091),U_2089),U_2088)) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

cnf(f_592_3,plain,
    ( hAPP(fun(U_2091,bool),fun(U_2092,bool),hAPP(fun(U_2091,U_2092),fun(fun(U_2091,bool),fun(U_2092,bool)),image(U_2091,U_2092),hAPP(fun(U_2092,U_2091),fun(U_2091,U_2092),hAPP(fun(U_2092,bool),fun(fun(U_2092,U_2091),fun(U_2091,U_2092)),hilbert_inv_into(U_2092,U_2091),U_2088),U_2089)),hAPP(fun(U_2092,bool),fun(U_2091,bool),hAPP(fun(U_2092,U_2091),fun(fun(U_2092,bool),fun(U_2091,bool)),image(U_2092,U_2091),U_2089),U_2090)) = ti(fun(U_2092,bool),U_2090)
    | ~ hBOOL(hAPP(fun(U_2092,bool),bool,hAPP(fun(U_2092,bool),fun(fun(U_2092,bool),bool),ord_less_eq(fun(U_2092,bool)),U_2090),U_2088))
    | ~ hBOOL(hAPP(fun(U_2092,bool),bool,hAPP(fun(U_2092,U_2091),fun(fun(U_2092,bool),bool),inj_on(U_2092,U_2091),U_2089),U_2088)) ),
    inference(clausify,[status(thm)],[f_592_2]) ).

fof(f_593_1,plain,
    ! [X_a,X_b,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F)),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_503_inj__on__inv__into]) ).

fof(f_593_2,plain,
    ! [U_2097,U_2096,U_2095,U_2094,U_2093] :
      ( hBOOL(hAPP(fun(U_2097,bool),bool,hAPP(fun(U_2097,U_2096),fun(fun(U_2097,bool),bool),inj_on(U_2097,U_2096),hAPP(fun(U_2096,U_2097),fun(U_2097,U_2096),hAPP(fun(U_2096,bool),fun(fun(U_2096,U_2097),fun(U_2097,U_2096)),hilbert_inv_into(U_2096,U_2097),U_2093),U_2094)),U_2095))
      | ~ hBOOL(hAPP(fun(U_2097,bool),bool,hAPP(fun(U_2097,bool),fun(fun(U_2097,bool),bool),ord_less_eq(fun(U_2097,bool)),U_2095),hAPP(fun(U_2096,bool),fun(U_2097,bool),hAPP(fun(U_2096,U_2097),fun(fun(U_2096,bool),fun(U_2097,bool)),image(U_2096,U_2097),U_2094),U_2093))) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

cnf(f_593_3,plain,
    ( hBOOL(hAPP(fun(U_2097,bool),bool,hAPP(fun(U_2097,U_2096),fun(fun(U_2097,bool),bool),inj_on(U_2097,U_2096),hAPP(fun(U_2096,U_2097),fun(U_2097,U_2096),hAPP(fun(U_2096,bool),fun(fun(U_2096,U_2097),fun(U_2097,U_2096)),hilbert_inv_into(U_2096,U_2097),U_2093),U_2094)),U_2095))
    | ~ hBOOL(hAPP(fun(U_2097,bool),bool,hAPP(fun(U_2097,bool),fun(fun(U_2097,bool),bool),ord_less_eq(fun(U_2097,bool)),U_2095),hAPP(fun(U_2096,bool),fun(U_2097,bool),hAPP(fun(U_2096,U_2097),fun(fun(U_2096,bool),fun(U_2097,bool)),image(U_2096,U_2097),U_2094),U_2093))) ),
    inference(clausify,[status(thm)],[f_593_2]) ).

fof(f_594_1,plain,
    ! [X_b,X_a,F] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F)),top_top(fun(X_a,bool))))
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) != top_top(fun(X_a,bool)) ),
    inference(fof_nnf,[status(thm)],[fact_504_surj__imp__inj__inv]) ).

fof(f_594_2,plain,
    ! [U_2100,U_2099,U_2098] :
      ( hBOOL(hAPP(fun(U_2099,bool),bool,hAPP(fun(U_2099,U_2100),fun(fun(U_2099,bool),bool),inj_on(U_2099,U_2100),hAPP(fun(U_2100,U_2099),fun(U_2099,U_2100),hAPP(fun(U_2100,bool),fun(fun(U_2100,U_2099),fun(U_2099,U_2100)),hilbert_inv_into(U_2100,U_2099),top_top(fun(U_2100,bool))),U_2098)),top_top(fun(U_2099,bool))))
      | hAPP(fun(U_2100,bool),fun(U_2099,bool),hAPP(fun(U_2100,U_2099),fun(fun(U_2100,bool),fun(U_2099,bool)),image(U_2100,U_2099),U_2098),top_top(fun(U_2100,bool))) != top_top(fun(U_2099,bool)) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

cnf(f_594_3,plain,
    ( hBOOL(hAPP(fun(U_2099,bool),bool,hAPP(fun(U_2099,U_2100),fun(fun(U_2099,bool),bool),inj_on(U_2099,U_2100),hAPP(fun(U_2100,U_2099),fun(U_2099,U_2100),hAPP(fun(U_2100,bool),fun(fun(U_2100,U_2099),fun(U_2099,U_2100)),hilbert_inv_into(U_2100,U_2099),top_top(fun(U_2100,bool))),U_2098)),top_top(fun(U_2099,bool))))
    | hAPP(fun(U_2100,bool),fun(U_2099,bool),hAPP(fun(U_2100,U_2099),fun(fun(U_2100,bool),fun(U_2099,bool)),image(U_2100,U_2099),U_2098),top_top(fun(U_2100,bool))) != top_top(fun(U_2099,bool)) ),
    inference(clausify,[status(thm)],[f_594_2]) ).

fof(f_595_1,plain,
    ! [X_a,X_b,X_4,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),X_4)) = ti(fun(X_a,bool),X_4)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_505_inv__image__comp]) ).

fof(f_595_2,plain,
    ! [U_2104,U_2103,U_2102,U_2101] :
      ( hAPP(fun(U_2103,bool),fun(U_2104,bool),hAPP(fun(U_2103,U_2104),fun(fun(U_2103,bool),fun(U_2104,bool)),image(U_2103,U_2104),hAPP(fun(U_2104,U_2103),fun(U_2103,U_2104),hAPP(fun(U_2104,bool),fun(fun(U_2104,U_2103),fun(U_2103,U_2104)),hilbert_inv_into(U_2104,U_2103),top_top(fun(U_2104,bool))),U_2101)),hAPP(fun(U_2104,bool),fun(U_2103,bool),hAPP(fun(U_2104,U_2103),fun(fun(U_2104,bool),fun(U_2103,bool)),image(U_2104,U_2103),U_2101),U_2102)) = ti(fun(U_2104,bool),U_2102)
      | ~ hBOOL(hAPP(fun(U_2104,bool),bool,hAPP(fun(U_2104,U_2103),fun(fun(U_2104,bool),bool),inj_on(U_2104,U_2103),U_2101),top_top(fun(U_2104,bool)))) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

cnf(f_595_3,plain,
    ( hAPP(fun(U_2103,bool),fun(U_2104,bool),hAPP(fun(U_2103,U_2104),fun(fun(U_2103,bool),fun(U_2104,bool)),image(U_2103,U_2104),hAPP(fun(U_2104,U_2103),fun(U_2103,U_2104),hAPP(fun(U_2104,bool),fun(fun(U_2104,U_2103),fun(U_2103,U_2104)),hilbert_inv_into(U_2104,U_2103),top_top(fun(U_2104,bool))),U_2101)),hAPP(fun(U_2104,bool),fun(U_2103,bool),hAPP(fun(U_2104,U_2103),fun(fun(U_2104,bool),fun(U_2103,bool)),image(U_2104,U_2103),U_2101),U_2102)) = ti(fun(U_2104,bool),U_2102)
    | ~ hBOOL(hAPP(fun(U_2104,bool),bool,hAPP(fun(U_2104,U_2103),fun(fun(U_2104,bool),bool),inj_on(U_2104,U_2103),U_2101),top_top(fun(U_2104,bool)))) ),
    inference(clausify,[status(thm)],[f_595_2]) ).

fof(f_596_1,plain,
    ! [X_a,X_b,A_1,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = ti(fun(X_a,bool),A_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_506_image__inv__f__f]) ).

fof(f_596_2,plain,
    ! [U_2108,U_2107,U_2106,U_2105] :
      ( hAPP(fun(U_2107,bool),fun(U_2108,bool),hAPP(fun(U_2107,U_2108),fun(fun(U_2107,bool),fun(U_2108,bool)),image(U_2107,U_2108),hAPP(fun(U_2108,U_2107),fun(U_2107,U_2108),hAPP(fun(U_2108,bool),fun(fun(U_2108,U_2107),fun(U_2107,U_2108)),hilbert_inv_into(U_2108,U_2107),top_top(fun(U_2108,bool))),U_2105)),hAPP(fun(U_2108,bool),fun(U_2107,bool),hAPP(fun(U_2108,U_2107),fun(fun(U_2108,bool),fun(U_2107,bool)),image(U_2108,U_2107),U_2105),U_2106)) = ti(fun(U_2108,bool),U_2106)
      | ~ hBOOL(hAPP(fun(U_2108,bool),bool,hAPP(fun(U_2108,U_2107),fun(fun(U_2108,bool),bool),inj_on(U_2108,U_2107),U_2105),top_top(fun(U_2108,bool)))) ),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

cnf(f_596_3,plain,
    ( hAPP(fun(U_2107,bool),fun(U_2108,bool),hAPP(fun(U_2107,U_2108),fun(fun(U_2107,bool),fun(U_2108,bool)),image(U_2107,U_2108),hAPP(fun(U_2108,U_2107),fun(U_2107,U_2108),hAPP(fun(U_2108,bool),fun(fun(U_2108,U_2107),fun(U_2107,U_2108)),hilbert_inv_into(U_2108,U_2107),top_top(fun(U_2108,bool))),U_2105)),hAPP(fun(U_2108,bool),fun(U_2107,bool),hAPP(fun(U_2108,U_2107),fun(fun(U_2108,bool),fun(U_2107,bool)),image(U_2108,U_2107),U_2105),U_2106)) = ti(fun(U_2108,bool),U_2106)
    | ~ hBOOL(hAPP(fun(U_2108,bool),bool,hAPP(fun(U_2108,U_2107),fun(fun(U_2108,bool),bool),inj_on(U_2108,U_2107),U_2105),top_top(fun(U_2108,bool)))) ),
    inference(clausify,[status(thm)],[f_596_2]) ).

fof(f_597_1,plain,
    ! [X_a,X_b,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F)),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_507_inj__imp__surj__inv]) ).

fof(f_597_2,plain,
    ! [U_2111,U_2110,U_2109] :
      ( hAPP(fun(U_2110,bool),fun(U_2111,bool),hAPP(fun(U_2110,U_2111),fun(fun(U_2110,bool),fun(U_2111,bool)),image(U_2110,U_2111),hAPP(fun(U_2111,U_2110),fun(U_2110,U_2111),hAPP(fun(U_2111,bool),fun(fun(U_2111,U_2110),fun(U_2110,U_2111)),hilbert_inv_into(U_2111,U_2110),top_top(fun(U_2111,bool))),U_2109)),top_top(fun(U_2110,bool))) = top_top(fun(U_2111,bool))
      | ~ hBOOL(hAPP(fun(U_2111,bool),bool,hAPP(fun(U_2111,U_2110),fun(fun(U_2111,bool),bool),inj_on(U_2111,U_2110),U_2109),top_top(fun(U_2111,bool)))) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

cnf(f_597_3,plain,
    ( hAPP(fun(U_2110,bool),fun(U_2111,bool),hAPP(fun(U_2110,U_2111),fun(fun(U_2110,bool),fun(U_2111,bool)),image(U_2110,U_2111),hAPP(fun(U_2111,U_2110),fun(U_2110,U_2111),hAPP(fun(U_2111,bool),fun(fun(U_2111,U_2110),fun(U_2110,U_2111)),hilbert_inv_into(U_2111,U_2110),top_top(fun(U_2111,bool))),U_2109)),top_top(fun(U_2110,bool))) = top_top(fun(U_2111,bool))
    | ~ hBOOL(hAPP(fun(U_2111,bool),bool,hAPP(fun(U_2111,U_2110),fun(fun(U_2111,bool),bool),inj_on(U_2111,U_2110),U_2109),top_top(fun(U_2111,bool)))) ),
    inference(clausify,[status(thm)],[f_597_2]) ).

fof(f_598_1,plain,
    ! [X_a,X_b,G,B,F,A_1] :
      ( hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_b,bool),nat,finite_card(X_b),B)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),B)),A_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),G),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_508_card__bij__eq]) ).

fof(f_598_2,plain,
    ! [U_2117,U_2116,U_2115,U_2114,U_2113,U_2112] :
      ( hAPP(fun(U_2117,bool),nat,finite_card(U_2117),U_2112) = hAPP(fun(U_2116,bool),nat,finite_card(U_2116),U_2114)
      | ~ hBOOL(hAPP(fun(U_2116,bool),bool,finite_finite_1(U_2116),U_2114))
      | ~ hBOOL(hAPP(fun(U_2117,bool),bool,finite_finite_1(U_2117),U_2112))
      | ~ hBOOL(hAPP(fun(U_2117,bool),bool,hAPP(fun(U_2117,bool),fun(fun(U_2117,bool),bool),ord_less_eq(fun(U_2117,bool)),hAPP(fun(U_2116,bool),fun(U_2117,bool),hAPP(fun(U_2116,U_2117),fun(fun(U_2116,bool),fun(U_2117,bool)),image(U_2116,U_2117),U_2115),U_2114)),U_2112))
      | ~ hBOOL(hAPP(fun(U_2116,bool),bool,hAPP(fun(U_2116,U_2117),fun(fun(U_2116,bool),bool),inj_on(U_2116,U_2117),U_2115),U_2114))
      | ~ hBOOL(hAPP(fun(U_2116,bool),bool,hAPP(fun(U_2116,bool),fun(fun(U_2116,bool),bool),ord_less_eq(fun(U_2116,bool)),hAPP(fun(U_2117,bool),fun(U_2116,bool),hAPP(fun(U_2117,U_2116),fun(fun(U_2117,bool),fun(U_2116,bool)),image(U_2117,U_2116),U_2113),U_2112)),U_2114))
      | ~ hBOOL(hAPP(fun(U_2117,bool),bool,hAPP(fun(U_2117,U_2116),fun(fun(U_2117,bool),bool),inj_on(U_2117,U_2116),U_2113),U_2112)) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

cnf(f_598_3,plain,
    ( hAPP(fun(U_2117,bool),nat,finite_card(U_2117),U_2112) = hAPP(fun(U_2116,bool),nat,finite_card(U_2116),U_2114)
    | ~ hBOOL(hAPP(fun(U_2116,bool),bool,finite_finite_1(U_2116),U_2114))
    | ~ hBOOL(hAPP(fun(U_2117,bool),bool,finite_finite_1(U_2117),U_2112))
    | ~ hBOOL(hAPP(fun(U_2117,bool),bool,hAPP(fun(U_2117,bool),fun(fun(U_2117,bool),bool),ord_less_eq(fun(U_2117,bool)),hAPP(fun(U_2116,bool),fun(U_2117,bool),hAPP(fun(U_2116,U_2117),fun(fun(U_2116,bool),fun(U_2117,bool)),image(U_2116,U_2117),U_2115),U_2114)),U_2112))
    | ~ hBOOL(hAPP(fun(U_2116,bool),bool,hAPP(fun(U_2116,U_2117),fun(fun(U_2116,bool),bool),inj_on(U_2116,U_2117),U_2115),U_2114))
    | ~ hBOOL(hAPP(fun(U_2116,bool),bool,hAPP(fun(U_2116,bool),fun(fun(U_2116,bool),bool),ord_less_eq(fun(U_2116,bool)),hAPP(fun(U_2117,bool),fun(U_2116,bool),hAPP(fun(U_2117,U_2116),fun(fun(U_2117,bool),fun(U_2116,bool)),image(U_2117,U_2116),U_2113),U_2112)),U_2114))
    | ~ hBOOL(hAPP(fun(U_2117,bool),bool,hAPP(fun(U_2117,U_2116),fun(fun(U_2117,bool),bool),inj_on(U_2117,U_2116),U_2113),U_2112)) ),
    inference(clausify,[status(thm)],[f_598_2]) ).

fof(f_599_1,plain,
    ! [X_a,X_b,B,F,A_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_509_card__inj__on__le]) ).

fof(f_599_2,plain,
    ! [U_2122,U_2121,U_2120,U_2119,U_2118] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2122,bool),nat,finite_card(U_2122),U_2118)),hAPP(fun(U_2121,bool),nat,finite_card(U_2121),U_2120)))
      | ~ hBOOL(hAPP(fun(U_2121,bool),bool,finite_finite_1(U_2121),U_2120))
      | ~ hBOOL(hAPP(fun(U_2121,bool),bool,hAPP(fun(U_2121,bool),fun(fun(U_2121,bool),bool),ord_less_eq(fun(U_2121,bool)),hAPP(fun(U_2122,bool),fun(U_2121,bool),hAPP(fun(U_2122,U_2121),fun(fun(U_2122,bool),fun(U_2121,bool)),image(U_2122,U_2121),U_2119),U_2118)),U_2120))
      | ~ hBOOL(hAPP(fun(U_2122,bool),bool,hAPP(fun(U_2122,U_2121),fun(fun(U_2122,bool),bool),inj_on(U_2122,U_2121),U_2119),U_2118)) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

cnf(f_599_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2122,bool),nat,finite_card(U_2122),U_2118)),hAPP(fun(U_2121,bool),nat,finite_card(U_2121),U_2120)))
    | ~ hBOOL(hAPP(fun(U_2121,bool),bool,finite_finite_1(U_2121),U_2120))
    | ~ hBOOL(hAPP(fun(U_2121,bool),bool,hAPP(fun(U_2121,bool),fun(fun(U_2121,bool),bool),ord_less_eq(fun(U_2121,bool)),hAPP(fun(U_2122,bool),fun(U_2121,bool),hAPP(fun(U_2122,U_2121),fun(fun(U_2122,bool),fun(U_2121,bool)),image(U_2122,U_2121),U_2119),U_2118)),U_2120))
    | ~ hBOOL(hAPP(fun(U_2122,bool),bool,hAPP(fun(U_2122,U_2121),fun(fun(U_2122,bool),bool),inj_on(U_2122,U_2121),U_2119),U_2118)) ),
    inference(clausify,[status(thm)],[f_599_2]) ).

fof(f_600_1,plain,
    ! [X_b,X_a,B,A_1] :
      ( ( ( ? [F_2] :
              ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F_2),A_1)),B))
              & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F_2),A_1)) )
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B))) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)))
          | ! [F_2] :
              ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F_2),A_1)),B))
              | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F_2),A_1)) ) ) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_510_inj__on__iff__card__le]) ).

fof(f_600_2,plain,
    ! [U_2128,U_2127,U_2126,U_2125] :
      ( ( ( ? [U_2124] :
              ( hBOOL(hAPP(fun(U_2128,bool),bool,hAPP(fun(U_2128,bool),fun(fun(U_2128,bool),bool),ord_less_eq(fun(U_2128,bool)),hAPP(fun(U_2127,bool),fun(U_2128,bool),hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),fun(U_2128,bool)),image(U_2127,U_2128),U_2124),U_2125)),U_2126))
              & hBOOL(hAPP(fun(U_2127,bool),bool,hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),bool),inj_on(U_2127,U_2128),U_2124),U_2125)) )
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2127,bool),nat,finite_card(U_2127),U_2125)),hAPP(fun(U_2128,bool),nat,finite_card(U_2128),U_2126))) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2127,bool),nat,finite_card(U_2127),U_2125)),hAPP(fun(U_2128,bool),nat,finite_card(U_2128),U_2126)))
          | ! [U_2123] :
              ( ~ hBOOL(hAPP(fun(U_2128,bool),bool,hAPP(fun(U_2128,bool),fun(fun(U_2128,bool),bool),ord_less_eq(fun(U_2128,bool)),hAPP(fun(U_2127,bool),fun(U_2128,bool),hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),fun(U_2128,bool)),image(U_2127,U_2128),U_2123),U_2125)),U_2126))
              | ~ hBOOL(hAPP(fun(U_2127,bool),bool,hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),bool),inj_on(U_2127,U_2128),U_2123),U_2125)) ) ) )
      | ~ hBOOL(hAPP(fun(U_2128,bool),bool,finite_finite_1(U_2128),U_2126))
      | ~ hBOOL(hAPP(fun(U_2127,bool),bool,finite_finite_1(U_2127),U_2125)) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ! [U_2128,U_2127,U_2126,U_2125] :
      ( ( ( ( hBOOL(hAPP(fun(U_2128,bool),bool,hAPP(fun(U_2128,bool),fun(fun(U_2128,bool),bool),ord_less_eq(fun(U_2128,bool)),hAPP(fun(U_2127,bool),fun(U_2128,bool),hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),fun(U_2128,bool)),image(U_2127,U_2128),sK115(U_2128,U_2127,U_2126,U_2125)),U_2125)),U_2126))
            & hBOOL(hAPP(fun(U_2127,bool),bool,hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),bool),inj_on(U_2127,U_2128),sK115(U_2128,U_2127,U_2126,U_2125)),U_2125)) )
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2127,bool),nat,finite_card(U_2127),U_2125)),hAPP(fun(U_2128,bool),nat,finite_card(U_2128),U_2126))) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2127,bool),nat,finite_card(U_2127),U_2125)),hAPP(fun(U_2128,bool),nat,finite_card(U_2128),U_2126)))
          | ! [U_2123] :
              ( ~ hBOOL(hAPP(fun(U_2128,bool),bool,hAPP(fun(U_2128,bool),fun(fun(U_2128,bool),bool),ord_less_eq(fun(U_2128,bool)),hAPP(fun(U_2127,bool),fun(U_2128,bool),hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),fun(U_2128,bool)),image(U_2127,U_2128),U_2123),U_2125)),U_2126))
              | ~ hBOOL(hAPP(fun(U_2127,bool),bool,hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),bool),inj_on(U_2127,U_2128),U_2123),U_2125)) ) ) )
      | ~ hBOOL(hAPP(fun(U_2128,bool),bool,finite_finite_1(U_2128),U_2126))
      | ~ hBOOL(hAPP(fun(U_2127,bool),bool,finite_finite_1(U_2127),U_2125)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_2124,sK115(U_2128,U_2127,U_2126,U_2125))],[f_600_2]) ).

cnf(f_600_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2127,bool),nat,finite_card(U_2127),U_2125)),hAPP(fun(U_2128,bool),nat,finite_card(U_2128),U_2126)))
    | ~ hBOOL(hAPP(fun(U_2128,bool),bool,hAPP(fun(U_2128,bool),fun(fun(U_2128,bool),bool),ord_less_eq(fun(U_2128,bool)),hAPP(fun(U_2127,bool),fun(U_2128,bool),hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),fun(U_2128,bool)),image(U_2127,U_2128),U_2123),U_2125)),U_2126))
    | ~ hBOOL(hAPP(fun(U_2127,bool),bool,hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),bool),inj_on(U_2127,U_2128),U_2123),U_2125))
    | ~ hBOOL(hAPP(fun(U_2128,bool),bool,finite_finite_1(U_2128),U_2126))
    | ~ hBOOL(hAPP(fun(U_2127,bool),bool,finite_finite_1(U_2127),U_2125)) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

cnf(f_600_5,plain,
    ( hBOOL(hAPP(fun(U_2127,bool),bool,hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),bool),inj_on(U_2127,U_2128),sK115(U_2128,U_2127,U_2126,U_2125)),U_2125))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2127,bool),nat,finite_card(U_2127),U_2125)),hAPP(fun(U_2128,bool),nat,finite_card(U_2128),U_2126)))
    | ~ hBOOL(hAPP(fun(U_2128,bool),bool,finite_finite_1(U_2128),U_2126))
    | ~ hBOOL(hAPP(fun(U_2127,bool),bool,finite_finite_1(U_2127),U_2125)) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

cnf(f_600_6,plain,
    ( hBOOL(hAPP(fun(U_2128,bool),bool,hAPP(fun(U_2128,bool),fun(fun(U_2128,bool),bool),ord_less_eq(fun(U_2128,bool)),hAPP(fun(U_2127,bool),fun(U_2128,bool),hAPP(fun(U_2127,U_2128),fun(fun(U_2127,bool),fun(U_2128,bool)),image(U_2127,U_2128),sK115(U_2128,U_2127,U_2126,U_2125)),U_2125)),U_2126))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_2127,bool),nat,finite_card(U_2127),U_2125)),hAPP(fun(U_2128,bool),nat,finite_card(U_2128),U_2126)))
    | ~ hBOOL(hAPP(fun(U_2128,bool),bool,finite_finite_1(U_2128),U_2126))
    | ~ hBOOL(hAPP(fun(U_2127,bool),bool,finite_finite_1(U_2127),U_2125)) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

fof(f_601_1,plain,
    ! [X_a,X_b,X_2,Pa,F] :
      ( hBOOL(hAPP(X_a,bool,Pa,X_2))
      | ? [Y_2] :
          ( ~ hBOOL(hAPP(X_a,bool,Pa,hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),Y_2)))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),top_top(fun(X_a,bool))))) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_511_inj__transfer]) ).

fof(f_601_2,plain,
    ! [U_2134,U_2133,U_2132,U_2131,U_2130] :
      ( hBOOL(hAPP(U_2134,bool,U_2131,U_2132))
      | ? [U_2129] :
          ( ~ hBOOL(hAPP(U_2134,bool,U_2131,hAPP(U_2133,U_2134,hAPP(fun(U_2134,U_2133),fun(U_2133,U_2134),hAPP(fun(U_2134,bool),fun(fun(U_2134,U_2133),fun(U_2133,U_2134)),hilbert_inv_into(U_2134,U_2133),top_top(fun(U_2134,bool))),U_2130),U_2129)))
          & hBOOL(hAPP(fun(U_2133,bool),bool,hAPP(U_2133,fun(fun(U_2133,bool),bool),member(U_2133),U_2129),hAPP(fun(U_2134,bool),fun(U_2133,bool),hAPP(fun(U_2134,U_2133),fun(fun(U_2134,bool),fun(U_2133,bool)),image(U_2134,U_2133),U_2130),top_top(fun(U_2134,bool))))) )
      | ~ hBOOL(hAPP(fun(U_2134,bool),bool,hAPP(fun(U_2134,U_2133),fun(fun(U_2134,bool),bool),inj_on(U_2134,U_2133),U_2130),top_top(fun(U_2134,bool)))) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

fof(f_601_3,plain,
    ! [U_2134,U_2133,U_2132,U_2131,U_2130] :
      ( hBOOL(hAPP(U_2134,bool,U_2131,U_2132))
      | ( ~ hBOOL(hAPP(U_2134,bool,U_2131,hAPP(U_2133,U_2134,hAPP(fun(U_2134,U_2133),fun(U_2133,U_2134),hAPP(fun(U_2134,bool),fun(fun(U_2134,U_2133),fun(U_2133,U_2134)),hilbert_inv_into(U_2134,U_2133),top_top(fun(U_2134,bool))),U_2130),sK116(U_2134,U_2133,U_2132,U_2131,U_2130))))
        & hBOOL(hAPP(fun(U_2133,bool),bool,hAPP(U_2133,fun(fun(U_2133,bool),bool),member(U_2133),sK116(U_2134,U_2133,U_2132,U_2131,U_2130)),hAPP(fun(U_2134,bool),fun(U_2133,bool),hAPP(fun(U_2134,U_2133),fun(fun(U_2134,bool),fun(U_2133,bool)),image(U_2134,U_2133),U_2130),top_top(fun(U_2134,bool))))) )
      | ~ hBOOL(hAPP(fun(U_2134,bool),bool,hAPP(fun(U_2134,U_2133),fun(fun(U_2134,bool),bool),inj_on(U_2134,U_2133),U_2130),top_top(fun(U_2134,bool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_2129,sK116(U_2134,U_2133,U_2132,U_2131,U_2130))],[f_601_2]) ).

cnf(f_601_4,plain,
    ( hBOOL(hAPP(fun(U_2133,bool),bool,hAPP(U_2133,fun(fun(U_2133,bool),bool),member(U_2133),sK116(U_2134,U_2133,U_2132,U_2131,U_2130)),hAPP(fun(U_2134,bool),fun(U_2133,bool),hAPP(fun(U_2134,U_2133),fun(fun(U_2134,bool),fun(U_2133,bool)),image(U_2134,U_2133),U_2130),top_top(fun(U_2134,bool)))))
    | hBOOL(hAPP(U_2134,bool,U_2131,U_2132))
    | ~ hBOOL(hAPP(fun(U_2134,bool),bool,hAPP(fun(U_2134,U_2133),fun(fun(U_2134,bool),bool),inj_on(U_2134,U_2133),U_2130),top_top(fun(U_2134,bool)))) ),
    inference(clausify,[status(thm)],[f_601_3]) ).

cnf(f_601_5,plain,
    ( ~ hBOOL(hAPP(U_2134,bool,U_2131,hAPP(U_2133,U_2134,hAPP(fun(U_2134,U_2133),fun(U_2133,U_2134),hAPP(fun(U_2134,bool),fun(fun(U_2134,U_2133),fun(U_2133,U_2134)),hilbert_inv_into(U_2134,U_2133),top_top(fun(U_2134,bool))),U_2130),sK116(U_2134,U_2133,U_2132,U_2131,U_2130))))
    | hBOOL(hAPP(U_2134,bool,U_2131,U_2132))
    | ~ hBOOL(hAPP(fun(U_2134,bool),bool,hAPP(fun(U_2134,U_2133),fun(fun(U_2134,bool),bool),inj_on(U_2134,U_2133),U_2130),top_top(fun(U_2134,bool)))) ),
    inference(clausify,[status(thm)],[f_601_3]) ).

fof(f_602_1,plain,
    ! [X_a,X_b,Ba,F,A_1] :
      ( ? [X_1] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))
          & ti(X_a,Ba) = hAPP(X_b,X_a,F,X_1) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_512_imageE]) ).

fof(f_602_2,plain,
    ! [U_2140,U_2139,U_2138,U_2137,U_2136] :
      ( ? [U_2135] :
          ( hBOOL(hAPP(fun(U_2139,bool),bool,hAPP(U_2139,fun(fun(U_2139,bool),bool),member(U_2139),U_2135),U_2136))
          & ti(U_2140,U_2138) = hAPP(U_2139,U_2140,U_2137,U_2135) )
      | ~ hBOOL(hAPP(fun(U_2140,bool),bool,hAPP(U_2140,fun(fun(U_2140,bool),bool),member(U_2140),U_2138),hAPP(fun(U_2139,bool),fun(U_2140,bool),hAPP(fun(U_2139,U_2140),fun(fun(U_2139,bool),fun(U_2140,bool)),image(U_2139,U_2140),U_2137),U_2136))) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

fof(f_602_3,plain,
    ! [U_2140,U_2139,U_2138,U_2137,U_2136] :
      ( ( hBOOL(hAPP(fun(U_2139,bool),bool,hAPP(U_2139,fun(fun(U_2139,bool),bool),member(U_2139),sK117(U_2140,U_2139,U_2138,U_2137,U_2136)),U_2136))
        & ti(U_2140,U_2138) = hAPP(U_2139,U_2140,U_2137,sK117(U_2140,U_2139,U_2138,U_2137,U_2136)) )
      | ~ hBOOL(hAPP(fun(U_2140,bool),bool,hAPP(U_2140,fun(fun(U_2140,bool),bool),member(U_2140),U_2138),hAPP(fun(U_2139,bool),fun(U_2140,bool),hAPP(fun(U_2139,U_2140),fun(fun(U_2139,bool),fun(U_2140,bool)),image(U_2139,U_2140),U_2137),U_2136))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_2135,sK117(U_2140,U_2139,U_2138,U_2137,U_2136))],[f_602_2]) ).

cnf(f_602_4,plain,
    ( ti(U_2140,U_2138) = hAPP(U_2139,U_2140,U_2137,sK117(U_2140,U_2139,U_2138,U_2137,U_2136))
    | ~ hBOOL(hAPP(fun(U_2140,bool),bool,hAPP(U_2140,fun(fun(U_2140,bool),bool),member(U_2140),U_2138),hAPP(fun(U_2139,bool),fun(U_2140,bool),hAPP(fun(U_2139,U_2140),fun(fun(U_2139,bool),fun(U_2140,bool)),image(U_2139,U_2140),U_2137),U_2136))) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

cnf(f_602_5,plain,
    ( hBOOL(hAPP(fun(U_2139,bool),bool,hAPP(U_2139,fun(fun(U_2139,bool),bool),member(U_2139),sK117(U_2140,U_2139,U_2138,U_2137,U_2136)),U_2136))
    | ~ hBOOL(hAPP(fun(U_2140,bool),bool,hAPP(U_2140,fun(fun(U_2140,bool),bool),member(U_2140),U_2138),hAPP(fun(U_2139,bool),fun(U_2140,bool),hAPP(fun(U_2139,U_2140),fun(fun(U_2139,bool),fun(U_2140,bool)),image(U_2139,U_2140),U_2137),U_2136))) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

fof(f_603_1,plain,
    ! [X_b,X_a,G,F] :
      ( hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),top_top(fun(X_b,bool))),F) = ti(fun(X_a,X_b),G)
      | ? [X_1] : hAPP(X_a,X_b,G,hAPP(X_b,X_a,F,X_1)) != ti(X_b,X_1)
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) != top_top(fun(X_a,bool)) ),
    inference(fof_nnf,[status(thm)],[fact_513_surj__imp__inv__eq]) ).

fof(f_603_2,plain,
    ! [U_2145,U_2144,U_2143,U_2142] :
      ( hAPP(fun(U_2145,U_2144),fun(U_2144,U_2145),hAPP(fun(U_2145,bool),fun(fun(U_2145,U_2144),fun(U_2144,U_2145)),hilbert_inv_into(U_2145,U_2144),top_top(fun(U_2145,bool))),U_2142) = ti(fun(U_2144,U_2145),U_2143)
      | ? [U_2141] : hAPP(U_2144,U_2145,U_2143,hAPP(U_2145,U_2144,U_2142,U_2141)) != ti(U_2145,U_2141)
      | hAPP(fun(U_2145,bool),fun(U_2144,bool),hAPP(fun(U_2145,U_2144),fun(fun(U_2145,bool),fun(U_2144,bool)),image(U_2145,U_2144),U_2142),top_top(fun(U_2145,bool))) != top_top(fun(U_2144,bool)) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

fof(f_603_3,plain,
    ! [U_2145,U_2144,U_2143,U_2142] :
      ( hAPP(fun(U_2145,U_2144),fun(U_2144,U_2145),hAPP(fun(U_2145,bool),fun(fun(U_2145,U_2144),fun(U_2144,U_2145)),hilbert_inv_into(U_2145,U_2144),top_top(fun(U_2145,bool))),U_2142) = ti(fun(U_2144,U_2145),U_2143)
      | hAPP(U_2144,U_2145,U_2143,hAPP(U_2145,U_2144,U_2142,sK118(U_2145,U_2144,U_2143,U_2142))) != ti(U_2145,sK118(U_2145,U_2144,U_2143,U_2142))
      | hAPP(fun(U_2145,bool),fun(U_2144,bool),hAPP(fun(U_2145,U_2144),fun(fun(U_2145,bool),fun(U_2144,bool)),image(U_2145,U_2144),U_2142),top_top(fun(U_2145,bool))) != top_top(fun(U_2144,bool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_2141,sK118(U_2145,U_2144,U_2143,U_2142))],[f_603_2]) ).

cnf(f_603_4,plain,
    ( hAPP(fun(U_2145,U_2144),fun(U_2144,U_2145),hAPP(fun(U_2145,bool),fun(fun(U_2145,U_2144),fun(U_2144,U_2145)),hilbert_inv_into(U_2145,U_2144),top_top(fun(U_2145,bool))),U_2142) = ti(fun(U_2144,U_2145),U_2143)
    | hAPP(U_2144,U_2145,U_2143,hAPP(U_2145,U_2144,U_2142,sK118(U_2145,U_2144,U_2143,U_2142))) != ti(U_2145,sK118(U_2145,U_2144,U_2143,U_2142))
    | hAPP(fun(U_2145,bool),fun(U_2144,bool),hAPP(fun(U_2145,U_2144),fun(fun(U_2145,bool),fun(U_2144,bool)),image(U_2145,U_2144),U_2142),top_top(fun(U_2145,bool))) != top_top(fun(U_2144,bool)) ),
    inference(clausify,[status(thm)],[f_603_3]) ).

fof(f_604_1,plain,
    ! [X_b,X_a,F,A_1,B] :
      ( ? [C_2] :
          ( ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C_2)
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),C_2))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_2),A_1)) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B)) ),
    inference(fof_nnf,[status(thm)],[fact_514_finite__subset__image]) ).

fof(f_604_2,plain,
    ! [U_2151,U_2150,U_2149,U_2148,U_2147] :
      ( ? [U_2146] :
          ( ti(fun(U_2150,bool),U_2147) = hAPP(fun(U_2151,bool),fun(U_2150,bool),hAPP(fun(U_2151,U_2150),fun(fun(U_2151,bool),fun(U_2150,bool)),image(U_2151,U_2150),U_2149),U_2146)
          & hBOOL(hAPP(fun(U_2151,bool),bool,finite_finite_1(U_2151),U_2146))
          & hBOOL(hAPP(fun(U_2151,bool),bool,hAPP(fun(U_2151,bool),fun(fun(U_2151,bool),bool),ord_less_eq(fun(U_2151,bool)),U_2146),U_2148)) )
      | ~ hBOOL(hAPP(fun(U_2150,bool),bool,hAPP(fun(U_2150,bool),fun(fun(U_2150,bool),bool),ord_less_eq(fun(U_2150,bool)),U_2147),hAPP(fun(U_2151,bool),fun(U_2150,bool),hAPP(fun(U_2151,U_2150),fun(fun(U_2151,bool),fun(U_2150,bool)),image(U_2151,U_2150),U_2149),U_2148)))
      | ~ hBOOL(hAPP(fun(U_2150,bool),bool,finite_finite_1(U_2150),U_2147)) ),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

fof(f_604_3,plain,
    ! [U_2151,U_2150,U_2149,U_2148,U_2147] :
      ( ( ti(fun(U_2150,bool),U_2147) = hAPP(fun(U_2151,bool),fun(U_2150,bool),hAPP(fun(U_2151,U_2150),fun(fun(U_2151,bool),fun(U_2150,bool)),image(U_2151,U_2150),U_2149),sK119(U_2151,U_2150,U_2149,U_2148,U_2147))
        & hBOOL(hAPP(fun(U_2151,bool),bool,finite_finite_1(U_2151),sK119(U_2151,U_2150,U_2149,U_2148,U_2147)))
        & hBOOL(hAPP(fun(U_2151,bool),bool,hAPP(fun(U_2151,bool),fun(fun(U_2151,bool),bool),ord_less_eq(fun(U_2151,bool)),sK119(U_2151,U_2150,U_2149,U_2148,U_2147)),U_2148)) )
      | ~ hBOOL(hAPP(fun(U_2150,bool),bool,hAPP(fun(U_2150,bool),fun(fun(U_2150,bool),bool),ord_less_eq(fun(U_2150,bool)),U_2147),hAPP(fun(U_2151,bool),fun(U_2150,bool),hAPP(fun(U_2151,U_2150),fun(fun(U_2151,bool),fun(U_2150,bool)),image(U_2151,U_2150),U_2149),U_2148)))
      | ~ hBOOL(hAPP(fun(U_2150,bool),bool,finite_finite_1(U_2150),U_2147)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_2146,sK119(U_2151,U_2150,U_2149,U_2148,U_2147))],[f_604_2]) ).

cnf(f_604_4,plain,
    ( hBOOL(hAPP(fun(U_2151,bool),bool,hAPP(fun(U_2151,bool),fun(fun(U_2151,bool),bool),ord_less_eq(fun(U_2151,bool)),sK119(U_2151,U_2150,U_2149,U_2148,U_2147)),U_2148))
    | ~ hBOOL(hAPP(fun(U_2150,bool),bool,hAPP(fun(U_2150,bool),fun(fun(U_2150,bool),bool),ord_less_eq(fun(U_2150,bool)),U_2147),hAPP(fun(U_2151,bool),fun(U_2150,bool),hAPP(fun(U_2151,U_2150),fun(fun(U_2151,bool),fun(U_2150,bool)),image(U_2151,U_2150),U_2149),U_2148)))
    | ~ hBOOL(hAPP(fun(U_2150,bool),bool,finite_finite_1(U_2150),U_2147)) ),
    inference(clausify,[status(thm)],[f_604_3]) ).

cnf(f_604_5,plain,
    ( hBOOL(hAPP(fun(U_2151,bool),bool,finite_finite_1(U_2151),sK119(U_2151,U_2150,U_2149,U_2148,U_2147)))
    | ~ hBOOL(hAPP(fun(U_2150,bool),bool,hAPP(fun(U_2150,bool),fun(fun(U_2150,bool),bool),ord_less_eq(fun(U_2150,bool)),U_2147),hAPP(fun(U_2151,bool),fun(U_2150,bool),hAPP(fun(U_2151,U_2150),fun(fun(U_2151,bool),fun(U_2150,bool)),image(U_2151,U_2150),U_2149),U_2148)))
    | ~ hBOOL(hAPP(fun(U_2150,bool),bool,finite_finite_1(U_2150),U_2147)) ),
    inference(clausify,[status(thm)],[f_604_3]) ).

cnf(f_604_6,plain,
    ( ti(fun(U_2150,bool),U_2147) = hAPP(fun(U_2151,bool),fun(U_2150,bool),hAPP(fun(U_2151,U_2150),fun(fun(U_2151,bool),fun(U_2150,bool)),image(U_2151,U_2150),U_2149),sK119(U_2151,U_2150,U_2149,U_2148,U_2147))
    | ~ hBOOL(hAPP(fun(U_2150,bool),bool,hAPP(fun(U_2150,bool),fun(fun(U_2150,bool),bool),ord_less_eq(fun(U_2150,bool)),U_2147),hAPP(fun(U_2151,bool),fun(U_2150,bool),hAPP(fun(U_2151,U_2150),fun(fun(U_2151,bool),fun(U_2150,bool)),image(U_2151,U_2150),U_2149),U_2148)))
    | ~ hBOOL(hAPP(fun(U_2150,bool),bool,finite_finite_1(U_2150),U_2147)) ),
    inference(clausify,[status(thm)],[f_604_3]) ).

fof(f_605_1,plain,
    ! [I,J] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J)),
    inference(fof_nnf,[status(thm)],[fact_515_image__Suc__atLeastLessThan]) ).

fof(f_605_2,plain,
    ! [U_2153,U_2152] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_2153),U_2152)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,U_2153)),hAPP(nat,nat,suc,U_2152)),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

cnf(f_605_3,plain,
    hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_2153),U_2152)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,U_2153)),hAPP(nat,nat,suc,U_2152)),
    inference(clausify,[status(thm)],[f_605_2]) ).

fof(f_606_1,plain,
    ! [X_a,A_1,F,Na] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ti(fun(X_a,bool),A_1) != hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na))) ),
    inference(fof_nnf,[status(thm)],[fact_516_nat__seg__image__imp__finite]) ).

fof(f_606_2,plain,
    ! [U_2157,U_2156,U_2155,U_2154] :
      ( hBOOL(hAPP(fun(U_2157,bool),bool,finite_finite_1(U_2157),U_2156))
      | ti(fun(U_2157,bool),U_2156) != hAPP(fun(nat,bool),fun(U_2157,bool),hAPP(fun(nat,U_2157),fun(fun(nat,bool),fun(U_2157,bool)),image(nat,U_2157),U_2155),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2154))) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

fof(f_606_3,plain,
    ! [U_2157,U_2156] :
      ( ! [U_2155,U_2154] : ti(fun(U_2157,bool),U_2156) != hAPP(fun(nat,bool),fun(U_2157,bool),hAPP(fun(nat,U_2157),fun(fun(nat,bool),fun(U_2157,bool)),image(nat,U_2157),U_2155),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2154)))
      | hBOOL(hAPP(fun(U_2157,bool),bool,finite_finite_1(U_2157),U_2156)) ),
    inference(miniscope,[status(thm)],[f_606_2]) ).

cnf(f_606_4,plain,
    ( ti(fun(U_2157,bool),U_2156) != hAPP(fun(nat,bool),fun(U_2157,bool),hAPP(fun(nat,U_2157),fun(fun(nat,bool),fun(U_2157,bool)),image(nat,U_2157),U_2155),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2154)))
    | hBOOL(hAPP(fun(U_2157,bool),bool,finite_finite_1(U_2157),U_2156)) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

fof(f_607_1,plain,
    ! [K,I,J] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(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_517_image__add__atLeastLessThan]) ).

fof(f_607_2,plain,
    ! [U_2160,U_2159,U_2158] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),U_2160)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_2159),U_2158)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2159),U_2160)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2158),U_2160)),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

cnf(f_607_3,plain,
    hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),U_2160)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_2159),U_2158)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2159),U_2160)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2158),U_2160)),
    inference(clausify,[status(thm)],[f_607_2]) ).

fof(f_608_1,plain,
    ! [Pa,Na] :
      ( ( ! [M_1] :
            ( hBOOL(hAPP(nat,bool,Pa,M_1))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) )
        | ? [X_1] :
            ( ~ hBOOL(hAPP(nat,bool,Pa,X_1))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))) ) )
      & ( ! [X_1] :
            ( hBOOL(hAPP(nat,bool,Pa,X_1))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))) )
        | ? [M_1] :
            ( ~ hBOOL(hAPP(nat,bool,Pa,M_1))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_518_all__nat__less__eq]) ).

fof(f_608_2,plain,
    ! [U_2166,U_2165] :
      ( ( ! [U_2164] :
            ( hBOOL(hAPP(nat,bool,U_2166,U_2164))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2164),U_2165)) )
        | ? [U_2163] :
            ( ~ hBOOL(hAPP(nat,bool,U_2166,U_2163))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2163),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2165))) ) )
      & ( ! [U_2162] :
            ( hBOOL(hAPP(nat,bool,U_2166,U_2162))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2162),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2165))) )
        | ? [U_2161] :
            ( ~ hBOOL(hAPP(nat,bool,U_2166,U_2161))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2161),U_2165)) ) ) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

fof(f_608_3,plain,
    ( ! [U_2170,U_2168] :
        ( ! [U_2164] :
            ( hBOOL(hAPP(nat,bool,U_2170,U_2164))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2164),U_2168)) )
        | ? [U_2163] :
            ( ~ hBOOL(hAPP(nat,bool,U_2170,U_2163))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2163),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2168))) ) )
    & ! [U_2169,U_2167] :
        ( ! [U_2162] :
            ( hBOOL(hAPP(nat,bool,U_2169,U_2162))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2162),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2167))) )
        | ? [U_2161] :
            ( ~ hBOOL(hAPP(nat,bool,U_2169,U_2161))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2161),U_2167)) ) ) ),
    inference(miniscope,[status(thm)],[f_608_2]) ).

fof(f_608_4,plain,
    ( ! [U_2170,U_2168] :
        ( ! [U_2164] :
            ( hBOOL(hAPP(nat,bool,U_2170,U_2164))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2164),U_2168)) )
        | ? [U_2163] :
            ( ~ hBOOL(hAPP(nat,bool,U_2170,U_2163))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2163),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2168))) ) )
    & ! [U_2169,U_2167] :
        ( ! [U_2162] :
            ( hBOOL(hAPP(nat,bool,U_2169,U_2162))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2162),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2167))) )
        | ( ~ hBOOL(hAPP(nat,bool,U_2169,sK120(U_2169,U_2167)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK120(U_2169,U_2167)),U_2167)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_2161,sK120(U_2169,U_2167))],[f_608_3]) ).

fof(f_608_5,plain,
    ( ! [U_2170,U_2168] :
        ( ! [U_2164] :
            ( hBOOL(hAPP(nat,bool,U_2170,U_2164))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2164),U_2168)) )
        | ( ~ hBOOL(hAPP(nat,bool,U_2170,sK121(U_2170,U_2168)))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK121(U_2170,U_2168)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2168))) ) )
    & ! [U_2169,U_2167] :
        ( ! [U_2162] :
            ( hBOOL(hAPP(nat,bool,U_2169,U_2162))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2162),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2167))) )
        | ( ~ hBOOL(hAPP(nat,bool,U_2169,sK120(U_2169,U_2167)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK120(U_2169,U_2167)),U_2167)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_2163,sK121(U_2170,U_2168))],[f_608_4]) ).

cnf(f_608_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK120(U_2169,U_2167)),U_2167))
    | hBOOL(hAPP(nat,bool,U_2169,U_2162))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2162),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2167))) ),
    inference(clausify,[status(thm)],[f_608_5]) ).

cnf(f_608_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2169,sK120(U_2169,U_2167)))
    | hBOOL(hAPP(nat,bool,U_2169,U_2162))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2162),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2167))) ),
    inference(clausify,[status(thm)],[f_608_5]) ).

cnf(f_608_8,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK121(U_2170,U_2168)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2168)))
    | hBOOL(hAPP(nat,bool,U_2170,U_2164))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2164),U_2168)) ),
    inference(clausify,[status(thm)],[f_608_5]) ).

cnf(f_608_9,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_2170,sK121(U_2170,U_2168)))
    | hBOOL(hAPP(nat,bool,U_2170,U_2164))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2164),U_2168)) ),
    inference(clausify,[status(thm)],[f_608_5]) ).

fof(f_609_1,plain,
    ! [Pa,Na] :
      ( ( ? [M_1] :
            ( hBOOL(hAPP(nat,bool,Pa,M_1))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) )
        | ! [X_1] :
            ( ~ hBOOL(hAPP(nat,bool,Pa,X_1))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))) ) )
      & ( ? [X_1] :
            ( hBOOL(hAPP(nat,bool,Pa,X_1))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))) )
        | ! [M_1] :
            ( ~ hBOOL(hAPP(nat,bool,Pa,M_1))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_519_ex__nat__less__eq]) ).

fof(f_609_2,plain,
    ! [U_2176,U_2175] :
      ( ( ? [U_2174] :
            ( hBOOL(hAPP(nat,bool,U_2176,U_2174))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2174),U_2175)) )
        | ! [U_2173] :
            ( ~ hBOOL(hAPP(nat,bool,U_2176,U_2173))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2173),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2175))) ) )
      & ( ? [U_2172] :
            ( hBOOL(hAPP(nat,bool,U_2176,U_2172))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2172),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2175))) )
        | ! [U_2171] :
            ( ~ hBOOL(hAPP(nat,bool,U_2176,U_2171))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2171),U_2175)) ) ) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

fof(f_609_3,plain,
    ( ! [U_2180,U_2178] :
        ( ? [U_2174] :
            ( hBOOL(hAPP(nat,bool,U_2180,U_2174))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2174),U_2178)) )
        | ! [U_2173] :
            ( ~ hBOOL(hAPP(nat,bool,U_2180,U_2173))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2173),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2178))) ) )
    & ! [U_2179,U_2177] :
        ( ? [U_2172] :
            ( hBOOL(hAPP(nat,bool,U_2179,U_2172))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2172),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2177))) )
        | ! [U_2171] :
            ( ~ hBOOL(hAPP(nat,bool,U_2179,U_2171))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2171),U_2177)) ) ) ),
    inference(miniscope,[status(thm)],[f_609_2]) ).

fof(f_609_4,plain,
    ( ! [U_2180,U_2178] :
        ( ? [U_2174] :
            ( hBOOL(hAPP(nat,bool,U_2180,U_2174))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2174),U_2178)) )
        | ! [U_2173] :
            ( ~ hBOOL(hAPP(nat,bool,U_2180,U_2173))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2173),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2178))) ) )
    & ! [U_2179,U_2177] :
        ( ( hBOOL(hAPP(nat,bool,U_2179,sK122(U_2179,U_2177)))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK122(U_2179,U_2177)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2177))) )
        | ! [U_2171] :
            ( ~ hBOOL(hAPP(nat,bool,U_2179,U_2171))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2171),U_2177)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_2172,sK122(U_2179,U_2177))],[f_609_3]) ).

fof(f_609_5,plain,
    ( ! [U_2180,U_2178] :
        ( ( hBOOL(hAPP(nat,bool,U_2180,sK123(U_2180,U_2178)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK123(U_2180,U_2178)),U_2178)) )
        | ! [U_2173] :
            ( ~ hBOOL(hAPP(nat,bool,U_2180,U_2173))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2173),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2178))) ) )
    & ! [U_2179,U_2177] :
        ( ( hBOOL(hAPP(nat,bool,U_2179,sK122(U_2179,U_2177)))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK122(U_2179,U_2177)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2177))) )
        | ! [U_2171] :
            ( ~ hBOOL(hAPP(nat,bool,U_2179,U_2171))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2171),U_2177)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_2174,sK123(U_2180,U_2178))],[f_609_4]) ).

cnf(f_609_6,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK122(U_2179,U_2177)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2177)))
    | ~ hBOOL(hAPP(nat,bool,U_2179,U_2171))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2171),U_2177)) ),
    inference(clausify,[status(thm)],[f_609_5]) ).

cnf(f_609_7,plain,
    ( hBOOL(hAPP(nat,bool,U_2179,sK122(U_2179,U_2177)))
    | ~ hBOOL(hAPP(nat,bool,U_2179,U_2171))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2171),U_2177)) ),
    inference(clausify,[status(thm)],[f_609_5]) ).

cnf(f_609_8,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK123(U_2180,U_2178)),U_2178))
    | ~ hBOOL(hAPP(nat,bool,U_2180,U_2173))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2173),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2178))) ),
    inference(clausify,[status(thm)],[f_609_5]) ).

cnf(f_609_9,plain,
    ( hBOOL(hAPP(nat,bool,U_2180,sK123(U_2180,U_2178)))
    | ~ hBOOL(hAPP(nat,bool,U_2180,U_2173))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_2173),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_2178))) ),
    inference(clausify,[status(thm)],[f_609_5]) ).

fof(f_610_1,plain,
    ! [X_a,X_b,Ba,F] :
      ( ? [X_1] : ti(X_a,Ba) = hAPP(X_b,X_a,F,X_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))))) ),
    inference(fof_nnf,[status(thm)],[fact_520_rangeE]) ).

fof(f_610_2,plain,
    ! [U_2185,U_2184,U_2183,U_2182] :
      ( ? [U_2181] : ti(U_2185,U_2183) = hAPP(U_2184,U_2185,U_2182,U_2181)
      | ~ hBOOL(hAPP(fun(U_2185,bool),bool,hAPP(U_2185,fun(fun(U_2185,bool),bool),member(U_2185),U_2183),hAPP(fun(U_2184,bool),fun(U_2185,bool),hAPP(fun(U_2184,U_2185),fun(fun(U_2184,bool),fun(U_2185,bool)),image(U_2184,U_2185),U_2182),top_top(fun(U_2184,bool))))) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

fof(f_610_3,plain,
    ! [U_2185,U_2184,U_2183,U_2182] :
      ( ti(U_2185,U_2183) = hAPP(U_2184,U_2185,U_2182,sK124(U_2185,U_2184,U_2183,U_2182))
      | ~ hBOOL(hAPP(fun(U_2185,bool),bool,hAPP(U_2185,fun(fun(U_2185,bool),bool),member(U_2185),U_2183),hAPP(fun(U_2184,bool),fun(U_2185,bool),hAPP(fun(U_2184,U_2185),fun(fun(U_2184,bool),fun(U_2185,bool)),image(U_2184,U_2185),U_2182),top_top(fun(U_2184,bool))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_2181,sK124(U_2185,U_2184,U_2183,U_2182))],[f_610_2]) ).

cnf(f_610_4,plain,
    ( ti(U_2185,U_2183) = hAPP(U_2184,U_2185,U_2182,sK124(U_2185,U_2184,U_2183,U_2182))
    | ~ hBOOL(hAPP(fun(U_2185,bool),bool,hAPP(U_2185,fun(fun(U_2185,bool),bool),member(U_2185),U_2183),hAPP(fun(U_2184,bool),fun(U_2185,bool),hAPP(fun(U_2184,U_2185),fun(fun(U_2184,bool),fun(U_2185,bool)),image(U_2184,U_2185),U_2182),top_top(fun(U_2184,bool))))) ),
    inference(clausify,[status(thm)],[f_610_3]) ).

fof(f_611_1,plain,
    ! [X_b,X_a,F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,bool))),combb(X_b,fun(X_b,bool),X_a),fequal(X_b)),F)),hAPP(X_a,X_b,F,X_1))))))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_521_pigeonhole__infinite]) ).

fof(f_611_2,plain,
    ! [U_2190,U_2189,U_2188,U_2187] :
      ( ? [U_2186] :
          ( ~ hBOOL(hAPP(fun(U_2189,bool),bool,finite_finite_1(U_2189),hAPP(fun(U_2189,bool),fun(U_2189,bool),collect(U_2189),hAPP(fun(U_2189,bool),fun(U_2189,bool),hAPP(fun(U_2189,fun(bool,bool)),fun(fun(U_2189,bool),fun(U_2189,bool)),combs(U_2189,bool,bool),hAPP(fun(U_2189,bool),fun(U_2189,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_2189,bool),fun(U_2189,fun(bool,bool))),combb(bool,fun(bool,bool),U_2189),fconj),hAPP(fun(U_2189,bool),fun(U_2189,bool),hAPP(fun(U_2189,fun(fun(U_2189,bool),bool)),fun(fun(U_2189,bool),fun(U_2189,bool)),combc(U_2189,fun(U_2189,bool),bool),member(U_2189)),U_2187))),hAPP(U_2190,fun(U_2189,bool),hAPP(fun(U_2189,fun(U_2190,bool)),fun(U_2190,fun(U_2189,bool)),combc(U_2189,U_2190,bool),hAPP(fun(U_2189,U_2190),fun(U_2189,fun(U_2190,bool)),hAPP(fun(U_2190,fun(U_2190,bool)),fun(fun(U_2189,U_2190),fun(U_2189,fun(U_2190,bool))),combb(U_2190,fun(U_2190,bool),U_2189),fequal(U_2190)),U_2188)),hAPP(U_2189,U_2190,U_2188,U_2186))))))
          & hBOOL(hAPP(fun(U_2189,bool),bool,hAPP(U_2189,fun(fun(U_2189,bool),bool),member(U_2189),U_2186),U_2187)) )
      | ~ hBOOL(hAPP(fun(U_2190,bool),bool,finite_finite_1(U_2190),hAPP(fun(U_2189,bool),fun(U_2190,bool),hAPP(fun(U_2189,U_2190),fun(fun(U_2189,bool),fun(U_2190,bool)),image(U_2189,U_2190),U_2188),U_2187)))
      | hBOOL(hAPP(fun(U_2189,bool),bool,finite_finite_1(U_2189),U_2187)) ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

fof(f_611_3,plain,
    ! [U_2190,U_2189,U_2188,U_2187] :
      ( ( ~ hBOOL(hAPP(fun(U_2189,bool),bool,finite_finite_1(U_2189),hAPP(fun(U_2189,bool),fun(U_2189,bool),collect(U_2189),hAPP(fun(U_2189,bool),fun(U_2189,bool),hAPP(fun(U_2189,fun(bool,bool)),fun(fun(U_2189,bool),fun(U_2189,bool)),combs(U_2189,bool,bool),hAPP(fun(U_2189,bool),fun(U_2189,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_2189,bool),fun(U_2189,fun(bool,bool))),combb(bool,fun(bool,bool),U_2189),fconj),hAPP(fun(U_2189,bool),fun(U_2189,bool),hAPP(fun(U_2189,fun(fun(U_2189,bool),bool)),fun(fun(U_2189,bool),fun(U_2189,bool)),combc(U_2189,fun(U_2189,bool),bool),member(U_2189)),U_2187))),hAPP(U_2190,fun(U_2189,bool),hAPP(fun(U_2189,fun(U_2190,bool)),fun(U_2190,fun(U_2189,bool)),combc(U_2189,U_2190,bool),hAPP(fun(U_2189,U_2190),fun(U_2189,fun(U_2190,bool)),hAPP(fun(U_2190,fun(U_2190,bool)),fun(fun(U_2189,U_2190),fun(U_2189,fun(U_2190,bool))),combb(U_2190,fun(U_2190,bool),U_2189),fequal(U_2190)),U_2188)),hAPP(U_2189,U_2190,U_2188,sK125(U_2190,U_2189,U_2188,U_2187)))))))
        & hBOOL(hAPP(fun(U_2189,bool),bool,hAPP(U_2189,fun(fun(U_2189,bool),bool),member(U_2189),sK125(U_2190,U_2189,U_2188,U_2187)),U_2187)) )
      | ~ hBOOL(hAPP(fun(U_2190,bool),bool,finite_finite_1(U_2190),hAPP(fun(U_2189,bool),fun(U_2190,bool),hAPP(fun(U_2189,U_2190),fun(fun(U_2189,bool),fun(U_2190,bool)),image(U_2189,U_2190),U_2188),U_2187)))
      | hBOOL(hAPP(fun(U_2189,bool),bool,finite_finite_1(U_2189),U_2187)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_2186,sK125(U_2190,U_2189,U_2188,U_2187))],[f_611_2]) ).

cnf(f_611_4,plain,
    ( hBOOL(hAPP(fun(U_2189,bool),bool,hAPP(U_2189,fun(fun(U_2189,bool),bool),member(U_2189),sK125(U_2190,U_2189,U_2188,U_2187)),U_2187))
    | ~ hBOOL(hAPP(fun(U_2190,bool),bool,finite_finite_1(U_2190),hAPP(fun(U_2189,bool),fun(U_2190,bool),hAPP(fun(U_2189,U_2190),fun(fun(U_2189,bool),fun(U_2190,bool)),image(U_2189,U_2190),U_2188),U_2187)))
    | hBOOL(hAPP(fun(U_2189,bool),bool,finite_finite_1(U_2189),U_2187)) ),
    inference(clausify,[status(thm)],[f_611_3]) ).

cnf(f_611_5,plain,
    ( ~ hBOOL(hAPP(fun(U_2189,bool),bool,finite_finite_1(U_2189),hAPP(fun(U_2189,bool),fun(U_2189,bool),collect(U_2189),hAPP(fun(U_2189,bool),fun(U_2189,bool),hAPP(fun(U_2189,fun(bool,bool)),fun(fun(U_2189,bool),fun(U_2189,bool)),combs(U_2189,bool,bool),hAPP(fun(U_2189,bool),fun(U_2189,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_2189,bool),fun(U_2189,fun(bool,bool))),combb(bool,fun(bool,bool),U_2189),fconj),hAPP(fun(U_2189,bool),fun(U_2189,bool),hAPP(fun(U_2189,fun(fun(U_2189,bool),bool)),fun(fun(U_2189,bool),fun(U_2189,bool)),combc(U_2189,fun(U_2189,bool),bool),member(U_2189)),U_2187))),hAPP(U_2190,fun(U_2189,bool),hAPP(fun(U_2189,fun(U_2190,bool)),fun(U_2190,fun(U_2189,bool)),combc(U_2189,U_2190,bool),hAPP(fun(U_2189,U_2190),fun(U_2189,fun(U_2190,bool)),hAPP(fun(U_2190,fun(U_2190,bool)),fun(fun(U_2189,U_2190),fun(U_2189,fun(U_2190,bool))),combb(U_2190,fun(U_2190,bool),U_2189),fequal(U_2190)),U_2188)),hAPP(U_2189,U_2190,U_2188,sK125(U_2190,U_2189,U_2188,U_2187)))))))
    | ~ hBOOL(hAPP(fun(U_2190,bool),bool,finite_finite_1(U_2190),hAPP(fun(U_2189,bool),fun(U_2190,bool),hAPP(fun(U_2189,U_2190),fun(fun(U_2189,bool),fun(U_2190,bool)),image(U_2189,U_2190),U_2188),U_2187)))
    | hBOOL(hAPP(fun(U_2189,bool),bool,finite_finite_1(U_2189),U_2187)) ),
    inference(clausify,[status(thm)],[f_611_3]) ).

fof(f_612_1,plain,
    ! [X_a,A_1] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
        | ! [N_2,F_2] : ti(fun(X_a,bool),A_1) != hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2))) )
      & ( ? [N_2,F_2] : ti(fun(X_a,bool),A_1) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2)))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_522_finite__conv__nat__seg__image]) ).

fof(f_612_2,plain,
    ! [U_2196,U_2195] :
      ( ( hBOOL(hAPP(fun(U_2196,bool),bool,finite_finite_1(U_2196),U_2195))
        | ! [U_2194,U_2193] : ti(fun(U_2196,bool),U_2195) != hAPP(fun(nat,bool),fun(U_2196,bool),hAPP(fun(nat,U_2196),fun(fun(nat,bool),fun(U_2196,bool)),image(nat,U_2196),U_2193),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2194))) )
      & ( ? [U_2192,U_2191] : ti(fun(U_2196,bool),U_2195) = hAPP(fun(nat,bool),fun(U_2196,bool),hAPP(fun(nat,U_2196),fun(fun(nat,bool),fun(U_2196,bool)),image(nat,U_2196),U_2191),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2192)))
        | ~ hBOOL(hAPP(fun(U_2196,bool),bool,finite_finite_1(U_2196),U_2195)) ) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

fof(f_612_3,plain,
    ( ! [U_2200,U_2198] :
        ( hBOOL(hAPP(fun(U_2200,bool),bool,finite_finite_1(U_2200),U_2198))
        | ! [U_2194,U_2193] : ti(fun(U_2200,bool),U_2198) != hAPP(fun(nat,bool),fun(U_2200,bool),hAPP(fun(nat,U_2200),fun(fun(nat,bool),fun(U_2200,bool)),image(nat,U_2200),U_2193),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2194))) )
    & ! [U_2199,U_2197] :
        ( ? [U_2192,U_2191] : ti(fun(U_2199,bool),U_2197) = hAPP(fun(nat,bool),fun(U_2199,bool),hAPP(fun(nat,U_2199),fun(fun(nat,bool),fun(U_2199,bool)),image(nat,U_2199),U_2191),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2192)))
        | ~ hBOOL(hAPP(fun(U_2199,bool),bool,finite_finite_1(U_2199),U_2197)) ) ),
    inference(miniscope,[status(thm)],[f_612_2]) ).

fof(f_612_4,plain,
    ( ! [U_2200,U_2198] :
        ( hBOOL(hAPP(fun(U_2200,bool),bool,finite_finite_1(U_2200),U_2198))
        | ! [U_2194,U_2193] : ti(fun(U_2200,bool),U_2198) != hAPP(fun(nat,bool),fun(U_2200,bool),hAPP(fun(nat,U_2200),fun(fun(nat,bool),fun(U_2200,bool)),image(nat,U_2200),U_2193),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2194))) )
    & ! [U_2199,U_2197] :
        ( ? [U_2191] : ti(fun(U_2199,bool),U_2197) = hAPP(fun(nat,bool),fun(U_2199,bool),hAPP(fun(nat,U_2199),fun(fun(nat,bool),fun(U_2199,bool)),image(nat,U_2199),U_2191),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK126(U_2199,U_2197))))
        | ~ hBOOL(hAPP(fun(U_2199,bool),bool,finite_finite_1(U_2199),U_2197)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_2192,sK126(U_2199,U_2197))],[f_612_3]) ).

fof(f_612_5,plain,
    ( ! [U_2200,U_2198] :
        ( hBOOL(hAPP(fun(U_2200,bool),bool,finite_finite_1(U_2200),U_2198))
        | ! [U_2194,U_2193] : ti(fun(U_2200,bool),U_2198) != hAPP(fun(nat,bool),fun(U_2200,bool),hAPP(fun(nat,U_2200),fun(fun(nat,bool),fun(U_2200,bool)),image(nat,U_2200),U_2193),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2194))) )
    & ! [U_2199,U_2197] :
        ( ti(fun(U_2199,bool),U_2197) = hAPP(fun(nat,bool),fun(U_2199,bool),hAPP(fun(nat,U_2199),fun(fun(nat,bool),fun(U_2199,bool)),image(nat,U_2199),sK127(U_2199,U_2197)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK126(U_2199,U_2197))))
        | ~ hBOOL(hAPP(fun(U_2199,bool),bool,finite_finite_1(U_2199),U_2197)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_2191,sK127(U_2199,U_2197))],[f_612_4]) ).

cnf(f_612_6,plain,
    ( ti(fun(U_2199,bool),U_2197) = hAPP(fun(nat,bool),fun(U_2199,bool),hAPP(fun(nat,U_2199),fun(fun(nat,bool),fun(U_2199,bool)),image(nat,U_2199),sK127(U_2199,U_2197)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK126(U_2199,U_2197))))
    | ~ hBOOL(hAPP(fun(U_2199,bool),bool,finite_finite_1(U_2199),U_2197)) ),
    inference(clausify,[status(thm)],[f_612_5]) ).

cnf(f_612_7,plain,
    ( hBOOL(hAPP(fun(U_2200,bool),bool,finite_finite_1(U_2200),U_2198))
    | ti(fun(U_2200,bool),U_2198) != hAPP(fun(nat,bool),fun(U_2200,bool),hAPP(fun(nat,U_2200),fun(fun(nat,bool),fun(U_2200,bool)),image(nat,U_2200),U_2193),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2194))) ),
    inference(clausify,[status(thm)],[f_612_5]) ).

fof(f_613_1,plain,
    ! [X_a,A_1] :
      ( ? [N_2,F_2] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X_a),fun(fun(nat,bool),bool),inj_on(nat,X_a),F_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2))))
          & ti(fun(X_a,bool),A_1) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F_2),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2))) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_523_finite__imp__nat__seg__image__inj__on]) ).

fof(f_613_2,plain,
    ! [U_2204,U_2203] :
      ( ? [U_2202,U_2201] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,U_2204),fun(fun(nat,bool),bool),inj_on(nat,U_2204),U_2201),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2202))))
          & ti(fun(U_2204,bool),U_2203) = hAPP(fun(nat,bool),fun(U_2204,bool),hAPP(fun(nat,U_2204),fun(fun(nat,bool),fun(U_2204,bool)),image(nat,U_2204),U_2201),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2202))) )
      | ~ hBOOL(hAPP(fun(U_2204,bool),bool,finite_finite_1(U_2204),U_2203)) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ! [U_2204,U_2203] :
      ( ? [U_2201] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,U_2204),fun(fun(nat,bool),bool),inj_on(nat,U_2204),U_2201),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK128(U_2204,U_2203)))))
          & ti(fun(U_2204,bool),U_2203) = hAPP(fun(nat,bool),fun(U_2204,bool),hAPP(fun(nat,U_2204),fun(fun(nat,bool),fun(U_2204,bool)),image(nat,U_2204),U_2201),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK128(U_2204,U_2203)))) )
      | ~ hBOOL(hAPP(fun(U_2204,bool),bool,finite_finite_1(U_2204),U_2203)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_2202,sK128(U_2204,U_2203))],[f_613_2]) ).

fof(f_613_4,plain,
    ! [U_2204,U_2203] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,U_2204),fun(fun(nat,bool),bool),inj_on(nat,U_2204),sK129(U_2204,U_2203)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK128(U_2204,U_2203)))))
        & ti(fun(U_2204,bool),U_2203) = hAPP(fun(nat,bool),fun(U_2204,bool),hAPP(fun(nat,U_2204),fun(fun(nat,bool),fun(U_2204,bool)),image(nat,U_2204),sK129(U_2204,U_2203)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK128(U_2204,U_2203)))) )
      | ~ hBOOL(hAPP(fun(U_2204,bool),bool,finite_finite_1(U_2204),U_2203)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_2201,sK129(U_2204,U_2203))],[f_613_3]) ).

cnf(f_613_5,plain,
    ( ti(fun(U_2204,bool),U_2203) = hAPP(fun(nat,bool),fun(U_2204,bool),hAPP(fun(nat,U_2204),fun(fun(nat,bool),fun(U_2204,bool)),image(nat,U_2204),sK129(U_2204,U_2203)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK128(U_2204,U_2203))))
    | ~ hBOOL(hAPP(fun(U_2204,bool),bool,finite_finite_1(U_2204),U_2203)) ),
    inference(clausify,[status(thm)],[f_613_4]) ).

cnf(f_613_6,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,U_2204),fun(fun(nat,bool),bool),inj_on(nat,U_2204),sK129(U_2204,U_2203)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK128(U_2204,U_2203)))))
    | ~ hBOOL(hAPP(fun(U_2204,bool),bool,finite_finite_1(U_2204),U_2203)) ),
    inference(clausify,[status(thm)],[f_613_4]) ).

fof(f_614_1,plain,
    ! [X_a,A_1] :
      ( ? [F_2,N_2] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,nat),fun(fun(X_a,bool),bool),inj_on(X_a,nat),F_2),A_1))
          & hAPP(fun(X_a,bool),fun(nat,bool),hAPP(fun(X_a,nat),fun(fun(X_a,bool),fun(nat,bool)),image(X_a,nat),F_2),A_1) = hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2)) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_524_finite__imp__inj__to__nat__seg]) ).

fof(f_614_2,plain,
    ! [U_2208,U_2207] :
      ( ? [U_2206,U_2205] :
          ( hBOOL(hAPP(fun(U_2208,bool),bool,hAPP(fun(U_2208,nat),fun(fun(U_2208,bool),bool),inj_on(U_2208,nat),U_2206),U_2207))
          & hAPP(fun(U_2208,bool),fun(nat,bool),hAPP(fun(U_2208,nat),fun(fun(U_2208,bool),fun(nat,bool)),image(U_2208,nat),U_2206),U_2207) = hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2205)) )
      | ~ hBOOL(hAPP(fun(U_2208,bool),bool,finite_finite_1(U_2208),U_2207)) ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

fof(f_614_3,plain,
    ! [U_2208,U_2207] :
      ( ? [U_2206] :
          ( ? [U_2205] : hAPP(fun(U_2208,bool),fun(nat,bool),hAPP(fun(U_2208,nat),fun(fun(U_2208,bool),fun(nat,bool)),image(U_2208,nat),U_2206),U_2207) = hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2205))
          & hBOOL(hAPP(fun(U_2208,bool),bool,hAPP(fun(U_2208,nat),fun(fun(U_2208,bool),bool),inj_on(U_2208,nat),U_2206),U_2207)) )
      | ~ hBOOL(hAPP(fun(U_2208,bool),bool,finite_finite_1(U_2208),U_2207)) ),
    inference(miniscope,[status(thm)],[f_614_2]) ).

fof(f_614_4,plain,
    ! [U_2208,U_2207] :
      ( ( ? [U_2205] : hAPP(fun(U_2208,bool),fun(nat,bool),hAPP(fun(U_2208,nat),fun(fun(U_2208,bool),fun(nat,bool)),image(U_2208,nat),sK130(U_2208,U_2207)),U_2207) = hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_2205))
        & hBOOL(hAPP(fun(U_2208,bool),bool,hAPP(fun(U_2208,nat),fun(fun(U_2208,bool),bool),inj_on(U_2208,nat),sK130(U_2208,U_2207)),U_2207)) )
      | ~ hBOOL(hAPP(fun(U_2208,bool),bool,finite_finite_1(U_2208),U_2207)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_2206,sK130(U_2208,U_2207))],[f_614_3]) ).

fof(f_614_5,plain,
    ! [U_2208,U_2207] :
      ( ( hAPP(fun(U_2208,bool),fun(nat,bool),hAPP(fun(U_2208,nat),fun(fun(U_2208,bool),fun(nat,bool)),image(U_2208,nat),sK130(U_2208,U_2207)),U_2207) = hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK131(U_2208,U_2207)))
        & hBOOL(hAPP(fun(U_2208,bool),bool,hAPP(fun(U_2208,nat),fun(fun(U_2208,bool),bool),inj_on(U_2208,nat),sK130(U_2208,U_2207)),U_2207)) )
      | ~ hBOOL(hAPP(fun(U_2208,bool),bool,finite_finite_1(U_2208),U_2207)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_2205,sK131(U_2208,U_2207))],[f_614_4]) ).

cnf(f_614_6,plain,
    ( hBOOL(hAPP(fun(U_2208,bool),bool,hAPP(fun(U_2208,nat),fun(fun(U_2208,bool),bool),inj_on(U_2208,nat),sK130(U_2208,U_2207)),U_2207))
    | ~ hBOOL(hAPP(fun(U_2208,bool),bool,finite_finite_1(U_2208),U_2207)) ),
    inference(clausify,[status(thm)],[f_614_5]) ).

cnf(f_614_7,plain,
    ( hAPP(fun(U_2208,bool),fun(nat,bool),hAPP(fun(U_2208,nat),fun(fun(U_2208,bool),fun(nat,bool)),image(U_2208,nat),sK130(U_2208,U_2207)),U_2207) = hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK131(U_2208,U_2207)))
    | ~ hBOOL(hAPP(fun(U_2208,bool),bool,finite_finite_1(U_2208),U_2207)) ),
    inference(clausify,[status(thm)],[f_614_5]) ).

fof(f_615_1,plain,
    ! [X_b,X_a,G,F,A_1] :
      ( ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1)))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),A_1)) )
        & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),A_1))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),F),A_1))) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),F),A_1))
      | ? [X_1] :
          ( ? [Xa] :
              ( ( ( hAPP(X_a,X_b,G,hAPP(X_a,X_a,F,X_1)) != hAPP(X_a,X_b,G,hAPP(X_a,X_a,F,Xa))
                  & hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,G,Xa) )
                | ( hAPP(X_a,X_b,G,X_1) != hAPP(X_a,X_b,G,Xa)
                  & hAPP(X_a,X_b,G,hAPP(X_a,X_a,F,X_1)) = hAPP(X_a,X_b,G,hAPP(X_a,X_a,F,Xa)) ) )
              & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) )
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_525_inj__on__image__iff]) ).

fof(f_615_2,plain,
    ! [U_2215,U_2214,U_2213,U_2212,U_2211] :
      ( ( ( hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
          | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211)) )
        & ( hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
          | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211))) ) )
      | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211))
      | ? [U_2210] :
          ( ? [U_2209] :
              ( ( ( hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,U_2210)) != hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,U_2209))
                  & hAPP(U_2214,U_2215,U_2213,U_2210) = hAPP(U_2214,U_2215,U_2213,U_2209) )
                | ( hAPP(U_2214,U_2215,U_2213,U_2210) != hAPP(U_2214,U_2215,U_2213,U_2209)
                  & hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,U_2210)) = hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,U_2209)) ) )
              & hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(U_2214,fun(fun(U_2214,bool),bool),member(U_2214),U_2209),U_2211)) )
          & hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(U_2214,fun(fun(U_2214,bool),bool),member(U_2214),U_2210),U_2211)) ) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

fof(f_615_3,plain,
    ! [U_2215,U_2214,U_2213,U_2212,U_2211] :
      ( ( ( hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
          | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211)) )
        & ( hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
          | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211))) ) )
      | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211))
      | ( ? [U_2209] :
            ( ( ( hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) != hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,U_2209))
                & hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) = hAPP(U_2214,U_2215,U_2213,U_2209) )
              | ( hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) != hAPP(U_2214,U_2215,U_2213,U_2209)
                & hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) = hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,U_2209)) ) )
            & hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(U_2214,fun(fun(U_2214,bool),bool),member(U_2214),U_2209),U_2211)) )
        & hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(U_2214,fun(fun(U_2214,bool),bool),member(U_2214),sK132(U_2215,U_2214,U_2213,U_2212,U_2211)),U_2211)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_2210,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))],[f_615_2]) ).

fof(f_615_4,plain,
    ! [U_2215,U_2214,U_2213,U_2212,U_2211] :
      ( ( ( hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
          | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211)) )
        & ( hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
          | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211))) ) )
      | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211))
      | ( ( ( hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) != hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK133(U_2215,U_2214,U_2213,U_2212,U_2211)))
            & hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) = hAPP(U_2214,U_2215,U_2213,sK133(U_2215,U_2214,U_2213,U_2212,U_2211)) )
          | ( hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) != hAPP(U_2214,U_2215,U_2213,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))
            & hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) = hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))) ) )
        & hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(U_2214,fun(fun(U_2214,bool),bool),member(U_2214),sK133(U_2215,U_2214,U_2213,U_2212,U_2211)),U_2211))
        & hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(U_2214,fun(fun(U_2214,bool),bool),member(U_2214),sK132(U_2215,U_2214,U_2213,U_2212,U_2211)),U_2211)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_2209,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))],[f_615_3]) ).

cnf(f_615_5,plain,
    ( hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(U_2214,fun(fun(U_2214,bool),bool),member(U_2214),sK132(U_2215,U_2214,U_2213,U_2212,U_2211)),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_6,plain,
    ( hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(U_2214,fun(fun(U_2214,bool),bool),member(U_2214),sK132(U_2215,U_2214,U_2213,U_2212,U_2211)),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_7,plain,
    ( hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(U_2214,fun(fun(U_2214,bool),bool),member(U_2214),sK133(U_2215,U_2214,U_2213,U_2212,U_2211)),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_8,plain,
    ( hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(U_2214,fun(fun(U_2214,bool),bool),member(U_2214),sK133(U_2215,U_2214,U_2213,U_2212,U_2211)),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_9,plain,
    ( hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) = hAPP(U_2214,U_2215,U_2213,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))
    | hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) = hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK133(U_2215,U_2214,U_2213,U_2212,U_2211)))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_10,plain,
    ( hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) != hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK133(U_2215,U_2214,U_2213,U_2212,U_2211)))
    | hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) = hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK133(U_2215,U_2214,U_2213,U_2212,U_2211)))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_11,plain,
    ( hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) = hAPP(U_2214,U_2215,U_2213,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))
    | hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) != hAPP(U_2214,U_2215,U_2213,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_12,plain,
    ( hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) != hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK133(U_2215,U_2214,U_2213,U_2212,U_2211)))
    | hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) != hAPP(U_2214,U_2215,U_2213,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_13,plain,
    ( hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) = hAPP(U_2214,U_2215,U_2213,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))
    | hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) = hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK133(U_2215,U_2214,U_2213,U_2212,U_2211)))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_14,plain,
    ( hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) != hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK133(U_2215,U_2214,U_2213,U_2212,U_2211)))
    | hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) = hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK133(U_2215,U_2214,U_2213,U_2212,U_2211)))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_15,plain,
    ( hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) = hAPP(U_2214,U_2215,U_2213,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))
    | hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) != hAPP(U_2214,U_2215,U_2213,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

cnf(f_615_16,plain,
    ( hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK132(U_2215,U_2214,U_2213,U_2212,U_2211))) != hAPP(U_2214,U_2215,U_2213,hAPP(U_2214,U_2214,U_2212,sK133(U_2215,U_2214,U_2213,U_2212,U_2211)))
    | hAPP(U_2214,U_2215,U_2213,sK132(U_2215,U_2214,U_2213,U_2212,U_2211)) != hAPP(U_2214,U_2215,U_2213,sK133(U_2215,U_2214,U_2213,U_2212,U_2211))
    | hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),hAPP(fun(U_2214,bool),fun(U_2214,bool),hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),fun(U_2214,bool)),image(U_2214,U_2214),U_2212),U_2211)))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2215),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2215),U_2213),U_2211))
    | ~ hBOOL(hAPP(fun(U_2214,bool),bool,hAPP(fun(U_2214,U_2214),fun(fun(U_2214,bool),bool),inj_on(U_2214,U_2214),U_2212),U_2211)) ),
    inference(clausify,[status(thm)],[f_615_4]) ).

fof(f_616_1,plain,
    ! [X_b,X_a,Y_1,F] :
      ( ? [X_1] : ti(X_a,Y_1) = hAPP(X_b,X_a,F,X_1)
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) != top_top(fun(X_a,bool)) ),
    inference(fof_nnf,[status(thm)],[fact_526_surjE]) ).

fof(f_616_2,plain,
    ! [U_2220,U_2219,U_2218,U_2217] :
      ( ? [U_2216] : ti(U_2219,U_2218) = hAPP(U_2220,U_2219,U_2217,U_2216)
      | hAPP(fun(U_2220,bool),fun(U_2219,bool),hAPP(fun(U_2220,U_2219),fun(fun(U_2220,bool),fun(U_2219,bool)),image(U_2220,U_2219),U_2217),top_top(fun(U_2220,bool))) != top_top(fun(U_2219,bool)) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

fof(f_616_3,plain,
    ! [U_2220,U_2219,U_2218,U_2217] :
      ( ti(U_2219,U_2218) = hAPP(U_2220,U_2219,U_2217,sK134(U_2220,U_2219,U_2218,U_2217))
      | hAPP(fun(U_2220,bool),fun(U_2219,bool),hAPP(fun(U_2220,U_2219),fun(fun(U_2220,bool),fun(U_2219,bool)),image(U_2220,U_2219),U_2217),top_top(fun(U_2220,bool))) != top_top(fun(U_2219,bool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_2216,sK134(U_2220,U_2219,U_2218,U_2217))],[f_616_2]) ).

cnf(f_616_4,plain,
    ( ti(U_2219,U_2218) = hAPP(U_2220,U_2219,U_2217,sK134(U_2220,U_2219,U_2218,U_2217))
    | hAPP(fun(U_2220,bool),fun(U_2219,bool),hAPP(fun(U_2220,U_2219),fun(fun(U_2220,bool),fun(U_2219,bool)),image(U_2220,U_2219),U_2217),top_top(fun(U_2220,bool))) != top_top(fun(U_2219,bool)) ),
    inference(clausify,[status(thm)],[f_616_3]) ).

fof(f_617_1,plain,
    ! [X_b,X_a,Y_1,F] :
      ( ? [X_1] : ti(X_a,Y_1) = hAPP(X_b,X_a,F,X_1)
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) != top_top(fun(X_a,bool)) ),
    inference(fof_nnf,[status(thm)],[fact_527_surjD]) ).

fof(f_617_2,plain,
    ! [U_2225,U_2224,U_2223,U_2222] :
      ( ? [U_2221] : ti(U_2224,U_2223) = hAPP(U_2225,U_2224,U_2222,U_2221)
      | hAPP(fun(U_2225,bool),fun(U_2224,bool),hAPP(fun(U_2225,U_2224),fun(fun(U_2225,bool),fun(U_2224,bool)),image(U_2225,U_2224),U_2222),top_top(fun(U_2225,bool))) != top_top(fun(U_2224,bool)) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

fof(f_617_3,plain,
    ! [U_2225,U_2224,U_2223,U_2222] :
      ( ti(U_2224,U_2223) = hAPP(U_2225,U_2224,U_2222,sK135(U_2225,U_2224,U_2223,U_2222))
      | hAPP(fun(U_2225,bool),fun(U_2224,bool),hAPP(fun(U_2225,U_2224),fun(fun(U_2225,bool),fun(U_2224,bool)),image(U_2225,U_2224),U_2222),top_top(fun(U_2225,bool))) != top_top(fun(U_2224,bool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_2221,sK135(U_2225,U_2224,U_2223,U_2222))],[f_617_2]) ).

cnf(f_617_4,plain,
    ( ti(U_2224,U_2223) = hAPP(U_2225,U_2224,U_2222,sK135(U_2225,U_2224,U_2223,U_2222))
    | hAPP(fun(U_2225,bool),fun(U_2224,bool),hAPP(fun(U_2225,U_2224),fun(fun(U_2225,bool),fun(U_2224,bool)),image(U_2225,U_2224),U_2222),top_top(fun(U_2225,bool))) != top_top(fun(U_2224,bool)) ),
    inference(clausify,[status(thm)],[f_617_3]) ).

fof(f_618_1,plain,
    ! [X_b,X_a,G,F] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
      | ? [X_1] : hAPP(X_b,X_a,G,hAPP(X_a,X_b,F,X_1)) != ti(X_a,X_1) ),
    inference(fof_nnf,[status(thm)],[fact_528_surjI]) ).

fof(f_618_2,plain,
    ! [U_2230,U_2229,U_2228,U_2227] :
      ( hAPP(fun(U_2230,bool),fun(U_2229,bool),hAPP(fun(U_2230,U_2229),fun(fun(U_2230,bool),fun(U_2229,bool)),image(U_2230,U_2229),U_2228),top_top(fun(U_2230,bool))) = top_top(fun(U_2229,bool))
      | ? [U_2226] : hAPP(U_2230,U_2229,U_2228,hAPP(U_2229,U_2230,U_2227,U_2226)) != ti(U_2229,U_2226) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

fof(f_618_3,plain,
    ! [U_2230,U_2229,U_2228] :
      ( ! [U_2227] :
        ? [U_2226] : hAPP(U_2230,U_2229,U_2228,hAPP(U_2229,U_2230,U_2227,U_2226)) != ti(U_2229,U_2226)
      | hAPP(fun(U_2230,bool),fun(U_2229,bool),hAPP(fun(U_2230,U_2229),fun(fun(U_2230,bool),fun(U_2229,bool)),image(U_2230,U_2229),U_2228),top_top(fun(U_2230,bool))) = top_top(fun(U_2229,bool)) ),
    inference(miniscope,[status(thm)],[f_618_2]) ).

fof(f_618_4,plain,
    ! [U_2230,U_2229,U_2228] :
      ( ! [U_2227] : hAPP(U_2230,U_2229,U_2228,hAPP(U_2229,U_2230,U_2227,sK136(U_2230,U_2229,U_2228,U_2227))) != ti(U_2229,sK136(U_2230,U_2229,U_2228,U_2227))
      | hAPP(fun(U_2230,bool),fun(U_2229,bool),hAPP(fun(U_2230,U_2229),fun(fun(U_2230,bool),fun(U_2229,bool)),image(U_2230,U_2229),U_2228),top_top(fun(U_2230,bool))) = top_top(fun(U_2229,bool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_2226,sK136(U_2230,U_2229,U_2228,U_2227))],[f_618_3]) ).

cnf(f_618_5,plain,
    ( hAPP(U_2230,U_2229,U_2228,hAPP(U_2229,U_2230,U_2227,sK136(U_2230,U_2229,U_2228,U_2227))) != ti(U_2229,sK136(U_2230,U_2229,U_2228,U_2227))
    | hAPP(fun(U_2230,bool),fun(U_2229,bool),hAPP(fun(U_2230,U_2229),fun(fun(U_2230,bool),fun(U_2229,bool)),image(U_2230,U_2229),U_2228),top_top(fun(U_2230,bool))) = top_top(fun(U_2229,bool)) ),
    inference(clausify,[status(thm)],[f_618_4]) ).

fof(f_619_1,plain,
    ! [X_b,X_a,F] :
      ( ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) = top_top(fun(X_a,bool))
        | ? [Y_2] :
          ! [X_1] : ti(X_a,Y_2) != hAPP(X_b,X_a,F,X_1) )
      & ( ! [Y_2] :
          ? [X_1] : ti(X_a,Y_2) = hAPP(X_b,X_a,F,X_1)
        | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) != top_top(fun(X_a,bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_529_surj__def]) ).

fof(f_619_2,plain,
    ! [U_2237,U_2236,U_2235] :
      ( ( hAPP(fun(U_2237,bool),fun(U_2236,bool),hAPP(fun(U_2237,U_2236),fun(fun(U_2237,bool),fun(U_2236,bool)),image(U_2237,U_2236),U_2235),top_top(fun(U_2237,bool))) = top_top(fun(U_2236,bool))
        | ? [U_2234] :
          ! [U_2233] : ti(U_2236,U_2234) != hAPP(U_2237,U_2236,U_2235,U_2233) )
      & ( ! [U_2232] :
          ? [U_2231] : ti(U_2236,U_2232) = hAPP(U_2237,U_2236,U_2235,U_2231)
        | hAPP(fun(U_2237,bool),fun(U_2236,bool),hAPP(fun(U_2237,U_2236),fun(fun(U_2237,bool),fun(U_2236,bool)),image(U_2237,U_2236),U_2235),top_top(fun(U_2237,bool))) != top_top(fun(U_2236,bool)) ) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

fof(f_619_3,plain,
    ( ! [U_2243,U_2241,U_2239] :
        ( hAPP(fun(U_2243,bool),fun(U_2241,bool),hAPP(fun(U_2243,U_2241),fun(fun(U_2243,bool),fun(U_2241,bool)),image(U_2243,U_2241),U_2239),top_top(fun(U_2243,bool))) = top_top(fun(U_2241,bool))
        | ? [U_2234] :
          ! [U_2233] : ti(U_2241,U_2234) != hAPP(U_2243,U_2241,U_2239,U_2233) )
    & ! [U_2242,U_2240,U_2238] :
        ( ! [U_2232] :
          ? [U_2231] : ti(U_2240,U_2232) = hAPP(U_2242,U_2240,U_2238,U_2231)
        | hAPP(fun(U_2242,bool),fun(U_2240,bool),hAPP(fun(U_2242,U_2240),fun(fun(U_2242,bool),fun(U_2240,bool)),image(U_2242,U_2240),U_2238),top_top(fun(U_2242,bool))) != top_top(fun(U_2240,bool)) ) ),
    inference(miniscope,[status(thm)],[f_619_2]) ).

fof(f_619_4,plain,
    ( ! [U_2243,U_2241,U_2239] :
        ( hAPP(fun(U_2243,bool),fun(U_2241,bool),hAPP(fun(U_2243,U_2241),fun(fun(U_2243,bool),fun(U_2241,bool)),image(U_2243,U_2241),U_2239),top_top(fun(U_2243,bool))) = top_top(fun(U_2241,bool))
        | ? [U_2234] :
          ! [U_2233] : ti(U_2241,U_2234) != hAPP(U_2243,U_2241,U_2239,U_2233) )
    & ! [U_2242,U_2240,U_2238] :
        ( ! [U_2232] : ti(U_2240,U_2232) = hAPP(U_2242,U_2240,U_2238,sK137(U_2242,U_2240,U_2238,U_2232))
        | hAPP(fun(U_2242,bool),fun(U_2240,bool),hAPP(fun(U_2242,U_2240),fun(fun(U_2242,bool),fun(U_2240,bool)),image(U_2242,U_2240),U_2238),top_top(fun(U_2242,bool))) != top_top(fun(U_2240,bool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_2231,sK137(U_2242,U_2240,U_2238,U_2232))],[f_619_3]) ).

fof(f_619_5,plain,
    ( ! [U_2243,U_2241,U_2239] :
        ( hAPP(fun(U_2243,bool),fun(U_2241,bool),hAPP(fun(U_2243,U_2241),fun(fun(U_2243,bool),fun(U_2241,bool)),image(U_2243,U_2241),U_2239),top_top(fun(U_2243,bool))) = top_top(fun(U_2241,bool))
        | ! [U_2233] : ti(U_2241,sK138(U_2243,U_2241,U_2239)) != hAPP(U_2243,U_2241,U_2239,U_2233) )
    & ! [U_2242,U_2240,U_2238] :
        ( ! [U_2232] : ti(U_2240,U_2232) = hAPP(U_2242,U_2240,U_2238,sK137(U_2242,U_2240,U_2238,U_2232))
        | hAPP(fun(U_2242,bool),fun(U_2240,bool),hAPP(fun(U_2242,U_2240),fun(fun(U_2242,bool),fun(U_2240,bool)),image(U_2242,U_2240),U_2238),top_top(fun(U_2242,bool))) != top_top(fun(U_2240,bool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_2234,sK138(U_2243,U_2241,U_2239))],[f_619_4]) ).

cnf(f_619_6,plain,
    ( ti(U_2240,U_2232) = hAPP(U_2242,U_2240,U_2238,sK137(U_2242,U_2240,U_2238,U_2232))
    | hAPP(fun(U_2242,bool),fun(U_2240,bool),hAPP(fun(U_2242,U_2240),fun(fun(U_2242,bool),fun(U_2240,bool)),image(U_2242,U_2240),U_2238),top_top(fun(U_2242,bool))) != top_top(fun(U_2240,bool)) ),
    inference(clausify,[status(thm)],[f_619_5]) ).

cnf(f_619_7,plain,
    ( hAPP(fun(U_2243,bool),fun(U_2241,bool),hAPP(fun(U_2243,U_2241),fun(fun(U_2243,bool),fun(U_2241,bool)),image(U_2243,U_2241),U_2239),top_top(fun(U_2243,bool))) = top_top(fun(U_2241,bool))
    | ti(U_2241,sK138(U_2243,U_2241,U_2239)) != hAPP(U_2243,U_2241,U_2239,U_2233) ),
    inference(clausify,[status(thm)],[f_619_5]) ).

fof(f_620_1,plain,
    ! [X_b,X_a,F,B,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_530_image__subsetI]) ).

fof(f_620_2,plain,
    ! [U_2249,U_2248,U_2247,U_2246,U_2245] :
      ( hBOOL(hAPP(fun(U_2249,bool),bool,hAPP(fun(U_2249,bool),fun(fun(U_2249,bool),bool),ord_less_eq(fun(U_2249,bool)),hAPP(fun(U_2248,bool),fun(U_2249,bool),hAPP(fun(U_2248,U_2249),fun(fun(U_2248,bool),fun(U_2249,bool)),image(U_2248,U_2249),U_2247),U_2245)),U_2246))
      | ? [U_2244] :
          ( ~ hBOOL(hAPP(fun(U_2249,bool),bool,hAPP(U_2249,fun(fun(U_2249,bool),bool),member(U_2249),hAPP(U_2248,U_2249,U_2247,U_2244)),U_2246))
          & hBOOL(hAPP(fun(U_2248,bool),bool,hAPP(U_2248,fun(fun(U_2248,bool),bool),member(U_2248),U_2244),U_2245)) ) ),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

fof(f_620_3,plain,
    ! [U_2249,U_2248,U_2247,U_2246,U_2245] :
      ( hBOOL(hAPP(fun(U_2249,bool),bool,hAPP(fun(U_2249,bool),fun(fun(U_2249,bool),bool),ord_less_eq(fun(U_2249,bool)),hAPP(fun(U_2248,bool),fun(U_2249,bool),hAPP(fun(U_2248,U_2249),fun(fun(U_2248,bool),fun(U_2249,bool)),image(U_2248,U_2249),U_2247),U_2245)),U_2246))
      | ( ~ hBOOL(hAPP(fun(U_2249,bool),bool,hAPP(U_2249,fun(fun(U_2249,bool),bool),member(U_2249),hAPP(U_2248,U_2249,U_2247,sK139(U_2249,U_2248,U_2247,U_2246,U_2245))),U_2246))
        & hBOOL(hAPP(fun(U_2248,bool),bool,hAPP(U_2248,fun(fun(U_2248,bool),bool),member(U_2248),sK139(U_2249,U_2248,U_2247,U_2246,U_2245)),U_2245)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_2244,sK139(U_2249,U_2248,U_2247,U_2246,U_2245))],[f_620_2]) ).

cnf(f_620_4,plain,
    ( hBOOL(hAPP(fun(U_2248,bool),bool,hAPP(U_2248,fun(fun(U_2248,bool),bool),member(U_2248),sK139(U_2249,U_2248,U_2247,U_2246,U_2245)),U_2245))
    | hBOOL(hAPP(fun(U_2249,bool),bool,hAPP(fun(U_2249,bool),fun(fun(U_2249,bool),bool),ord_less_eq(fun(U_2249,bool)),hAPP(fun(U_2248,bool),fun(U_2249,bool),hAPP(fun(U_2248,U_2249),fun(fun(U_2248,bool),fun(U_2249,bool)),image(U_2248,U_2249),U_2247),U_2245)),U_2246)) ),
    inference(clausify,[status(thm)],[f_620_3]) ).

cnf(f_620_5,plain,
    ( ~ hBOOL(hAPP(fun(U_2249,bool),bool,hAPP(U_2249,fun(fun(U_2249,bool),bool),member(U_2249),hAPP(U_2248,U_2249,U_2247,sK139(U_2249,U_2248,U_2247,U_2246,U_2245))),U_2246))
    | hBOOL(hAPP(fun(U_2249,bool),bool,hAPP(fun(U_2249,bool),fun(fun(U_2249,bool),bool),ord_less_eq(fun(U_2249,bool)),hAPP(fun(U_2248,bool),fun(U_2249,bool),hAPP(fun(U_2248,U_2249),fun(fun(U_2248,bool),fun(U_2249,bool)),image(U_2248,U_2249),U_2247),U_2245)),U_2246)) ),
    inference(clausify,[status(thm)],[f_620_3]) ).

fof(f_621_1,plain,
    hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))),
    inference(fof_nnf,[status(thm)],[fact_531_greaterThan__0]) ).

cnf(f_621_2,plain,
    hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))),
    inference(clausify,[status(thm)],[f_621_1]) ).

fof(f_622_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a)))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) )
            & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a)))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a))) ) )
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) )
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_532_Ints__odd__less__0]) ).

fof(f_622_2,plain,
    ! [U_2251] :
      ( ! [U_2250] :
          ( ( ( hBOOL(hAPP(U_2251,bool,hAPP(U_2251,fun(U_2251,bool),ord_less(U_2251),hAPP(U_2251,U_2251,hAPP(U_2251,fun(U_2251,U_2251),plus_plus(U_2251),hAPP(U_2251,U_2251,hAPP(U_2251,fun(U_2251,U_2251),plus_plus(U_2251),one_one(U_2251)),U_2250)),U_2250)),zero_zero(U_2251)))
              | ~ hBOOL(hAPP(U_2251,bool,hAPP(U_2251,fun(U_2251,bool),ord_less(U_2251),U_2250),zero_zero(U_2251))) )
            & ( hBOOL(hAPP(U_2251,bool,hAPP(U_2251,fun(U_2251,bool),ord_less(U_2251),U_2250),zero_zero(U_2251)))
              | ~ hBOOL(hAPP(U_2251,bool,hAPP(U_2251,fun(U_2251,bool),ord_less(U_2251),hAPP(U_2251,U_2251,hAPP(U_2251,fun(U_2251,U_2251),plus_plus(U_2251),hAPP(U_2251,U_2251,hAPP(U_2251,fun(U_2251,U_2251),plus_plus(U_2251),one_one(U_2251)),U_2250)),U_2250)),zero_zero(U_2251))) ) )
          | ~ hBOOL(hAPP(fun(U_2251,bool),bool,hAPP(U_2251,fun(fun(U_2251,bool),bool),member(U_2251),U_2250),ring_1_Ints(U_2251))) )
      | ~ linordered_idom(U_2251) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

cnf(f_622_3,plain,
    ( hBOOL(hAPP(U_2251,bool,hAPP(U_2251,fun(U_2251,bool),ord_less(U_2251),U_2250),zero_zero(U_2251)))
    | ~ hBOOL(hAPP(U_2251,bool,hAPP(U_2251,fun(U_2251,bool),ord_less(U_2251),hAPP(U_2251,U_2251,hAPP(U_2251,fun(U_2251,U_2251),plus_plus(U_2251),hAPP(U_2251,U_2251,hAPP(U_2251,fun(U_2251,U_2251),plus_plus(U_2251),one_one(U_2251)),U_2250)),U_2250)),zero_zero(U_2251)))
    | ~ hBOOL(hAPP(fun(U_2251,bool),bool,hAPP(U_2251,fun(fun(U_2251,bool),bool),member(U_2251),U_2250),ring_1_Ints(U_2251)))
    | ~ linordered_idom(U_2251) ),
    inference(clausify,[status(thm)],[f_622_2]) ).

cnf(f_622_4,plain,
    ( hBOOL(hAPP(U_2251,bool,hAPP(U_2251,fun(U_2251,bool),ord_less(U_2251),hAPP(U_2251,U_2251,hAPP(U_2251,fun(U_2251,U_2251),plus_plus(U_2251),hAPP(U_2251,U_2251,hAPP(U_2251,fun(U_2251,U_2251),plus_plus(U_2251),one_one(U_2251)),U_2250)),U_2250)),zero_zero(U_2251)))
    | ~ hBOOL(hAPP(U_2251,bool,hAPP(U_2251,fun(U_2251,bool),ord_less(U_2251),U_2250),zero_zero(U_2251)))
    | ~ hBOOL(hAPP(fun(U_2251,bool),bool,hAPP(U_2251,fun(fun(U_2251,bool),bool),member(U_2251),U_2250),ring_1_Ints(U_2251)))
    | ~ linordered_idom(U_2251) ),
    inference(clausify,[status(thm)],[f_622_2]) ).

fof(f_623_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),M)),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),M)),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_533_less__eq__nat_Osimps_I2_J]) ).

fof(f_623_2,plain,
    ! [U_2253,U_2252] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_2253)),U_2252))
        | ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2253)),U_2252)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2253)),U_2252))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_2253)),U_2252)) ) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

fof(f_623_3,plain,
    ( ! [U_2257,U_2255] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_2257)),U_2255))
        | ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2257)),U_2255)) )
    & ! [U_2256,U_2254] :
        ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2256)),U_2254))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_2256)),U_2254)) ) ),
    inference(miniscope,[status(thm)],[f_623_2]) ).

cnf(f_623_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2256)),U_2254))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_2256)),U_2254)) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

cnf(f_623_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_2257)),U_2255))
    | ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2257)),U_2255)) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

fof(f_624_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),X_2) = hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),Y_1)
            | ti(X_a,X_2) != ti(X_a,Y_1) )
          & ( ti(X_a,X_2) = ti(X_a,Y_1)
            | hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),X_2) != hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),Y_1) ) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_534_greaterThan__eq__iff]) ).

fof(f_624_2,plain,
    ! [U_2260] :
      ( ! [U_2259,U_2258] :
          ( ( hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2259) = hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2258)
            | ti(U_2260,U_2259) != ti(U_2260,U_2258) )
          & ( ti(U_2260,U_2259) = ti(U_2260,U_2258)
            | hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2259) != hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2258) ) )
      | ~ linorder(U_2260) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ! [U_2260] :
      ( ( ! [U_2264,U_2262] :
            ( hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2264) = hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2262)
            | ti(U_2260,U_2264) != ti(U_2260,U_2262) )
        & ! [U_2263,U_2261] :
            ( ti(U_2260,U_2263) = ti(U_2260,U_2261)
            | hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2263) != hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2261) ) )
      | ~ linorder(U_2260) ),
    inference(miniscope,[status(thm)],[f_624_2]) ).

cnf(f_624_4,plain,
    ( ti(U_2260,U_2263) = ti(U_2260,U_2261)
    | hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2263) != hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2261)
    | ~ linorder(U_2260) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

cnf(f_624_5,plain,
    ( hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2264) = hAPP(U_2260,fun(U_2260,bool),ord_greaterThan(U_2260),U_2262)
    | ti(U_2260,U_2264) != ti(U_2260,U_2262)
    | ~ linorder(U_2260) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

fof(f_625_1,plain,
    ! [X_a] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),ring_1_Ints(X_a)))
      | ~ ring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_535_Ints__0]) ).

fof(f_625_2,plain,
    ! [U_2265] :
      ( hBOOL(hAPP(fun(U_2265,bool),bool,hAPP(U_2265,fun(fun(U_2265,bool),bool),member(U_2265),zero_zero(U_2265)),ring_1_Ints(U_2265)))
      | ~ ring_1(U_2265) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

cnf(f_625_3,plain,
    ( hBOOL(hAPP(fun(U_2265,bool),bool,hAPP(U_2265,fun(fun(U_2265,bool),bool),member(U_2265),zero_zero(U_2265)),ring_1_Ints(U_2265)))
    | ~ ring_1(U_2265) ),
    inference(clausify,[status(thm)],[f_625_2]) ).

fof(f_626_1,plain,
    ! [X_a] :
      ( ! [Ba,Aa] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)),ring_1_Ints(X_a)))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) )
      | ~ ring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_536_Ints__add]) ).

fof(f_626_2,plain,
    ! [U_2268] :
      ( ! [U_2267,U_2266] :
          ( hBOOL(hAPP(fun(U_2268,bool),bool,hAPP(U_2268,fun(fun(U_2268,bool),bool),member(U_2268),hAPP(U_2268,U_2268,hAPP(U_2268,fun(U_2268,U_2268),plus_plus(U_2268),U_2266),U_2267)),ring_1_Ints(U_2268)))
          | ~ hBOOL(hAPP(fun(U_2268,bool),bool,hAPP(U_2268,fun(fun(U_2268,bool),bool),member(U_2268),U_2267),ring_1_Ints(U_2268)))
          | ~ hBOOL(hAPP(fun(U_2268,bool),bool,hAPP(U_2268,fun(fun(U_2268,bool),bool),member(U_2268),U_2266),ring_1_Ints(U_2268))) )
      | ~ ring_1(U_2268) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

cnf(f_626_3,plain,
    ( hBOOL(hAPP(fun(U_2268,bool),bool,hAPP(U_2268,fun(fun(U_2268,bool),bool),member(U_2268),hAPP(U_2268,U_2268,hAPP(U_2268,fun(U_2268,U_2268),plus_plus(U_2268),U_2266),U_2267)),ring_1_Ints(U_2268)))
    | ~ hBOOL(hAPP(fun(U_2268,bool),bool,hAPP(U_2268,fun(fun(U_2268,bool),bool),member(U_2268),U_2267),ring_1_Ints(U_2268)))
    | ~ hBOOL(hAPP(fun(U_2268,bool),bool,hAPP(U_2268,fun(fun(U_2268,bool),bool),member(U_2268),U_2266),ring_1_Ints(U_2268)))
    | ~ ring_1(U_2268) ),
    inference(clausify,[status(thm)],[f_626_2]) ).

fof(f_627_1,plain,
    ! [X_a] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),ring_1_Ints(X_a)))
      | ~ ring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_537_Ints__1]) ).

fof(f_627_2,plain,
    ! [U_2269] :
      ( hBOOL(hAPP(fun(U_2269,bool),bool,hAPP(U_2269,fun(fun(U_2269,bool),bool),member(U_2269),one_one(U_2269)),ring_1_Ints(U_2269)))
      | ~ ring_1(U_2269) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

cnf(f_627_3,plain,
    ( hBOOL(hAPP(fun(U_2269,bool),bool,hAPP(U_2269,fun(fun(U_2269,bool),bool),member(U_2269),one_one(U_2269)),ring_1_Ints(U_2269)))
    | ~ ring_1(U_2269) ),
    inference(clausify,[status(thm)],[f_627_2]) ).

fof(f_628_1,plain,
    ! [X_a] :
      ( ! [I,K] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),K)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),K),I)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),K),I))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),K))) ) )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_538_greaterThan__iff]) ).

fof(f_628_2,plain,
    ! [U_2272] :
      ( ! [U_2271,U_2270] :
          ( ( hBOOL(hAPP(fun(U_2272,bool),bool,hAPP(U_2272,fun(fun(U_2272,bool),bool),member(U_2272),U_2271),hAPP(U_2272,fun(U_2272,bool),ord_greaterThan(U_2272),U_2270)))
            | ~ hBOOL(hAPP(U_2272,bool,hAPP(U_2272,fun(U_2272,bool),ord_less(U_2272),U_2270),U_2271)) )
          & ( hBOOL(hAPP(U_2272,bool,hAPP(U_2272,fun(U_2272,bool),ord_less(U_2272),U_2270),U_2271))
            | ~ hBOOL(hAPP(fun(U_2272,bool),bool,hAPP(U_2272,fun(fun(U_2272,bool),bool),member(U_2272),U_2271),hAPP(U_2272,fun(U_2272,bool),ord_greaterThan(U_2272),U_2270))) ) )
      | ~ ord(U_2272) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

fof(f_628_3,plain,
    ! [U_2272] :
      ( ( ! [U_2276,U_2274] :
            ( hBOOL(hAPP(fun(U_2272,bool),bool,hAPP(U_2272,fun(fun(U_2272,bool),bool),member(U_2272),U_2276),hAPP(U_2272,fun(U_2272,bool),ord_greaterThan(U_2272),U_2274)))
            | ~ hBOOL(hAPP(U_2272,bool,hAPP(U_2272,fun(U_2272,bool),ord_less(U_2272),U_2274),U_2276)) )
        & ! [U_2275,U_2273] :
            ( hBOOL(hAPP(U_2272,bool,hAPP(U_2272,fun(U_2272,bool),ord_less(U_2272),U_2273),U_2275))
            | ~ hBOOL(hAPP(fun(U_2272,bool),bool,hAPP(U_2272,fun(fun(U_2272,bool),bool),member(U_2272),U_2275),hAPP(U_2272,fun(U_2272,bool),ord_greaterThan(U_2272),U_2273))) ) )
      | ~ ord(U_2272) ),
    inference(miniscope,[status(thm)],[f_628_2]) ).

cnf(f_628_4,plain,
    ( hBOOL(hAPP(U_2272,bool,hAPP(U_2272,fun(U_2272,bool),ord_less(U_2272),U_2273),U_2275))
    | ~ hBOOL(hAPP(fun(U_2272,bool),bool,hAPP(U_2272,fun(fun(U_2272,bool),bool),member(U_2272),U_2275),hAPP(U_2272,fun(U_2272,bool),ord_greaterThan(U_2272),U_2273)))
    | ~ ord(U_2272) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

cnf(f_628_5,plain,
    ( hBOOL(hAPP(fun(U_2272,bool),bool,hAPP(U_2272,fun(fun(U_2272,bool),bool),member(U_2272),U_2276),hAPP(U_2272,fun(U_2272,bool),ord_greaterThan(U_2272),U_2274)))
    | ~ hBOOL(hAPP(U_2272,bool,hAPP(U_2272,fun(U_2272,bool),ord_less(U_2272),U_2274),U_2276))
    | ~ ord(U_2272) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

fof(f_629_1,plain,
    ! [X_a,F1,F2] : hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),zero_zero(nat)) = ti(X_a,F1),
    inference(fof_nnf,[status(thm)],[fact_539_nat__case__0]) ).

fof(f_629_2,plain,
    ! [U_2279,U_2278,U_2277] : hAPP(nat,U_2279,hAPP(fun(nat,U_2279),fun(nat,U_2279),hAPP(U_2279,fun(fun(nat,U_2279),fun(nat,U_2279)),nat_case(U_2279),U_2278),U_2277),zero_zero(nat)) = ti(U_2279,U_2278),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

cnf(f_629_3,plain,
    hAPP(nat,U_2279,hAPP(fun(nat,U_2279),fun(nat,U_2279),hAPP(U_2279,fun(fun(nat,U_2279),fun(nat,U_2279)),nat_case(U_2279),U_2278),U_2277),zero_zero(nat)) = ti(U_2279,U_2278),
    inference(clausify,[status(thm)],[f_629_2]) ).

fof(f_630_1,plain,
    ! [X_a,F1,F2,Nat_1] : hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),hAPP(nat,nat,suc,Nat_1)) = hAPP(nat,X_a,F2,Nat_1),
    inference(fof_nnf,[status(thm)],[fact_540_nat__case__Suc]) ).

fof(f_630_2,plain,
    ! [U_2283,U_2282,U_2281,U_2280] : hAPP(nat,U_2283,hAPP(fun(nat,U_2283),fun(nat,U_2283),hAPP(U_2283,fun(fun(nat,U_2283),fun(nat,U_2283)),nat_case(U_2283),U_2282),U_2281),hAPP(nat,nat,suc,U_2280)) = hAPP(nat,U_2283,U_2281,U_2280),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

cnf(f_630_3,plain,
    hAPP(nat,U_2283,hAPP(fun(nat,U_2283),fun(nat,U_2283),hAPP(U_2283,fun(fun(nat,U_2283),fun(nat,U_2283)),nat_case(U_2283),U_2282),U_2281),hAPP(nat,nat,suc,U_2280)) = hAPP(nat,U_2283,U_2281,U_2280),
    inference(clausify,[status(thm)],[f_630_2]) ).

fof(f_631_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( ( ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a)
              | ti(X_a,Aa) != zero_zero(X_a) )
            & ( ti(X_a,Aa) = zero_zero(X_a)
              | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) != zero_zero(X_a) ) )
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) )
      | ~ ring_char_0(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_541_Ints__double__eq__0__iff]) ).

fof(f_631_2,plain,
    ! [U_2285] :
      ( ! [U_2284] :
          ( ( ( hAPP(U_2285,U_2285,hAPP(U_2285,fun(U_2285,U_2285),plus_plus(U_2285),U_2284),U_2284) = zero_zero(U_2285)
              | ti(U_2285,U_2284) != zero_zero(U_2285) )
            & ( ti(U_2285,U_2284) = zero_zero(U_2285)
              | hAPP(U_2285,U_2285,hAPP(U_2285,fun(U_2285,U_2285),plus_plus(U_2285),U_2284),U_2284) != zero_zero(U_2285) ) )
          | ~ hBOOL(hAPP(fun(U_2285,bool),bool,hAPP(U_2285,fun(fun(U_2285,bool),bool),member(U_2285),U_2284),ring_1_Ints(U_2285))) )
      | ~ ring_char_0(U_2285) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

cnf(f_631_3,plain,
    ( ti(U_2285,U_2284) = zero_zero(U_2285)
    | hAPP(U_2285,U_2285,hAPP(U_2285,fun(U_2285,U_2285),plus_plus(U_2285),U_2284),U_2284) != zero_zero(U_2285)
    | ~ hBOOL(hAPP(fun(U_2285,bool),bool,hAPP(U_2285,fun(fun(U_2285,bool),bool),member(U_2285),U_2284),ring_1_Ints(U_2285)))
    | ~ ring_char_0(U_2285) ),
    inference(clausify,[status(thm)],[f_631_2]) ).

cnf(f_631_4,plain,
    ( hAPP(U_2285,U_2285,hAPP(U_2285,fun(U_2285,U_2285),plus_plus(U_2285),U_2284),U_2284) = zero_zero(U_2285)
    | ti(U_2285,U_2284) != zero_zero(U_2285)
    | ~ hBOOL(hAPP(fun(U_2285,bool),bool,hAPP(U_2285,fun(fun(U_2285,bool),bool),member(U_2285),U_2284),ring_1_Ints(U_2285)))
    | ~ ring_char_0(U_2285) ),
    inference(clausify,[status(thm)],[f_631_2]) ).

fof(f_632_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),X_2)),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),Y_1)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),X_2)),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),Y_1))) ) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_542_greaterThan__subset__iff]) ).

fof(f_632_2,plain,
    ! [U_2288] :
      ( ! [U_2287,U_2286] :
          ( ( hBOOL(hAPP(fun(U_2288,bool),bool,hAPP(fun(U_2288,bool),fun(fun(U_2288,bool),bool),ord_less_eq(fun(U_2288,bool)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2287)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2286)))
            | ~ hBOOL(hAPP(U_2288,bool,hAPP(U_2288,fun(U_2288,bool),ord_less_eq(U_2288),U_2286),U_2287)) )
          & ( hBOOL(hAPP(U_2288,bool,hAPP(U_2288,fun(U_2288,bool),ord_less_eq(U_2288),U_2286),U_2287))
            | ~ hBOOL(hAPP(fun(U_2288,bool),bool,hAPP(fun(U_2288,bool),fun(fun(U_2288,bool),bool),ord_less_eq(fun(U_2288,bool)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2287)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2286))) ) )
      | ~ linorder(U_2288) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

fof(f_632_3,plain,
    ! [U_2288] :
      ( ( ! [U_2292,U_2290] :
            ( hBOOL(hAPP(fun(U_2288,bool),bool,hAPP(fun(U_2288,bool),fun(fun(U_2288,bool),bool),ord_less_eq(fun(U_2288,bool)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2292)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2290)))
            | ~ hBOOL(hAPP(U_2288,bool,hAPP(U_2288,fun(U_2288,bool),ord_less_eq(U_2288),U_2290),U_2292)) )
        & ! [U_2291,U_2289] :
            ( hBOOL(hAPP(U_2288,bool,hAPP(U_2288,fun(U_2288,bool),ord_less_eq(U_2288),U_2289),U_2291))
            | ~ hBOOL(hAPP(fun(U_2288,bool),bool,hAPP(fun(U_2288,bool),fun(fun(U_2288,bool),bool),ord_less_eq(fun(U_2288,bool)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2291)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2289))) ) )
      | ~ linorder(U_2288) ),
    inference(miniscope,[status(thm)],[f_632_2]) ).

cnf(f_632_4,plain,
    ( hBOOL(hAPP(U_2288,bool,hAPP(U_2288,fun(U_2288,bool),ord_less_eq(U_2288),U_2289),U_2291))
    | ~ hBOOL(hAPP(fun(U_2288,bool),bool,hAPP(fun(U_2288,bool),fun(fun(U_2288,bool),bool),ord_less_eq(fun(U_2288,bool)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2291)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2289)))
    | ~ linorder(U_2288) ),
    inference(clausify,[status(thm)],[f_632_3]) ).

cnf(f_632_5,plain,
    ( hBOOL(hAPP(fun(U_2288,bool),bool,hAPP(fun(U_2288,bool),fun(fun(U_2288,bool),bool),ord_less_eq(fun(U_2288,bool)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2292)),hAPP(U_2288,fun(U_2288,bool),ord_greaterThan(U_2288),U_2290)))
    | ~ hBOOL(hAPP(U_2288,bool,hAPP(U_2288,fun(U_2288,bool),ord_less_eq(U_2288),U_2290),U_2292))
    | ~ linorder(U_2288) ),
    inference(clausify,[status(thm)],[f_632_3]) ).

fof(f_633_1,plain,
    ! [X_a] :
      ( ! [Aa] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa) != zero_zero(X_a)
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) )
      | ~ ring_char_0(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_543_Ints__odd__nonzero]) ).

fof(f_633_2,plain,
    ! [U_2294] :
      ( ! [U_2293] :
          ( hAPP(U_2294,U_2294,hAPP(U_2294,fun(U_2294,U_2294),plus_plus(U_2294),hAPP(U_2294,U_2294,hAPP(U_2294,fun(U_2294,U_2294),plus_plus(U_2294),one_one(U_2294)),U_2293)),U_2293) != zero_zero(U_2294)
          | ~ hBOOL(hAPP(fun(U_2294,bool),bool,hAPP(U_2294,fun(fun(U_2294,bool),bool),member(U_2294),U_2293),ring_1_Ints(U_2294))) )
      | ~ ring_char_0(U_2294) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

cnf(f_633_3,plain,
    ( hAPP(U_2294,U_2294,hAPP(U_2294,fun(U_2294,U_2294),plus_plus(U_2294),hAPP(U_2294,U_2294,hAPP(U_2294,fun(U_2294,U_2294),plus_plus(U_2294),one_one(U_2294)),U_2293)),U_2293) != zero_zero(U_2294)
    | ~ hBOOL(hAPP(fun(U_2294,bool),bool,hAPP(U_2294,fun(fun(U_2294,bool),bool),member(U_2294),U_2293),ring_1_Ints(U_2294)))
    | ~ ring_char_0(U_2294) ),
    inference(clausify,[status(thm)],[f_633_2]) ).

fof(f_634_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Da))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da))) ) )
      | ~ dense_linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_544_greaterThanAtMost__subseteq__atLeastLessThan__iff]) ).

fof(f_634_2,plain,
    ! [U_2299] :
      ( ! [U_2298,U_2297,U_2296,U_2295] :
          ( ( hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_gr1471790799AtMost(U_2299),U_2298),U_2297)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_atLeastLessThan(U_2299),U_2296),U_2295)))
            | ( ( ~ hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2297),U_2295))
                | ~ hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less_eq(U_2299),U_2296),U_2298)) )
              & hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2298),U_2297)) ) )
          & ( ( hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2297),U_2295))
              & hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less_eq(U_2299),U_2296),U_2298)) )
            | ~ hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2298),U_2297))
            | ~ hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_gr1471790799AtMost(U_2299),U_2298),U_2297)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_atLeastLessThan(U_2299),U_2296),U_2295))) ) )
      | ~ dense_linorder(U_2299) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

fof(f_634_3,plain,
    ! [U_2299] :
      ( ( ! [U_2307,U_2305,U_2303,U_2301] :
            ( hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_gr1471790799AtMost(U_2299),U_2307),U_2305)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_atLeastLessThan(U_2299),U_2303),U_2301)))
            | ( ( ~ hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2305),U_2301))
                | ~ hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less_eq(U_2299),U_2303),U_2307)) )
              & hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2307),U_2305)) ) )
        & ! [U_2306,U_2304,U_2302,U_2300] :
            ( ( hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2304),U_2300))
              & hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less_eq(U_2299),U_2302),U_2306)) )
            | ~ hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2306),U_2304))
            | ~ hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_gr1471790799AtMost(U_2299),U_2306),U_2304)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_atLeastLessThan(U_2299),U_2302),U_2300))) ) )
      | ~ dense_linorder(U_2299) ),
    inference(miniscope,[status(thm)],[f_634_2]) ).

cnf(f_634_4,plain,
    ( hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less_eq(U_2299),U_2302),U_2306))
    | ~ hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2306),U_2304))
    | ~ hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_gr1471790799AtMost(U_2299),U_2306),U_2304)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_atLeastLessThan(U_2299),U_2302),U_2300)))
    | ~ dense_linorder(U_2299) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

cnf(f_634_5,plain,
    ( hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2304),U_2300))
    | ~ hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2306),U_2304))
    | ~ hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_gr1471790799AtMost(U_2299),U_2306),U_2304)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_atLeastLessThan(U_2299),U_2302),U_2300)))
    | ~ dense_linorder(U_2299) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

cnf(f_634_6,plain,
    ( hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2307),U_2305))
    | hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_gr1471790799AtMost(U_2299),U_2307),U_2305)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_atLeastLessThan(U_2299),U_2303),U_2301)))
    | ~ dense_linorder(U_2299) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

cnf(f_634_7,plain,
    ( ~ hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less(U_2299),U_2305),U_2301))
    | ~ hBOOL(hAPP(U_2299,bool,hAPP(U_2299,fun(U_2299,bool),ord_less_eq(U_2299),U_2303),U_2307))
    | hBOOL(hAPP(fun(U_2299,bool),bool,hAPP(fun(U_2299,bool),fun(fun(U_2299,bool),bool),ord_less_eq(fun(U_2299,bool)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_gr1471790799AtMost(U_2299),U_2307),U_2305)),hAPP(U_2299,fun(U_2299,bool),hAPP(U_2299,fun(U_2299,fun(U_2299,bool)),ord_atLeastLessThan(U_2299),U_2303),U_2301)))
    | ~ dense_linorder(U_2299) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

fof(f_635_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da))) ) )
      | ~ dense_linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_545_greaterThanLessThan__subseteq__atLeastLessThan__iff]) ).

fof(f_635_2,plain,
    ! [U_2312] :
      ( ! [U_2311,U_2310,U_2309,U_2308] :
          ( ( hBOOL(hAPP(fun(U_2312,bool),bool,hAPP(fun(U_2312,bool),fun(fun(U_2312,bool),bool),ord_less_eq(fun(U_2312,bool)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_gr676655987ssThan(U_2312),U_2311),U_2310)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_atLeastLessThan(U_2312),U_2309),U_2308)))
            | ( ( ~ hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2310),U_2308))
                | ~ hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2309),U_2311)) )
              & hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less(U_2312),U_2311),U_2310)) ) )
          & ( ( hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2310),U_2308))
              & hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2309),U_2311)) )
            | ~ hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less(U_2312),U_2311),U_2310))
            | ~ hBOOL(hAPP(fun(U_2312,bool),bool,hAPP(fun(U_2312,bool),fun(fun(U_2312,bool),bool),ord_less_eq(fun(U_2312,bool)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_gr676655987ssThan(U_2312),U_2311),U_2310)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_atLeastLessThan(U_2312),U_2309),U_2308))) ) )
      | ~ dense_linorder(U_2312) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

fof(f_635_3,plain,
    ! [U_2312] :
      ( ( ! [U_2320,U_2318,U_2316,U_2314] :
            ( hBOOL(hAPP(fun(U_2312,bool),bool,hAPP(fun(U_2312,bool),fun(fun(U_2312,bool),bool),ord_less_eq(fun(U_2312,bool)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_gr676655987ssThan(U_2312),U_2320),U_2318)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_atLeastLessThan(U_2312),U_2316),U_2314)))
            | ( ( ~ hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2318),U_2314))
                | ~ hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2316),U_2320)) )
              & hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less(U_2312),U_2320),U_2318)) ) )
        & ! [U_2319,U_2317,U_2315,U_2313] :
            ( ( hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2317),U_2313))
              & hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2315),U_2319)) )
            | ~ hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less(U_2312),U_2319),U_2317))
            | ~ hBOOL(hAPP(fun(U_2312,bool),bool,hAPP(fun(U_2312,bool),fun(fun(U_2312,bool),bool),ord_less_eq(fun(U_2312,bool)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_gr676655987ssThan(U_2312),U_2319),U_2317)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_atLeastLessThan(U_2312),U_2315),U_2313))) ) )
      | ~ dense_linorder(U_2312) ),
    inference(miniscope,[status(thm)],[f_635_2]) ).

cnf(f_635_4,plain,
    ( hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2315),U_2319))
    | ~ hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less(U_2312),U_2319),U_2317))
    | ~ hBOOL(hAPP(fun(U_2312,bool),bool,hAPP(fun(U_2312,bool),fun(fun(U_2312,bool),bool),ord_less_eq(fun(U_2312,bool)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_gr676655987ssThan(U_2312),U_2319),U_2317)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_atLeastLessThan(U_2312),U_2315),U_2313)))
    | ~ dense_linorder(U_2312) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

cnf(f_635_5,plain,
    ( hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2317),U_2313))
    | ~ hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less(U_2312),U_2319),U_2317))
    | ~ hBOOL(hAPP(fun(U_2312,bool),bool,hAPP(fun(U_2312,bool),fun(fun(U_2312,bool),bool),ord_less_eq(fun(U_2312,bool)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_gr676655987ssThan(U_2312),U_2319),U_2317)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_atLeastLessThan(U_2312),U_2315),U_2313)))
    | ~ dense_linorder(U_2312) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

cnf(f_635_6,plain,
    ( hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less(U_2312),U_2320),U_2318))
    | hBOOL(hAPP(fun(U_2312,bool),bool,hAPP(fun(U_2312,bool),fun(fun(U_2312,bool),bool),ord_less_eq(fun(U_2312,bool)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_gr676655987ssThan(U_2312),U_2320),U_2318)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_atLeastLessThan(U_2312),U_2316),U_2314)))
    | ~ dense_linorder(U_2312) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

cnf(f_635_7,plain,
    ( ~ hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2318),U_2314))
    | ~ hBOOL(hAPP(U_2312,bool,hAPP(U_2312,fun(U_2312,bool),ord_less_eq(U_2312),U_2316),U_2320))
    | hBOOL(hAPP(fun(U_2312,bool),bool,hAPP(fun(U_2312,bool),fun(fun(U_2312,bool),bool),ord_less_eq(fun(U_2312,bool)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_gr676655987ssThan(U_2312),U_2320),U_2318)),hAPP(U_2312,fun(U_2312,bool),hAPP(U_2312,fun(U_2312,fun(U_2312,bool)),ord_atLeastLessThan(U_2312),U_2316),U_2314)))
    | ~ dense_linorder(U_2312) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

fof(f_636_1,plain,
    ! [X_b,X_a,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F)),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),B),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),A_1))))
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) != ti(fun(X_a,bool),B) ),
    inference(fof_nnf,[status(thm)],[fact_546_inv__into__funcset]) ).

fof(f_636_2,plain,
    ! [U_2325,U_2324,U_2323,U_2322,U_2321] :
      ( hBOOL(hAPP(fun(fun(U_2324,U_2325),bool),bool,hAPP(fun(U_2324,U_2325),fun(fun(fun(U_2324,U_2325),bool),bool),member(fun(U_2324,U_2325)),hAPP(fun(U_2324,bool),fun(U_2324,U_2325),hAPP(fun(U_2324,U_2325),fun(fun(U_2324,bool),fun(U_2324,U_2325)),restrict(U_2324,U_2325),hAPP(fun(U_2325,U_2324),fun(U_2324,U_2325),hAPP(fun(U_2325,bool),fun(fun(U_2325,U_2324),fun(U_2324,U_2325)),hilbert_inv_into(U_2325,U_2324),U_2322),U_2323)),U_2321)),hAPP(fun(U_2324,fun(U_2325,bool)),fun(fun(U_2324,U_2325),bool),hAPP(fun(U_2324,bool),fun(fun(U_2324,fun(U_2325,bool)),fun(fun(U_2324,U_2325),bool)),pi(U_2324,U_2325),U_2321),hAPP(fun(U_2325,bool),fun(U_2324,fun(U_2325,bool)),combk(fun(U_2325,bool),U_2324),U_2322))))
      | hAPP(fun(U_2325,bool),fun(U_2324,bool),hAPP(fun(U_2325,U_2324),fun(fun(U_2325,bool),fun(U_2324,bool)),image(U_2325,U_2324),U_2323),U_2322) != ti(fun(U_2324,bool),U_2321) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

cnf(f_636_3,plain,
    ( hBOOL(hAPP(fun(fun(U_2324,U_2325),bool),bool,hAPP(fun(U_2324,U_2325),fun(fun(fun(U_2324,U_2325),bool),bool),member(fun(U_2324,U_2325)),hAPP(fun(U_2324,bool),fun(U_2324,U_2325),hAPP(fun(U_2324,U_2325),fun(fun(U_2324,bool),fun(U_2324,U_2325)),restrict(U_2324,U_2325),hAPP(fun(U_2325,U_2324),fun(U_2324,U_2325),hAPP(fun(U_2325,bool),fun(fun(U_2325,U_2324),fun(U_2324,U_2325)),hilbert_inv_into(U_2325,U_2324),U_2322),U_2323)),U_2321)),hAPP(fun(U_2324,fun(U_2325,bool)),fun(fun(U_2324,U_2325),bool),hAPP(fun(U_2324,bool),fun(fun(U_2324,fun(U_2325,bool)),fun(fun(U_2324,U_2325),bool)),pi(U_2324,U_2325),U_2321),hAPP(fun(U_2325,bool),fun(U_2324,fun(U_2325,bool)),combk(fun(U_2325,bool),U_2324),U_2322))))
    | hAPP(fun(U_2325,bool),fun(U_2324,bool),hAPP(fun(U_2325,U_2324),fun(fun(U_2325,bool),fun(U_2324,bool)),image(U_2325,U_2324),U_2323),U_2322) != ti(fun(U_2324,bool),U_2321) ),
    inference(clausify,[status(thm)],[f_636_2]) ).

fof(f_637_1,plain,
    ! [X_a,X_b,B,X_2,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),X_2)),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_547_the__inv__into__into]) ).

fof(f_637_2,plain,
    ! [U_2331,U_2330,U_2329,U_2328,U_2327,U_2326] :
      ( hBOOL(hAPP(fun(U_2331,bool),bool,hAPP(U_2331,fun(fun(U_2331,bool),bool),member(U_2331),hAPP(U_2330,U_2331,hAPP(fun(U_2331,U_2330),fun(U_2330,U_2331),hAPP(fun(U_2331,bool),fun(fun(U_2331,U_2330),fun(U_2330,U_2331)),the_inv_into(U_2331,U_2330),U_2326),U_2327),U_2328)),U_2329))
      | ~ hBOOL(hAPP(fun(U_2331,bool),bool,hAPP(fun(U_2331,bool),fun(fun(U_2331,bool),bool),ord_less_eq(fun(U_2331,bool)),U_2326),U_2329))
      | ~ hBOOL(hAPP(fun(U_2330,bool),bool,hAPP(U_2330,fun(fun(U_2330,bool),bool),member(U_2330),U_2328),hAPP(fun(U_2331,bool),fun(U_2330,bool),hAPP(fun(U_2331,U_2330),fun(fun(U_2331,bool),fun(U_2330,bool)),image(U_2331,U_2330),U_2327),U_2326)))
      | ~ hBOOL(hAPP(fun(U_2331,bool),bool,hAPP(fun(U_2331,U_2330),fun(fun(U_2331,bool),bool),inj_on(U_2331,U_2330),U_2327),U_2326)) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

cnf(f_637_3,plain,
    ( hBOOL(hAPP(fun(U_2331,bool),bool,hAPP(U_2331,fun(fun(U_2331,bool),bool),member(U_2331),hAPP(U_2330,U_2331,hAPP(fun(U_2331,U_2330),fun(U_2330,U_2331),hAPP(fun(U_2331,bool),fun(fun(U_2331,U_2330),fun(U_2330,U_2331)),the_inv_into(U_2331,U_2330),U_2326),U_2327),U_2328)),U_2329))
    | ~ hBOOL(hAPP(fun(U_2331,bool),bool,hAPP(fun(U_2331,bool),fun(fun(U_2331,bool),bool),ord_less_eq(fun(U_2331,bool)),U_2326),U_2329))
    | ~ hBOOL(hAPP(fun(U_2330,bool),bool,hAPP(U_2330,fun(fun(U_2330,bool),bool),member(U_2330),U_2328),hAPP(fun(U_2331,bool),fun(U_2330,bool),hAPP(fun(U_2331,U_2330),fun(fun(U_2331,bool),fun(U_2330,bool)),image(U_2331,U_2330),U_2327),U_2326)))
    | ~ hBOOL(hAPP(fun(U_2331,bool),bool,hAPP(fun(U_2331,U_2330),fun(fun(U_2331,bool),bool),inj_on(U_2331,U_2330),U_2327),U_2326)) ),
    inference(clausify,[status(thm)],[f_637_2]) ).

fof(f_638_1,plain,
    ! [L,U] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),L),U))),
    inference(fof_nnf,[status(thm)],[fact_548_finite__greaterThanAtMost]) ).

fof(f_638_2,plain,
    ! [U_2333,U_2332] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),U_2333),U_2332))),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

cnf(f_638_3,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),U_2333),U_2332))),
    inference(clausify,[status(thm)],[f_638_2]) ).

fof(f_639_1,plain,
    ! [L,U] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U))),
    inference(fof_nnf,[status(thm)],[fact_549_finite__greaterThanLessThan]) ).

fof(f_639_2,plain,
    ! [U_2335,U_2334] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),U_2335),U_2334))),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

cnf(f_639_3,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),U_2335),U_2334))),
    inference(clausify,[status(thm)],[f_639_2]) ).

fof(f_640_1,plain,
    ! [X_b,X_a,F,A_1] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,bool),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_b,X_a)),restrict(X_b,X_a),F),A_1)),A_1) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1),
    inference(fof_nnf,[status(thm)],[fact_550_image__restrict__eq]) ).

fof(f_640_2,plain,
    ! [U_2339,U_2338,U_2337,U_2336] : hAPP(fun(U_2339,bool),fun(U_2338,bool),hAPP(fun(U_2339,U_2338),fun(fun(U_2339,bool),fun(U_2338,bool)),image(U_2339,U_2338),hAPP(fun(U_2339,bool),fun(U_2339,U_2338),hAPP(fun(U_2339,U_2338),fun(fun(U_2339,bool),fun(U_2339,U_2338)),restrict(U_2339,U_2338),U_2337),U_2336)),U_2336) = hAPP(fun(U_2339,bool),fun(U_2338,bool),hAPP(fun(U_2339,U_2338),fun(fun(U_2339,bool),fun(U_2338,bool)),image(U_2339,U_2338),U_2337),U_2336),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

cnf(f_640_3,plain,
    hAPP(fun(U_2339,bool),fun(U_2338,bool),hAPP(fun(U_2339,U_2338),fun(fun(U_2339,bool),fun(U_2338,bool)),image(U_2339,U_2338),hAPP(fun(U_2339,bool),fun(U_2339,U_2338),hAPP(fun(U_2339,U_2338),fun(fun(U_2339,bool),fun(U_2339,U_2338)),restrict(U_2339,U_2338),U_2337),U_2336)),U_2336) = hAPP(fun(U_2339,bool),fun(U_2338,bool),hAPP(fun(U_2339,U_2338),fun(fun(U_2339,bool),fun(U_2338,bool)),image(U_2339,U_2338),U_2337),U_2336),
    inference(clausify,[status(thm)],[f_640_2]) ).

fof(f_641_1,plain,
    ! [X_a,X_b,F,A_1] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1)),A_1))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) )
      & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1)),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_551_inj__on__restrict__eq]) ).

fof(f_641_2,plain,
    ! [U_2343,U_2342,U_2341,U_2340] :
      ( ( hBOOL(hAPP(fun(U_2343,bool),bool,hAPP(fun(U_2343,U_2342),fun(fun(U_2343,bool),bool),inj_on(U_2343,U_2342),hAPP(fun(U_2343,bool),fun(U_2343,U_2342),hAPP(fun(U_2343,U_2342),fun(fun(U_2343,bool),fun(U_2343,U_2342)),restrict(U_2343,U_2342),U_2341),U_2340)),U_2340))
        | ~ hBOOL(hAPP(fun(U_2343,bool),bool,hAPP(fun(U_2343,U_2342),fun(fun(U_2343,bool),bool),inj_on(U_2343,U_2342),U_2341),U_2340)) )
      & ( hBOOL(hAPP(fun(U_2343,bool),bool,hAPP(fun(U_2343,U_2342),fun(fun(U_2343,bool),bool),inj_on(U_2343,U_2342),U_2341),U_2340))
        | ~ hBOOL(hAPP(fun(U_2343,bool),bool,hAPP(fun(U_2343,U_2342),fun(fun(U_2343,bool),bool),inj_on(U_2343,U_2342),hAPP(fun(U_2343,bool),fun(U_2343,U_2342),hAPP(fun(U_2343,U_2342),fun(fun(U_2343,bool),fun(U_2343,U_2342)),restrict(U_2343,U_2342),U_2341),U_2340)),U_2340)) ) ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

fof(f_641_3,plain,
    ( ! [U_2351,U_2349,U_2347,U_2345] :
        ( hBOOL(hAPP(fun(U_2351,bool),bool,hAPP(fun(U_2351,U_2349),fun(fun(U_2351,bool),bool),inj_on(U_2351,U_2349),hAPP(fun(U_2351,bool),fun(U_2351,U_2349),hAPP(fun(U_2351,U_2349),fun(fun(U_2351,bool),fun(U_2351,U_2349)),restrict(U_2351,U_2349),U_2347),U_2345)),U_2345))
        | ~ hBOOL(hAPP(fun(U_2351,bool),bool,hAPP(fun(U_2351,U_2349),fun(fun(U_2351,bool),bool),inj_on(U_2351,U_2349),U_2347),U_2345)) )
    & ! [U_2350,U_2348,U_2346,U_2344] :
        ( hBOOL(hAPP(fun(U_2350,bool),bool,hAPP(fun(U_2350,U_2348),fun(fun(U_2350,bool),bool),inj_on(U_2350,U_2348),U_2346),U_2344))
        | ~ hBOOL(hAPP(fun(U_2350,bool),bool,hAPP(fun(U_2350,U_2348),fun(fun(U_2350,bool),bool),inj_on(U_2350,U_2348),hAPP(fun(U_2350,bool),fun(U_2350,U_2348),hAPP(fun(U_2350,U_2348),fun(fun(U_2350,bool),fun(U_2350,U_2348)),restrict(U_2350,U_2348),U_2346),U_2344)),U_2344)) ) ),
    inference(miniscope,[status(thm)],[f_641_2]) ).

cnf(f_641_4,plain,
    ( hBOOL(hAPP(fun(U_2350,bool),bool,hAPP(fun(U_2350,U_2348),fun(fun(U_2350,bool),bool),inj_on(U_2350,U_2348),U_2346),U_2344))
    | ~ hBOOL(hAPP(fun(U_2350,bool),bool,hAPP(fun(U_2350,U_2348),fun(fun(U_2350,bool),bool),inj_on(U_2350,U_2348),hAPP(fun(U_2350,bool),fun(U_2350,U_2348),hAPP(fun(U_2350,U_2348),fun(fun(U_2350,bool),fun(U_2350,U_2348)),restrict(U_2350,U_2348),U_2346),U_2344)),U_2344)) ),
    inference(clausify,[status(thm)],[f_641_3]) ).

cnf(f_641_5,plain,
    ( hBOOL(hAPP(fun(U_2351,bool),bool,hAPP(fun(U_2351,U_2349),fun(fun(U_2351,bool),bool),inj_on(U_2351,U_2349),hAPP(fun(U_2351,bool),fun(U_2351,U_2349),hAPP(fun(U_2351,U_2349),fun(fun(U_2351,bool),fun(U_2351,U_2349)),restrict(U_2351,U_2349),U_2347),U_2345)),U_2345))
    | ~ hBOOL(hAPP(fun(U_2351,bool),bool,hAPP(fun(U_2351,U_2349),fun(fun(U_2351,bool),bool),inj_on(U_2351,U_2349),U_2347),U_2345)) ),
    inference(clausify,[status(thm)],[f_641_3]) ).

fof(f_642_1,plain,
    ! [X_a,X_b,X_2,Y_1,F,A_1] :
      ( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),Y_1) = ti(X_a,X_2)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | hAPP(X_a,X_b,F,X_2) != ti(X_b,Y_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_552_the__inv__into__f__eq]) ).

fof(f_642_2,plain,
    ! [U_2357,U_2356,U_2355,U_2354,U_2353,U_2352] :
      ( hAPP(U_2356,U_2357,hAPP(fun(U_2357,U_2356),fun(U_2356,U_2357),hAPP(fun(U_2357,bool),fun(fun(U_2357,U_2356),fun(U_2356,U_2357)),the_inv_into(U_2357,U_2356),U_2352),U_2353),U_2354) = ti(U_2357,U_2355)
      | ~ hBOOL(hAPP(fun(U_2357,bool),bool,hAPP(U_2357,fun(fun(U_2357,bool),bool),member(U_2357),U_2355),U_2352))
      | hAPP(U_2357,U_2356,U_2353,U_2355) != ti(U_2356,U_2354)
      | ~ hBOOL(hAPP(fun(U_2357,bool),bool,hAPP(fun(U_2357,U_2356),fun(fun(U_2357,bool),bool),inj_on(U_2357,U_2356),U_2353),U_2352)) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

cnf(f_642_3,plain,
    ( hAPP(U_2356,U_2357,hAPP(fun(U_2357,U_2356),fun(U_2356,U_2357),hAPP(fun(U_2357,bool),fun(fun(U_2357,U_2356),fun(U_2356,U_2357)),the_inv_into(U_2357,U_2356),U_2352),U_2353),U_2354) = ti(U_2357,U_2355)
    | ~ hBOOL(hAPP(fun(U_2357,bool),bool,hAPP(U_2357,fun(fun(U_2357,bool),bool),member(U_2357),U_2355),U_2352))
    | hAPP(U_2357,U_2356,U_2353,U_2355) != ti(U_2356,U_2354)
    | ~ hBOOL(hAPP(fun(U_2357,bool),bool,hAPP(fun(U_2357,U_2356),fun(fun(U_2357,bool),bool),inj_on(U_2357,U_2356),U_2353),U_2352)) ),
    inference(clausify,[status(thm)],[f_642_2]) ).

fof(f_643_1,plain,
    ! [X_a,X_b,X_2,F,A_1] :
      ( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_553_the__inv__into__f__f]) ).

fof(f_643_2,plain,
    ! [U_2362,U_2361,U_2360,U_2359,U_2358] :
      ( hAPP(U_2361,U_2362,hAPP(fun(U_2362,U_2361),fun(U_2361,U_2362),hAPP(fun(U_2362,bool),fun(fun(U_2362,U_2361),fun(U_2361,U_2362)),the_inv_into(U_2362,U_2361),U_2358),U_2359),hAPP(U_2362,U_2361,U_2359,U_2360)) = ti(U_2362,U_2360)
      | ~ hBOOL(hAPP(fun(U_2362,bool),bool,hAPP(U_2362,fun(fun(U_2362,bool),bool),member(U_2362),U_2360),U_2358))
      | ~ hBOOL(hAPP(fun(U_2362,bool),bool,hAPP(fun(U_2362,U_2361),fun(fun(U_2362,bool),bool),inj_on(U_2362,U_2361),U_2359),U_2358)) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

cnf(f_643_3,plain,
    ( hAPP(U_2361,U_2362,hAPP(fun(U_2362,U_2361),fun(U_2361,U_2362),hAPP(fun(U_2362,bool),fun(fun(U_2362,U_2361),fun(U_2361,U_2362)),the_inv_into(U_2362,U_2361),U_2358),U_2359),hAPP(U_2362,U_2361,U_2359,U_2360)) = ti(U_2362,U_2360)
    | ~ hBOOL(hAPP(fun(U_2362,bool),bool,hAPP(U_2362,fun(fun(U_2362,bool),bool),member(U_2362),U_2360),U_2358))
    | ~ hBOOL(hAPP(fun(U_2362,bool),bool,hAPP(fun(U_2362,U_2361),fun(fun(U_2362,bool),bool),inj_on(U_2362,U_2361),U_2359),U_2358)) ),
    inference(clausify,[status(thm)],[f_643_2]) ).

fof(f_644_1,plain,
    ! [L,U] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,L)),U) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U),
    inference(fof_nnf,[status(thm)],[fact_554_atLeastSucLessThan__greaterThanLessThan]) ).

fof(f_644_2,plain,
    ! [U_2364,U_2363] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,U_2364)),U_2363) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),U_2364),U_2363),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

cnf(f_644_3,plain,
    hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,U_2364)),U_2363) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),U_2364),U_2363),
    inference(clausify,[status(thm)],[f_644_2]) ).

fof(f_645_1,plain,
    ! [X_a,X_b,X_2,F] :
      ( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_555_the__inv__f__f]) ).

fof(f_645_2,plain,
    ! [U_2368,U_2367,U_2366,U_2365] :
      ( hAPP(U_2367,U_2368,hAPP(fun(U_2368,U_2367),fun(U_2367,U_2368),hAPP(fun(U_2368,bool),fun(fun(U_2368,U_2367),fun(U_2367,U_2368)),the_inv_into(U_2368,U_2367),top_top(fun(U_2368,bool))),U_2365),hAPP(U_2368,U_2367,U_2365,U_2366)) = ti(U_2368,U_2366)
      | ~ hBOOL(hAPP(fun(U_2368,bool),bool,hAPP(fun(U_2368,U_2367),fun(fun(U_2368,bool),bool),inj_on(U_2368,U_2367),U_2365),top_top(fun(U_2368,bool)))) ),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

cnf(f_645_3,plain,
    ( hAPP(U_2367,U_2368,hAPP(fun(U_2368,U_2367),fun(U_2367,U_2368),hAPP(fun(U_2368,bool),fun(fun(U_2368,U_2367),fun(U_2367,U_2368)),the_inv_into(U_2368,U_2367),top_top(fun(U_2368,bool))),U_2365),hAPP(U_2368,U_2367,U_2365,U_2366)) = ti(U_2368,U_2366)
    | ~ hBOOL(hAPP(fun(U_2368,bool),bool,hAPP(fun(U_2368,U_2367),fun(fun(U_2368,bool),bool),inj_on(U_2368,U_2367),U_2365),top_top(fun(U_2368,bool)))) ),
    inference(clausify,[status(thm)],[f_645_2]) ).

fof(f_646_1,plain,
    ! [X_a,X_b,F,A_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_556_inj__on__the__inv__into]) ).

fof(f_646_2,plain,
    ! [U_2372,U_2371,U_2370,U_2369] :
      ( hBOOL(hAPP(fun(U_2371,bool),bool,hAPP(fun(U_2371,U_2372),fun(fun(U_2371,bool),bool),inj_on(U_2371,U_2372),hAPP(fun(U_2372,U_2371),fun(U_2371,U_2372),hAPP(fun(U_2372,bool),fun(fun(U_2372,U_2371),fun(U_2371,U_2372)),the_inv_into(U_2372,U_2371),U_2369),U_2370)),hAPP(fun(U_2372,bool),fun(U_2371,bool),hAPP(fun(U_2372,U_2371),fun(fun(U_2372,bool),fun(U_2371,bool)),image(U_2372,U_2371),U_2370),U_2369)))
      | ~ hBOOL(hAPP(fun(U_2372,bool),bool,hAPP(fun(U_2372,U_2371),fun(fun(U_2372,bool),bool),inj_on(U_2372,U_2371),U_2370),U_2369)) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

cnf(f_646_3,plain,
    ( hBOOL(hAPP(fun(U_2371,bool),bool,hAPP(fun(U_2371,U_2372),fun(fun(U_2371,bool),bool),inj_on(U_2371,U_2372),hAPP(fun(U_2372,U_2371),fun(U_2371,U_2372),hAPP(fun(U_2372,bool),fun(fun(U_2372,U_2371),fun(U_2371,U_2372)),the_inv_into(U_2372,U_2371),U_2369),U_2370)),hAPP(fun(U_2372,bool),fun(U_2371,bool),hAPP(fun(U_2372,U_2371),fun(fun(U_2372,bool),fun(U_2371,bool)),image(U_2372,U_2371),U_2370),U_2369)))
    | ~ hBOOL(hAPP(fun(U_2372,bool),bool,hAPP(fun(U_2372,U_2371),fun(fun(U_2372,bool),bool),inj_on(U_2372,U_2371),U_2370),U_2369)) ),
    inference(clausify,[status(thm)],[f_646_2]) ).

fof(f_647_1,plain,
    ! [X_a,X_b,F,A_1] :
      ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = ti(fun(X_a,bool),A_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_557_the__inv__into__onto]) ).

fof(f_647_2,plain,
    ! [U_2376,U_2375,U_2374,U_2373] :
      ( hAPP(fun(U_2375,bool),fun(U_2376,bool),hAPP(fun(U_2375,U_2376),fun(fun(U_2375,bool),fun(U_2376,bool)),image(U_2375,U_2376),hAPP(fun(U_2376,U_2375),fun(U_2375,U_2376),hAPP(fun(U_2376,bool),fun(fun(U_2376,U_2375),fun(U_2375,U_2376)),the_inv_into(U_2376,U_2375),U_2373),U_2374)),hAPP(fun(U_2376,bool),fun(U_2375,bool),hAPP(fun(U_2376,U_2375),fun(fun(U_2376,bool),fun(U_2375,bool)),image(U_2376,U_2375),U_2374),U_2373)) = ti(fun(U_2376,bool),U_2373)
      | ~ hBOOL(hAPP(fun(U_2376,bool),bool,hAPP(fun(U_2376,U_2375),fun(fun(U_2376,bool),bool),inj_on(U_2376,U_2375),U_2374),U_2373)) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

cnf(f_647_3,plain,
    ( hAPP(fun(U_2375,bool),fun(U_2376,bool),hAPP(fun(U_2375,U_2376),fun(fun(U_2375,bool),fun(U_2376,bool)),image(U_2375,U_2376),hAPP(fun(U_2376,U_2375),fun(U_2375,U_2376),hAPP(fun(U_2376,bool),fun(fun(U_2376,U_2375),fun(U_2375,U_2376)),the_inv_into(U_2376,U_2375),U_2373),U_2374)),hAPP(fun(U_2376,bool),fun(U_2375,bool),hAPP(fun(U_2376,U_2375),fun(fun(U_2376,bool),fun(U_2375,bool)),image(U_2376,U_2375),U_2374),U_2373)) = ti(fun(U_2376,bool),U_2373)
    | ~ hBOOL(hAPP(fun(U_2376,bool),bool,hAPP(fun(U_2376,U_2375),fun(fun(U_2376,bool),bool),inj_on(U_2376,U_2375),U_2374),U_2373)) ),
    inference(clausify,[status(thm)],[f_647_2]) ).

fof(f_648_1,plain,
    ! [X_a,X_b,Y_1,F,A_1] :
      ( hAPP(X_a,X_b,F,hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),A_1),F),Y_1)) = ti(X_b,Y_1)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_558_f__the__inv__into__f]) ).

fof(f_648_2,plain,
    ! [U_2381,U_2380,U_2379,U_2378,U_2377] :
      ( hAPP(U_2381,U_2380,U_2378,hAPP(U_2380,U_2381,hAPP(fun(U_2381,U_2380),fun(U_2380,U_2381),hAPP(fun(U_2381,bool),fun(fun(U_2381,U_2380),fun(U_2380,U_2381)),the_inv_into(U_2381,U_2380),U_2377),U_2378),U_2379)) = ti(U_2380,U_2379)
      | ~ hBOOL(hAPP(fun(U_2380,bool),bool,hAPP(U_2380,fun(fun(U_2380,bool),bool),member(U_2380),U_2379),hAPP(fun(U_2381,bool),fun(U_2380,bool),hAPP(fun(U_2381,U_2380),fun(fun(U_2381,bool),fun(U_2380,bool)),image(U_2381,U_2380),U_2378),U_2377)))
      | ~ hBOOL(hAPP(fun(U_2381,bool),bool,hAPP(fun(U_2381,U_2380),fun(fun(U_2381,bool),bool),inj_on(U_2381,U_2380),U_2378),U_2377)) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

cnf(f_648_3,plain,
    ( hAPP(U_2381,U_2380,U_2378,hAPP(U_2380,U_2381,hAPP(fun(U_2381,U_2380),fun(U_2380,U_2381),hAPP(fun(U_2381,bool),fun(fun(U_2381,U_2380),fun(U_2380,U_2381)),the_inv_into(U_2381,U_2380),U_2377),U_2378),U_2379)) = ti(U_2380,U_2379)
    | ~ hBOOL(hAPP(fun(U_2380,bool),bool,hAPP(U_2380,fun(fun(U_2380,bool),bool),member(U_2380),U_2379),hAPP(fun(U_2381,bool),fun(U_2380,bool),hAPP(fun(U_2381,U_2380),fun(fun(U_2381,bool),fun(U_2380,bool)),image(U_2381,U_2380),U_2378),U_2377)))
    | ~ hBOOL(hAPP(fun(U_2381,bool),bool,hAPP(fun(U_2381,U_2380),fun(fun(U_2381,bool),bool),inj_on(U_2381,U_2380),U_2378),U_2377)) ),
    inference(clausify,[status(thm)],[f_648_2]) ).

fof(f_649_1,plain,
    ! [X_b,X_a,F,B,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1)))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_559_restrictI]) ).

fof(f_649_2,plain,
    ! [U_2387,U_2386,U_2385,U_2384,U_2383] :
      ( hBOOL(hAPP(fun(fun(U_2386,U_2387),bool),bool,hAPP(fun(U_2386,U_2387),fun(fun(fun(U_2386,U_2387),bool),bool),member(fun(U_2386,U_2387)),hAPP(fun(U_2386,bool),fun(U_2386,U_2387),hAPP(fun(U_2386,U_2387),fun(fun(U_2386,bool),fun(U_2386,U_2387)),restrict(U_2386,U_2387),U_2385),U_2383)),hAPP(fun(U_2386,fun(U_2387,bool)),fun(fun(U_2386,U_2387),bool),hAPP(fun(U_2386,bool),fun(fun(U_2386,fun(U_2387,bool)),fun(fun(U_2386,U_2387),bool)),pi(U_2386,U_2387),U_2383),U_2384)))
      | ? [U_2382] :
          ( ~ hBOOL(hAPP(fun(U_2387,bool),bool,hAPP(U_2387,fun(fun(U_2387,bool),bool),member(U_2387),hAPP(U_2386,U_2387,U_2385,U_2382)),hAPP(U_2386,fun(U_2387,bool),U_2384,U_2382)))
          & hBOOL(hAPP(fun(U_2386,bool),bool,hAPP(U_2386,fun(fun(U_2386,bool),bool),member(U_2386),U_2382),U_2383)) ) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

fof(f_649_3,plain,
    ! [U_2387,U_2386,U_2385,U_2384,U_2383] :
      ( hBOOL(hAPP(fun(fun(U_2386,U_2387),bool),bool,hAPP(fun(U_2386,U_2387),fun(fun(fun(U_2386,U_2387),bool),bool),member(fun(U_2386,U_2387)),hAPP(fun(U_2386,bool),fun(U_2386,U_2387),hAPP(fun(U_2386,U_2387),fun(fun(U_2386,bool),fun(U_2386,U_2387)),restrict(U_2386,U_2387),U_2385),U_2383)),hAPP(fun(U_2386,fun(U_2387,bool)),fun(fun(U_2386,U_2387),bool),hAPP(fun(U_2386,bool),fun(fun(U_2386,fun(U_2387,bool)),fun(fun(U_2386,U_2387),bool)),pi(U_2386,U_2387),U_2383),U_2384)))
      | ( ~ hBOOL(hAPP(fun(U_2387,bool),bool,hAPP(U_2387,fun(fun(U_2387,bool),bool),member(U_2387),hAPP(U_2386,U_2387,U_2385,sK140(U_2387,U_2386,U_2385,U_2384,U_2383))),hAPP(U_2386,fun(U_2387,bool),U_2384,sK140(U_2387,U_2386,U_2385,U_2384,U_2383))))
        & hBOOL(hAPP(fun(U_2386,bool),bool,hAPP(U_2386,fun(fun(U_2386,bool),bool),member(U_2386),sK140(U_2387,U_2386,U_2385,U_2384,U_2383)),U_2383)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_2382,sK140(U_2387,U_2386,U_2385,U_2384,U_2383))],[f_649_2]) ).

cnf(f_649_4,plain,
    ( hBOOL(hAPP(fun(U_2386,bool),bool,hAPP(U_2386,fun(fun(U_2386,bool),bool),member(U_2386),sK140(U_2387,U_2386,U_2385,U_2384,U_2383)),U_2383))
    | hBOOL(hAPP(fun(fun(U_2386,U_2387),bool),bool,hAPP(fun(U_2386,U_2387),fun(fun(fun(U_2386,U_2387),bool),bool),member(fun(U_2386,U_2387)),hAPP(fun(U_2386,bool),fun(U_2386,U_2387),hAPP(fun(U_2386,U_2387),fun(fun(U_2386,bool),fun(U_2386,U_2387)),restrict(U_2386,U_2387),U_2385),U_2383)),hAPP(fun(U_2386,fun(U_2387,bool)),fun(fun(U_2386,U_2387),bool),hAPP(fun(U_2386,bool),fun(fun(U_2386,fun(U_2387,bool)),fun(fun(U_2386,U_2387),bool)),pi(U_2386,U_2387),U_2383),U_2384))) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

cnf(f_649_5,plain,
    ( ~ hBOOL(hAPP(fun(U_2387,bool),bool,hAPP(U_2387,fun(fun(U_2387,bool),bool),member(U_2387),hAPP(U_2386,U_2387,U_2385,sK140(U_2387,U_2386,U_2385,U_2384,U_2383))),hAPP(U_2386,fun(U_2387,bool),U_2384,sK140(U_2387,U_2386,U_2385,U_2384,U_2383))))
    | hBOOL(hAPP(fun(fun(U_2386,U_2387),bool),bool,hAPP(fun(U_2386,U_2387),fun(fun(fun(U_2386,U_2387),bool),bool),member(fun(U_2386,U_2387)),hAPP(fun(U_2386,bool),fun(U_2386,U_2387),hAPP(fun(U_2386,U_2387),fun(fun(U_2386,bool),fun(U_2386,U_2387)),restrict(U_2386,U_2387),U_2385),U_2383)),hAPP(fun(U_2386,fun(U_2387,bool)),fun(fun(U_2386,U_2387),bool),hAPP(fun(U_2386,bool),fun(fun(U_2386,fun(U_2387,bool)),fun(fun(U_2386,U_2387),bool)),pi(U_2386,U_2387),U_2383),U_2384))) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

fof(f_650_1,plain,
    ! [X_b,X_a,F,B,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_560_restrict__in__funcset]) ).

fof(f_650_2,plain,
    ! [U_2393,U_2392,U_2391,U_2390,U_2389] :
      ( hBOOL(hAPP(fun(fun(U_2392,U_2393),bool),bool,hAPP(fun(U_2392,U_2393),fun(fun(fun(U_2392,U_2393),bool),bool),member(fun(U_2392,U_2393)),hAPP(fun(U_2392,bool),fun(U_2392,U_2393),hAPP(fun(U_2392,U_2393),fun(fun(U_2392,bool),fun(U_2392,U_2393)),restrict(U_2392,U_2393),U_2391),U_2389)),hAPP(fun(U_2392,fun(U_2393,bool)),fun(fun(U_2392,U_2393),bool),hAPP(fun(U_2392,bool),fun(fun(U_2392,fun(U_2393,bool)),fun(fun(U_2392,U_2393),bool)),pi(U_2392,U_2393),U_2389),hAPP(fun(U_2393,bool),fun(U_2392,fun(U_2393,bool)),combk(fun(U_2393,bool),U_2392),U_2390))))
      | ? [U_2388] :
          ( ~ hBOOL(hAPP(fun(U_2393,bool),bool,hAPP(U_2393,fun(fun(U_2393,bool),bool),member(U_2393),hAPP(U_2392,U_2393,U_2391,U_2388)),U_2390))
          & hBOOL(hAPP(fun(U_2392,bool),bool,hAPP(U_2392,fun(fun(U_2392,bool),bool),member(U_2392),U_2388),U_2389)) ) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ! [U_2393,U_2392,U_2391,U_2390,U_2389] :
      ( hBOOL(hAPP(fun(fun(U_2392,U_2393),bool),bool,hAPP(fun(U_2392,U_2393),fun(fun(fun(U_2392,U_2393),bool),bool),member(fun(U_2392,U_2393)),hAPP(fun(U_2392,bool),fun(U_2392,U_2393),hAPP(fun(U_2392,U_2393),fun(fun(U_2392,bool),fun(U_2392,U_2393)),restrict(U_2392,U_2393),U_2391),U_2389)),hAPP(fun(U_2392,fun(U_2393,bool)),fun(fun(U_2392,U_2393),bool),hAPP(fun(U_2392,bool),fun(fun(U_2392,fun(U_2393,bool)),fun(fun(U_2392,U_2393),bool)),pi(U_2392,U_2393),U_2389),hAPP(fun(U_2393,bool),fun(U_2392,fun(U_2393,bool)),combk(fun(U_2393,bool),U_2392),U_2390))))
      | ( ~ hBOOL(hAPP(fun(U_2393,bool),bool,hAPP(U_2393,fun(fun(U_2393,bool),bool),member(U_2393),hAPP(U_2392,U_2393,U_2391,sK141(U_2393,U_2392,U_2391,U_2390,U_2389))),U_2390))
        & hBOOL(hAPP(fun(U_2392,bool),bool,hAPP(U_2392,fun(fun(U_2392,bool),bool),member(U_2392),sK141(U_2393,U_2392,U_2391,U_2390,U_2389)),U_2389)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_2388,sK141(U_2393,U_2392,U_2391,U_2390,U_2389))],[f_650_2]) ).

cnf(f_650_4,plain,
    ( hBOOL(hAPP(fun(U_2392,bool),bool,hAPP(U_2392,fun(fun(U_2392,bool),bool),member(U_2392),sK141(U_2393,U_2392,U_2391,U_2390,U_2389)),U_2389))
    | hBOOL(hAPP(fun(fun(U_2392,U_2393),bool),bool,hAPP(fun(U_2392,U_2393),fun(fun(fun(U_2392,U_2393),bool),bool),member(fun(U_2392,U_2393)),hAPP(fun(U_2392,bool),fun(U_2392,U_2393),hAPP(fun(U_2392,U_2393),fun(fun(U_2392,bool),fun(U_2392,U_2393)),restrict(U_2392,U_2393),U_2391),U_2389)),hAPP(fun(U_2392,fun(U_2393,bool)),fun(fun(U_2392,U_2393),bool),hAPP(fun(U_2392,bool),fun(fun(U_2392,fun(U_2393,bool)),fun(fun(U_2392,U_2393),bool)),pi(U_2392,U_2393),U_2389),hAPP(fun(U_2393,bool),fun(U_2392,fun(U_2393,bool)),combk(fun(U_2393,bool),U_2392),U_2390)))) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

cnf(f_650_5,plain,
    ( ~ hBOOL(hAPP(fun(U_2393,bool),bool,hAPP(U_2393,fun(fun(U_2393,bool),bool),member(U_2393),hAPP(U_2392,U_2393,U_2391,sK141(U_2393,U_2392,U_2391,U_2390,U_2389))),U_2390))
    | hBOOL(hAPP(fun(fun(U_2392,U_2393),bool),bool,hAPP(fun(U_2392,U_2393),fun(fun(fun(U_2392,U_2393),bool),bool),member(fun(U_2392,U_2393)),hAPP(fun(U_2392,bool),fun(U_2392,U_2393),hAPP(fun(U_2392,U_2393),fun(fun(U_2392,bool),fun(U_2392,U_2393)),restrict(U_2392,U_2393),U_2391),U_2389)),hAPP(fun(U_2392,fun(U_2393,bool)),fun(fun(U_2392,U_2393),bool),hAPP(fun(U_2392,bool),fun(fun(U_2392,fun(U_2393,bool)),fun(fun(U_2392,U_2393),bool)),pi(U_2392,U_2393),U_2389),hAPP(fun(U_2393,bool),fun(U_2392,fun(U_2393,bool)),combk(fun(U_2393,bool),U_2392),U_2390)))) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

fof(f_651_1,plain,
    ! [X_b,X_a,F,G,A_1] :
      ( hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1) = hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),G),A_1)
      | ? [X_1] :
          ( hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,G,X_1)
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_561_restrict__ext]) ).

fof(f_651_2,plain,
    ! [U_2399,U_2398,U_2397,U_2396,U_2395] :
      ( hAPP(fun(U_2398,bool),fun(U_2398,U_2399),hAPP(fun(U_2398,U_2399),fun(fun(U_2398,bool),fun(U_2398,U_2399)),restrict(U_2398,U_2399),U_2397),U_2395) = hAPP(fun(U_2398,bool),fun(U_2398,U_2399),hAPP(fun(U_2398,U_2399),fun(fun(U_2398,bool),fun(U_2398,U_2399)),restrict(U_2398,U_2399),U_2396),U_2395)
      | ? [U_2394] :
          ( hAPP(U_2398,U_2399,U_2397,U_2394) != hAPP(U_2398,U_2399,U_2396,U_2394)
          & hBOOL(hAPP(fun(U_2398,bool),bool,hAPP(U_2398,fun(fun(U_2398,bool),bool),member(U_2398),U_2394),U_2395)) ) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

fof(f_651_3,plain,
    ! [U_2399,U_2398,U_2397,U_2396,U_2395] :
      ( hAPP(fun(U_2398,bool),fun(U_2398,U_2399),hAPP(fun(U_2398,U_2399),fun(fun(U_2398,bool),fun(U_2398,U_2399)),restrict(U_2398,U_2399),U_2397),U_2395) = hAPP(fun(U_2398,bool),fun(U_2398,U_2399),hAPP(fun(U_2398,U_2399),fun(fun(U_2398,bool),fun(U_2398,U_2399)),restrict(U_2398,U_2399),U_2396),U_2395)
      | ( hAPP(U_2398,U_2399,U_2397,sK142(U_2399,U_2398,U_2397,U_2396,U_2395)) != hAPP(U_2398,U_2399,U_2396,sK142(U_2399,U_2398,U_2397,U_2396,U_2395))
        & hBOOL(hAPP(fun(U_2398,bool),bool,hAPP(U_2398,fun(fun(U_2398,bool),bool),member(U_2398),sK142(U_2399,U_2398,U_2397,U_2396,U_2395)),U_2395)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_2394,sK142(U_2399,U_2398,U_2397,U_2396,U_2395))],[f_651_2]) ).

cnf(f_651_4,plain,
    ( hBOOL(hAPP(fun(U_2398,bool),bool,hAPP(U_2398,fun(fun(U_2398,bool),bool),member(U_2398),sK142(U_2399,U_2398,U_2397,U_2396,U_2395)),U_2395))
    | hAPP(fun(U_2398,bool),fun(U_2398,U_2399),hAPP(fun(U_2398,U_2399),fun(fun(U_2398,bool),fun(U_2398,U_2399)),restrict(U_2398,U_2399),U_2397),U_2395) = hAPP(fun(U_2398,bool),fun(U_2398,U_2399),hAPP(fun(U_2398,U_2399),fun(fun(U_2398,bool),fun(U_2398,U_2399)),restrict(U_2398,U_2399),U_2396),U_2395) ),
    inference(clausify,[status(thm)],[f_651_3]) ).

cnf(f_651_5,plain,
    ( hAPP(U_2398,U_2399,U_2397,sK142(U_2399,U_2398,U_2397,U_2396,U_2395)) != hAPP(U_2398,U_2399,U_2396,sK142(U_2399,U_2398,U_2397,U_2396,U_2395))
    | hAPP(fun(U_2398,bool),fun(U_2398,U_2399),hAPP(fun(U_2398,U_2399),fun(fun(U_2398,bool),fun(U_2398,U_2399)),restrict(U_2398,U_2399),U_2397),U_2395) = hAPP(fun(U_2398,bool),fun(U_2398,U_2399),hAPP(fun(U_2398,U_2399),fun(fun(U_2398,bool),fun(U_2398,U_2399)),restrict(U_2398,U_2399),U_2396),U_2395) ),
    inference(clausify,[status(thm)],[f_651_3]) ).

fof(f_652_1,plain,
    ! [X_b,X_a,F,A_1,B] :
      ( hAPP(fun(X_a,X_b),fun(X_a,X_a),hAPP(fun(X_b,X_a),fun(fun(X_a,X_b),fun(X_a,X_a)),hAPP(fun(X_a,bool),fun(fun(X_b,X_a),fun(fun(X_a,X_b),fun(X_a,X_a))),compose(X_a,X_b,X_a),B),F),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),hAPP(fun(X_b,X_a),fun(X_a,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,X_a),fun(X_a,X_b)),hilbert_inv_into(X_b,X_a),A_1),F)),B)) = hAPP(fun(X_a,bool),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,X_a)),restrict(X_a,X_a),combi(X_a)),B)
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) != ti(fun(X_a,bool),B) ),
    inference(fof_nnf,[status(thm)],[fact_562_compose__id__inv__into]) ).

fof(f_652_2,plain,
    ! [U_2404,U_2403,U_2402,U_2401,U_2400] :
      ( hAPP(fun(U_2403,U_2404),fun(U_2403,U_2403),hAPP(fun(U_2404,U_2403),fun(fun(U_2403,U_2404),fun(U_2403,U_2403)),hAPP(fun(U_2403,bool),fun(fun(U_2404,U_2403),fun(fun(U_2403,U_2404),fun(U_2403,U_2403))),compose(U_2403,U_2404,U_2403),U_2400),U_2402),hAPP(fun(U_2403,bool),fun(U_2403,U_2404),hAPP(fun(U_2403,U_2404),fun(fun(U_2403,bool),fun(U_2403,U_2404)),restrict(U_2403,U_2404),hAPP(fun(U_2404,U_2403),fun(U_2403,U_2404),hAPP(fun(U_2404,bool),fun(fun(U_2404,U_2403),fun(U_2403,U_2404)),hilbert_inv_into(U_2404,U_2403),U_2401),U_2402)),U_2400)) = hAPP(fun(U_2403,bool),fun(U_2403,U_2403),hAPP(fun(U_2403,U_2403),fun(fun(U_2403,bool),fun(U_2403,U_2403)),restrict(U_2403,U_2403),combi(U_2403)),U_2400)
      | hAPP(fun(U_2404,bool),fun(U_2403,bool),hAPP(fun(U_2404,U_2403),fun(fun(U_2404,bool),fun(U_2403,bool)),image(U_2404,U_2403),U_2402),U_2401) != ti(fun(U_2403,bool),U_2400) ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

cnf(f_652_3,plain,
    ( hAPP(fun(U_2403,U_2404),fun(U_2403,U_2403),hAPP(fun(U_2404,U_2403),fun(fun(U_2403,U_2404),fun(U_2403,U_2403)),hAPP(fun(U_2403,bool),fun(fun(U_2404,U_2403),fun(fun(U_2403,U_2404),fun(U_2403,U_2403))),compose(U_2403,U_2404,U_2403),U_2400),U_2402),hAPP(fun(U_2403,bool),fun(U_2403,U_2404),hAPP(fun(U_2403,U_2404),fun(fun(U_2403,bool),fun(U_2403,U_2404)),restrict(U_2403,U_2404),hAPP(fun(U_2404,U_2403),fun(U_2403,U_2404),hAPP(fun(U_2404,bool),fun(fun(U_2404,U_2403),fun(U_2403,U_2404)),hilbert_inv_into(U_2404,U_2403),U_2401),U_2402)),U_2400)) = hAPP(fun(U_2403,bool),fun(U_2403,U_2403),hAPP(fun(U_2403,U_2403),fun(fun(U_2403,bool),fun(U_2403,U_2403)),restrict(U_2403,U_2403),combi(U_2403)),U_2400)
    | hAPP(fun(U_2404,bool),fun(U_2403,bool),hAPP(fun(U_2404,U_2403),fun(fun(U_2404,bool),fun(U_2403,bool)),image(U_2404,U_2403),U_2402),U_2401) != ti(fun(U_2403,bool),U_2400) ),
    inference(clausify,[status(thm)],[f_652_2]) ).

fof(f_653_1,plain,
    ! [X_b,X_c,X_a,G,F,X_2,A_1] :
      ( hAPP(X_a,X_b,hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b))),compose(X_a,X_c,X_b),A_1),G),F),X_2) = hAPP(X_c,X_b,G,hAPP(X_a,X_c,F,X_2))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_563_compose__eq]) ).

fof(f_653_2,plain,
    ! [U_2411,U_2410,U_2409,U_2408,U_2407,U_2406,U_2405] :
      ( hAPP(U_2409,U_2411,hAPP(fun(U_2409,U_2410),fun(U_2409,U_2411),hAPP(fun(U_2410,U_2411),fun(fun(U_2409,U_2410),fun(U_2409,U_2411)),hAPP(fun(U_2409,bool),fun(fun(U_2410,U_2411),fun(fun(U_2409,U_2410),fun(U_2409,U_2411))),compose(U_2409,U_2410,U_2411),U_2405),U_2408),U_2407),U_2406) = hAPP(U_2410,U_2411,U_2408,hAPP(U_2409,U_2410,U_2407,U_2406))
      | ~ hBOOL(hAPP(fun(U_2409,bool),bool,hAPP(U_2409,fun(fun(U_2409,bool),bool),member(U_2409),U_2406),U_2405)) ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

cnf(f_653_3,plain,
    ( hAPP(U_2409,U_2411,hAPP(fun(U_2409,U_2410),fun(U_2409,U_2411),hAPP(fun(U_2410,U_2411),fun(fun(U_2409,U_2410),fun(U_2409,U_2411)),hAPP(fun(U_2409,bool),fun(fun(U_2410,U_2411),fun(fun(U_2409,U_2410),fun(U_2409,U_2411))),compose(U_2409,U_2410,U_2411),U_2405),U_2408),U_2407),U_2406) = hAPP(U_2410,U_2411,U_2408,hAPP(U_2409,U_2410,U_2407,U_2406))
    | ~ hBOOL(hAPP(fun(U_2409,bool),bool,hAPP(U_2409,fun(fun(U_2409,bool),bool),member(U_2409),U_2406),U_2405)) ),
    inference(clausify,[status(thm)],[f_653_2]) ).

fof(f_654_1,plain,
    ! [X_c,X_b,X_a,G,C,F,A_1,B] :
      ( hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),hAPP(fun(X_b,bool),fun(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c))),compose(X_b,X_a,X_c),A_1),G),F)),A_1) = ti(fun(X_c,bool),C)
      | hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),G),B) != ti(fun(X_c,bool),C)
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) != ti(fun(X_a,bool),B) ),
    inference(fof_nnf,[status(thm)],[fact_564_surj__compose]) ).

fof(f_654_2,plain,
    ! [U_2419,U_2418,U_2417,U_2416,U_2415,U_2414,U_2413,U_2412] :
      ( hAPP(fun(U_2418,bool),fun(U_2419,bool),hAPP(fun(U_2418,U_2419),fun(fun(U_2418,bool),fun(U_2419,bool)),image(U_2418,U_2419),hAPP(fun(U_2418,U_2417),fun(U_2418,U_2419),hAPP(fun(U_2417,U_2419),fun(fun(U_2418,U_2417),fun(U_2418,U_2419)),hAPP(fun(U_2418,bool),fun(fun(U_2417,U_2419),fun(fun(U_2418,U_2417),fun(U_2418,U_2419))),compose(U_2418,U_2417,U_2419),U_2413),U_2416),U_2414)),U_2413) = ti(fun(U_2419,bool),U_2415)
      | hAPP(fun(U_2417,bool),fun(U_2419,bool),hAPP(fun(U_2417,U_2419),fun(fun(U_2417,bool),fun(U_2419,bool)),image(U_2417,U_2419),U_2416),U_2412) != ti(fun(U_2419,bool),U_2415)
      | hAPP(fun(U_2418,bool),fun(U_2417,bool),hAPP(fun(U_2418,U_2417),fun(fun(U_2418,bool),fun(U_2417,bool)),image(U_2418,U_2417),U_2414),U_2413) != ti(fun(U_2417,bool),U_2412) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

cnf(f_654_3,plain,
    ( hAPP(fun(U_2418,bool),fun(U_2419,bool),hAPP(fun(U_2418,U_2419),fun(fun(U_2418,bool),fun(U_2419,bool)),image(U_2418,U_2419),hAPP(fun(U_2418,U_2417),fun(U_2418,U_2419),hAPP(fun(U_2417,U_2419),fun(fun(U_2418,U_2417),fun(U_2418,U_2419)),hAPP(fun(U_2418,bool),fun(fun(U_2417,U_2419),fun(fun(U_2418,U_2417),fun(U_2418,U_2419))),compose(U_2418,U_2417,U_2419),U_2413),U_2416),U_2414)),U_2413) = ti(fun(U_2419,bool),U_2415)
    | hAPP(fun(U_2417,bool),fun(U_2419,bool),hAPP(fun(U_2417,U_2419),fun(fun(U_2417,bool),fun(U_2419,bool)),image(U_2417,U_2419),U_2416),U_2412) != ti(fun(U_2419,bool),U_2415)
    | hAPP(fun(U_2418,bool),fun(U_2417,bool),hAPP(fun(U_2418,U_2417),fun(fun(U_2418,bool),fun(U_2417,bool)),image(U_2418,U_2417),U_2414),U_2413) != ti(fun(U_2417,bool),U_2412) ),
    inference(clausify,[status(thm)],[f_654_2]) ).

fof(f_655_1,plain,
    ! [X_d,X_c,X_a,X_b,Ha,D_1,G,C,F,A_1,B] :
      ( hAPP(fun(X_a,X_c),fun(X_a,X_d),hAPP(fun(X_c,X_d),fun(fun(X_a,X_c),fun(X_a,X_d)),hAPP(fun(X_a,bool),fun(fun(X_c,X_d),fun(fun(X_a,X_c),fun(X_a,X_d))),compose(X_a,X_c,X_d),A_1),Ha),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),hAPP(fun(X_a,bool),fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),compose(X_a,X_b,X_c),A_1),G),F)) = hAPP(fun(X_a,X_b),fun(X_a,X_d),hAPP(fun(X_b,X_d),fun(fun(X_a,X_b),fun(X_a,X_d)),hAPP(fun(X_a,bool),fun(fun(X_b,X_d),fun(fun(X_a,X_b),fun(X_a,X_d))),compose(X_a,X_b,X_d),A_1),hAPP(fun(X_b,X_c),fun(X_b,X_d),hAPP(fun(X_c,X_d),fun(fun(X_b,X_c),fun(X_b,X_d)),hAPP(fun(X_b,bool),fun(fun(X_c,X_d),fun(fun(X_b,X_c),fun(X_b,X_d))),compose(X_b,X_c,X_d),B),Ha),G)),F)
      | ~ hBOOL(hAPP(fun(fun(X_c,X_d),bool),bool,hAPP(fun(X_c,X_d),fun(fun(fun(X_c,X_d),bool),bool),member(fun(X_c,X_d)),Ha),hAPP(fun(X_c,fun(X_d,bool)),fun(fun(X_c,X_d),bool),hAPP(fun(X_c,bool),fun(fun(X_c,fun(X_d,bool)),fun(fun(X_c,X_d),bool)),pi(X_c,X_d),C),hAPP(fun(X_d,bool),fun(X_c,fun(X_d,bool)),combk(fun(X_d,bool),X_c),D_1))))
      | ~ hBOOL(hAPP(fun(fun(X_b,X_c),bool),bool,hAPP(fun(X_b,X_c),fun(fun(fun(X_b,X_c),bool),bool),member(fun(X_b,X_c)),G),hAPP(fun(X_b,fun(X_c,bool)),fun(fun(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_b,fun(X_c,bool)),fun(fun(X_b,X_c),bool)),pi(X_b,X_c),B),hAPP(fun(X_c,bool),fun(X_b,fun(X_c,bool)),combk(fun(X_c,bool),X_b),C))))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
    inference(fof_nnf,[status(thm)],[fact_565_compose__assoc]) ).

fof(f_655_2,plain,
    ! [U_2430,U_2429,U_2428,U_2427,U_2426,U_2425,U_2424,U_2423,U_2422,U_2421,U_2420] :
      ( hAPP(fun(U_2428,U_2429),fun(U_2428,U_2430),hAPP(fun(U_2429,U_2430),fun(fun(U_2428,U_2429),fun(U_2428,U_2430)),hAPP(fun(U_2428,bool),fun(fun(U_2429,U_2430),fun(fun(U_2428,U_2429),fun(U_2428,U_2430))),compose(U_2428,U_2429,U_2430),U_2421),U_2426),hAPP(fun(U_2428,U_2427),fun(U_2428,U_2429),hAPP(fun(U_2427,U_2429),fun(fun(U_2428,U_2427),fun(U_2428,U_2429)),hAPP(fun(U_2428,bool),fun(fun(U_2427,U_2429),fun(fun(U_2428,U_2427),fun(U_2428,U_2429))),compose(U_2428,U_2427,U_2429),U_2421),U_2424),U_2422)) = hAPP(fun(U_2428,U_2427),fun(U_2428,U_2430),hAPP(fun(U_2427,U_2430),fun(fun(U_2428,U_2427),fun(U_2428,U_2430)),hAPP(fun(U_2428,bool),fun(fun(U_2427,U_2430),fun(fun(U_2428,U_2427),fun(U_2428,U_2430))),compose(U_2428,U_2427,U_2430),U_2421),hAPP(fun(U_2427,U_2429),fun(U_2427,U_2430),hAPP(fun(U_2429,U_2430),fun(fun(U_2427,U_2429),fun(U_2427,U_2430)),hAPP(fun(U_2427,bool),fun(fun(U_2429,U_2430),fun(fun(U_2427,U_2429),fun(U_2427,U_2430))),compose(U_2427,U_2429,U_2430),U_2420),U_2426),U_2424)),U_2422)
      | ~ hBOOL(hAPP(fun(fun(U_2429,U_2430),bool),bool,hAPP(fun(U_2429,U_2430),fun(fun(fun(U_2429,U_2430),bool),bool),member(fun(U_2429,U_2430)),U_2426),hAPP(fun(U_2429,fun(U_2430,bool)),fun(fun(U_2429,U_2430),bool),hAPP(fun(U_2429,bool),fun(fun(U_2429,fun(U_2430,bool)),fun(fun(U_2429,U_2430),bool)),pi(U_2429,U_2430),U_2423),hAPP(fun(U_2430,bool),fun(U_2429,fun(U_2430,bool)),combk(fun(U_2430,bool),U_2429),U_2425))))
      | ~ hBOOL(hAPP(fun(fun(U_2427,U_2429),bool),bool,hAPP(fun(U_2427,U_2429),fun(fun(fun(U_2427,U_2429),bool),bool),member(fun(U_2427,U_2429)),U_2424),hAPP(fun(U_2427,fun(U_2429,bool)),fun(fun(U_2427,U_2429),bool),hAPP(fun(U_2427,bool),fun(fun(U_2427,fun(U_2429,bool)),fun(fun(U_2427,U_2429),bool)),pi(U_2427,U_2429),U_2420),hAPP(fun(U_2429,bool),fun(U_2427,fun(U_2429,bool)),combk(fun(U_2429,bool),U_2427),U_2423))))
      | ~ hBOOL(hAPP(fun(fun(U_2428,U_2427),bool),bool,hAPP(fun(U_2428,U_2427),fun(fun(fun(U_2428,U_2427),bool),bool),member(fun(U_2428,U_2427)),U_2422),hAPP(fun(U_2428,fun(U_2427,bool)),fun(fun(U_2428,U_2427),bool),hAPP(fun(U_2428,bool),fun(fun(U_2428,fun(U_2427,bool)),fun(fun(U_2428,U_2427),bool)),pi(U_2428,U_2427),U_2421),hAPP(fun(U_2427,bool),fun(U_2428,fun(U_2427,bool)),combk(fun(U_2427,bool),U_2428),U_2420)))) ),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

cnf(f_655_3,plain,
    ( hAPP(fun(U_2428,U_2429),fun(U_2428,U_2430),hAPP(fun(U_2429,U_2430),fun(fun(U_2428,U_2429),fun(U_2428,U_2430)),hAPP(fun(U_2428,bool),fun(fun(U_2429,U_2430),fun(fun(U_2428,U_2429),fun(U_2428,U_2430))),compose(U_2428,U_2429,U_2430),U_2421),U_2426),hAPP(fun(U_2428,U_2427),fun(U_2428,U_2429),hAPP(fun(U_2427,U_2429),fun(fun(U_2428,U_2427),fun(U_2428,U_2429)),hAPP(fun(U_2428,bool),fun(fun(U_2427,U_2429),fun(fun(U_2428,U_2427),fun(U_2428,U_2429))),compose(U_2428,U_2427,U_2429),U_2421),U_2424),U_2422)) = hAPP(fun(U_2428,U_2427),fun(U_2428,U_2430),hAPP(fun(U_2427,U_2430),fun(fun(U_2428,U_2427),fun(U_2428,U_2430)),hAPP(fun(U_2428,bool),fun(fun(U_2427,U_2430),fun(fun(U_2428,U_2427),fun(U_2428,U_2430))),compose(U_2428,U_2427,U_2430),U_2421),hAPP(fun(U_2427,U_2429),fun(U_2427,U_2430),hAPP(fun(U_2429,U_2430),fun(fun(U_2427,U_2429),fun(U_2427,U_2430)),hAPP(fun(U_2427,bool),fun(fun(U_2429,U_2430),fun(fun(U_2427,U_2429),fun(U_2427,U_2430))),compose(U_2427,U_2429,U_2430),U_2420),U_2426),U_2424)),U_2422)
    | ~ hBOOL(hAPP(fun(fun(U_2429,U_2430),bool),bool,hAPP(fun(U_2429,U_2430),fun(fun(fun(U_2429,U_2430),bool),bool),member(fun(U_2429,U_2430)),U_2426),hAPP(fun(U_2429,fun(U_2430,bool)),fun(fun(U_2429,U_2430),bool),hAPP(fun(U_2429,bool),fun(fun(U_2429,fun(U_2430,bool)),fun(fun(U_2429,U_2430),bool)),pi(U_2429,U_2430),U_2423),hAPP(fun(U_2430,bool),fun(U_2429,fun(U_2430,bool)),combk(fun(U_2430,bool),U_2429),U_2425))))
    | ~ hBOOL(hAPP(fun(fun(U_2427,U_2429),bool),bool,hAPP(fun(U_2427,U_2429),fun(fun(fun(U_2427,U_2429),bool),bool),member(fun(U_2427,U_2429)),U_2424),hAPP(fun(U_2427,fun(U_2429,bool)),fun(fun(U_2427,U_2429),bool),hAPP(fun(U_2427,bool),fun(fun(U_2427,fun(U_2429,bool)),fun(fun(U_2427,U_2429),bool)),pi(U_2427,U_2429),U_2420),hAPP(fun(U_2429,bool),fun(U_2427,fun(U_2429,bool)),combk(fun(U_2429,bool),U_2427),U_2423))))
    | ~ hBOOL(hAPP(fun(fun(U_2428,U_2427),bool),bool,hAPP(fun(U_2428,U_2427),fun(fun(fun(U_2428,U_2427),bool),bool),member(fun(U_2428,U_2427)),U_2422),hAPP(fun(U_2428,fun(U_2427,bool)),fun(fun(U_2428,U_2427),bool),hAPP(fun(U_2428,bool),fun(fun(U_2428,fun(U_2427,bool)),fun(fun(U_2428,U_2427),bool)),pi(U_2428,U_2427),U_2421),hAPP(fun(U_2427,bool),fun(U_2428,fun(U_2427,bool)),combk(fun(U_2427,bool),U_2428),U_2420)))) ),
    inference(clausify,[status(thm)],[f_655_2]) ).

fof(f_656_1,plain,
    ! [X_c,X_a,X_b,G,C,F,A_1,B] :
      ( hBOOL(hAPP(fun(fun(X_a,X_c),bool),bool,hAPP(fun(X_a,X_c),fun(fun(fun(X_a,X_c),bool),bool),member(fun(X_a,X_c)),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),hAPP(fun(X_a,bool),fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),compose(X_a,X_b,X_c),A_1),G),F)),hAPP(fun(X_a,fun(X_c,bool)),fun(fun(X_a,X_c),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_c,bool)),fun(fun(X_a,X_c),bool)),pi(X_a,X_c),A_1),hAPP(fun(X_c,bool),fun(X_a,fun(X_c,bool)),combk(fun(X_c,bool),X_a),C))))
      | ~ hBOOL(hAPP(fun(fun(X_b,X_c),bool),bool,hAPP(fun(X_b,X_c),fun(fun(fun(X_b,X_c),bool),bool),member(fun(X_b,X_c)),G),hAPP(fun(X_b,fun(X_c,bool)),fun(fun(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_b,fun(X_c,bool)),fun(fun(X_b,X_c),bool)),pi(X_b,X_c),B),hAPP(fun(X_c,bool),fun(X_b,fun(X_c,bool)),combk(fun(X_c,bool),X_b),C))))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
    inference(fof_nnf,[status(thm)],[fact_566_funcset__compose]) ).

fof(f_656_2,plain,
    ! [U_2438,U_2437,U_2436,U_2435,U_2434,U_2433,U_2432,U_2431] :
      ( hBOOL(hAPP(fun(fun(U_2437,U_2438),bool),bool,hAPP(fun(U_2437,U_2438),fun(fun(fun(U_2437,U_2438),bool),bool),member(fun(U_2437,U_2438)),hAPP(fun(U_2437,U_2436),fun(U_2437,U_2438),hAPP(fun(U_2436,U_2438),fun(fun(U_2437,U_2436),fun(U_2437,U_2438)),hAPP(fun(U_2437,bool),fun(fun(U_2436,U_2438),fun(fun(U_2437,U_2436),fun(U_2437,U_2438))),compose(U_2437,U_2436,U_2438),U_2432),U_2435),U_2433)),hAPP(fun(U_2437,fun(U_2438,bool)),fun(fun(U_2437,U_2438),bool),hAPP(fun(U_2437,bool),fun(fun(U_2437,fun(U_2438,bool)),fun(fun(U_2437,U_2438),bool)),pi(U_2437,U_2438),U_2432),hAPP(fun(U_2438,bool),fun(U_2437,fun(U_2438,bool)),combk(fun(U_2438,bool),U_2437),U_2434))))
      | ~ hBOOL(hAPP(fun(fun(U_2436,U_2438),bool),bool,hAPP(fun(U_2436,U_2438),fun(fun(fun(U_2436,U_2438),bool),bool),member(fun(U_2436,U_2438)),U_2435),hAPP(fun(U_2436,fun(U_2438,bool)),fun(fun(U_2436,U_2438),bool),hAPP(fun(U_2436,bool),fun(fun(U_2436,fun(U_2438,bool)),fun(fun(U_2436,U_2438),bool)),pi(U_2436,U_2438),U_2431),hAPP(fun(U_2438,bool),fun(U_2436,fun(U_2438,bool)),combk(fun(U_2438,bool),U_2436),U_2434))))
      | ~ hBOOL(hAPP(fun(fun(U_2437,U_2436),bool),bool,hAPP(fun(U_2437,U_2436),fun(fun(fun(U_2437,U_2436),bool),bool),member(fun(U_2437,U_2436)),U_2433),hAPP(fun(U_2437,fun(U_2436,bool)),fun(fun(U_2437,U_2436),bool),hAPP(fun(U_2437,bool),fun(fun(U_2437,fun(U_2436,bool)),fun(fun(U_2437,U_2436),bool)),pi(U_2437,U_2436),U_2432),hAPP(fun(U_2436,bool),fun(U_2437,fun(U_2436,bool)),combk(fun(U_2436,bool),U_2437),U_2431)))) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

cnf(f_656_3,plain,
    ( hBOOL(hAPP(fun(fun(U_2437,U_2438),bool),bool,hAPP(fun(U_2437,U_2438),fun(fun(fun(U_2437,U_2438),bool),bool),member(fun(U_2437,U_2438)),hAPP(fun(U_2437,U_2436),fun(U_2437,U_2438),hAPP(fun(U_2436,U_2438),fun(fun(U_2437,U_2436),fun(U_2437,U_2438)),hAPP(fun(U_2437,bool),fun(fun(U_2436,U_2438),fun(fun(U_2437,U_2436),fun(U_2437,U_2438))),compose(U_2437,U_2436,U_2438),U_2432),U_2435),U_2433)),hAPP(fun(U_2437,fun(U_2438,bool)),fun(fun(U_2437,U_2438),bool),hAPP(fun(U_2437,bool),fun(fun(U_2437,fun(U_2438,bool)),fun(fun(U_2437,U_2438),bool)),pi(U_2437,U_2438),U_2432),hAPP(fun(U_2438,bool),fun(U_2437,fun(U_2438,bool)),combk(fun(U_2438,bool),U_2437),U_2434))))
    | ~ hBOOL(hAPP(fun(fun(U_2436,U_2438),bool),bool,hAPP(fun(U_2436,U_2438),fun(fun(fun(U_2436,U_2438),bool),bool),member(fun(U_2436,U_2438)),U_2435),hAPP(fun(U_2436,fun(U_2438,bool)),fun(fun(U_2436,U_2438),bool),hAPP(fun(U_2436,bool),fun(fun(U_2436,fun(U_2438,bool)),fun(fun(U_2436,U_2438),bool)),pi(U_2436,U_2438),U_2431),hAPP(fun(U_2438,bool),fun(U_2436,fun(U_2438,bool)),combk(fun(U_2438,bool),U_2436),U_2434))))
    | ~ hBOOL(hAPP(fun(fun(U_2437,U_2436),bool),bool,hAPP(fun(U_2437,U_2436),fun(fun(fun(U_2437,U_2436),bool),bool),member(fun(U_2437,U_2436)),U_2433),hAPP(fun(U_2437,fun(U_2436,bool)),fun(fun(U_2437,U_2436),bool),hAPP(fun(U_2437,bool),fun(fun(U_2437,fun(U_2436,bool)),fun(fun(U_2437,U_2436),bool)),pi(U_2437,U_2436),U_2432),hAPP(fun(U_2436,bool),fun(U_2437,fun(U_2436,bool)),combk(fun(U_2436,bool),U_2437),U_2431)))) ),
    inference(clausify,[status(thm)],[f_656_2]) ).

fof(f_657_1,plain,
    ! [X_a,X_c,X_b,A_1,G,F] : hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b))),compose(X_a,X_c,X_b),A_1),G),F) = hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),combb(X_c,X_b,X_a),G),F)),A_1),
    inference(fof_nnf,[status(thm)],[fact_567_compose__def]) ).

fof(f_657_2,plain,
    ! [U_2444,U_2443,U_2442,U_2441,U_2440,U_2439] : hAPP(fun(U_2444,U_2443),fun(U_2444,U_2442),hAPP(fun(U_2443,U_2442),fun(fun(U_2444,U_2443),fun(U_2444,U_2442)),hAPP(fun(U_2444,bool),fun(fun(U_2443,U_2442),fun(fun(U_2444,U_2443),fun(U_2444,U_2442))),compose(U_2444,U_2443,U_2442),U_2441),U_2440),U_2439) = hAPP(fun(U_2444,bool),fun(U_2444,U_2442),hAPP(fun(U_2444,U_2442),fun(fun(U_2444,bool),fun(U_2444,U_2442)),restrict(U_2444,U_2442),hAPP(fun(U_2444,U_2443),fun(U_2444,U_2442),hAPP(fun(U_2443,U_2442),fun(fun(U_2444,U_2443),fun(U_2444,U_2442)),combb(U_2443,U_2442,U_2444),U_2440),U_2439)),U_2441),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

cnf(f_657_3,plain,
    hAPP(fun(U_2444,U_2443),fun(U_2444,U_2442),hAPP(fun(U_2443,U_2442),fun(fun(U_2444,U_2443),fun(U_2444,U_2442)),hAPP(fun(U_2444,bool),fun(fun(U_2443,U_2442),fun(fun(U_2444,U_2443),fun(U_2444,U_2442))),compose(U_2444,U_2443,U_2442),U_2441),U_2440),U_2439) = hAPP(fun(U_2444,bool),fun(U_2444,U_2442),hAPP(fun(U_2444,U_2442),fun(fun(U_2444,bool),fun(U_2444,U_2442)),restrict(U_2444,U_2442),hAPP(fun(U_2444,U_2443),fun(U_2444,U_2442),hAPP(fun(U_2443,U_2442),fun(fun(U_2444,U_2443),fun(U_2444,U_2442)),combb(U_2443,U_2442,U_2444),U_2440),U_2439)),U_2441),
    inference(clausify,[status(thm)],[f_657_2]) ).

fof(f_658_1,plain,
    ! [X_a,X_b,G,A_1,B] :
      ( hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b))),compose(X_a,X_a,X_b),A_1),G),hAPP(fun(X_a,bool),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,X_a)),restrict(X_a,X_a),combi(X_a)),A_1)) = ti(fun(X_a,X_b),G)
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1)))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
    inference(fof_nnf,[status(thm)],[fact_568_compose__Id]) ).

fof(f_658_2,plain,
    ! [U_2449,U_2448,U_2447,U_2446,U_2445] :
      ( hAPP(fun(U_2449,U_2449),fun(U_2449,U_2448),hAPP(fun(U_2449,U_2448),fun(fun(U_2449,U_2449),fun(U_2449,U_2448)),hAPP(fun(U_2449,bool),fun(fun(U_2449,U_2448),fun(fun(U_2449,U_2449),fun(U_2449,U_2448))),compose(U_2449,U_2449,U_2448),U_2446),U_2447),hAPP(fun(U_2449,bool),fun(U_2449,U_2449),hAPP(fun(U_2449,U_2449),fun(fun(U_2449,bool),fun(U_2449,U_2449)),restrict(U_2449,U_2449),combi(U_2449)),U_2446)) = ti(fun(U_2449,U_2448),U_2447)
      | ~ hBOOL(hAPP(fun(fun(U_2449,U_2448),bool),bool,hAPP(fun(U_2449,U_2448),fun(fun(fun(U_2449,U_2448),bool),bool),member(fun(U_2449,U_2448)),U_2447),hAPP(fun(U_2449,bool),fun(fun(U_2449,U_2448),bool),extensional(U_2449,U_2448),U_2446)))
      | ~ hBOOL(hAPP(fun(fun(U_2449,U_2448),bool),bool,hAPP(fun(U_2449,U_2448),fun(fun(fun(U_2449,U_2448),bool),bool),member(fun(U_2449,U_2448)),U_2447),hAPP(fun(U_2449,fun(U_2448,bool)),fun(fun(U_2449,U_2448),bool),hAPP(fun(U_2449,bool),fun(fun(U_2449,fun(U_2448,bool)),fun(fun(U_2449,U_2448),bool)),pi(U_2449,U_2448),U_2446),hAPP(fun(U_2448,bool),fun(U_2449,fun(U_2448,bool)),combk(fun(U_2448,bool),U_2449),U_2445)))) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

fof(f_658_3,plain,
    ! [U_2449,U_2448,U_2447,U_2446] :
      ( ! [U_2445] : ~ hBOOL(hAPP(fun(fun(U_2449,U_2448),bool),bool,hAPP(fun(U_2449,U_2448),fun(fun(fun(U_2449,U_2448),bool),bool),member(fun(U_2449,U_2448)),U_2447),hAPP(fun(U_2449,fun(U_2448,bool)),fun(fun(U_2449,U_2448),bool),hAPP(fun(U_2449,bool),fun(fun(U_2449,fun(U_2448,bool)),fun(fun(U_2449,U_2448),bool)),pi(U_2449,U_2448),U_2446),hAPP(fun(U_2448,bool),fun(U_2449,fun(U_2448,bool)),combk(fun(U_2448,bool),U_2449),U_2445))))
      | hAPP(fun(U_2449,U_2449),fun(U_2449,U_2448),hAPP(fun(U_2449,U_2448),fun(fun(U_2449,U_2449),fun(U_2449,U_2448)),hAPP(fun(U_2449,bool),fun(fun(U_2449,U_2448),fun(fun(U_2449,U_2449),fun(U_2449,U_2448))),compose(U_2449,U_2449,U_2448),U_2446),U_2447),hAPP(fun(U_2449,bool),fun(U_2449,U_2449),hAPP(fun(U_2449,U_2449),fun(fun(U_2449,bool),fun(U_2449,U_2449)),restrict(U_2449,U_2449),combi(U_2449)),U_2446)) = ti(fun(U_2449,U_2448),U_2447)
      | ~ hBOOL(hAPP(fun(fun(U_2449,U_2448),bool),bool,hAPP(fun(U_2449,U_2448),fun(fun(fun(U_2449,U_2448),bool),bool),member(fun(U_2449,U_2448)),U_2447),hAPP(fun(U_2449,bool),fun(fun(U_2449,U_2448),bool),extensional(U_2449,U_2448),U_2446))) ),
    inference(miniscope,[status(thm)],[f_658_2]) ).

cnf(f_658_4,plain,
    ( ~ hBOOL(hAPP(fun(fun(U_2449,U_2448),bool),bool,hAPP(fun(U_2449,U_2448),fun(fun(fun(U_2449,U_2448),bool),bool),member(fun(U_2449,U_2448)),U_2447),hAPP(fun(U_2449,fun(U_2448,bool)),fun(fun(U_2449,U_2448),bool),hAPP(fun(U_2449,bool),fun(fun(U_2449,fun(U_2448,bool)),fun(fun(U_2449,U_2448),bool)),pi(U_2449,U_2448),U_2446),hAPP(fun(U_2448,bool),fun(U_2449,fun(U_2448,bool)),combk(fun(U_2448,bool),U_2449),U_2445))))
    | hAPP(fun(U_2449,U_2449),fun(U_2449,U_2448),hAPP(fun(U_2449,U_2448),fun(fun(U_2449,U_2449),fun(U_2449,U_2448)),hAPP(fun(U_2449,bool),fun(fun(U_2449,U_2448),fun(fun(U_2449,U_2449),fun(U_2449,U_2448))),compose(U_2449,U_2449,U_2448),U_2446),U_2447),hAPP(fun(U_2449,bool),fun(U_2449,U_2449),hAPP(fun(U_2449,U_2449),fun(fun(U_2449,bool),fun(U_2449,U_2449)),restrict(U_2449,U_2449),combi(U_2449)),U_2446)) = ti(fun(U_2449,U_2448),U_2447)
    | ~ hBOOL(hAPP(fun(fun(U_2449,U_2448),bool),bool,hAPP(fun(U_2449,U_2448),fun(fun(fun(U_2449,U_2448),bool),bool),member(fun(U_2449,U_2448)),U_2447),hAPP(fun(U_2449,bool),fun(fun(U_2449,U_2448),bool),extensional(U_2449,U_2448),U_2446))) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

fof(f_659_1,plain,
    ! [X_a,X_b,F,A_1,B] :
      ( hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b))),compose(X_a,X_b,X_b),A_1),hAPP(fun(X_b,bool),fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,X_b)),restrict(X_b,X_b),combi(X_b)),B)),F) = ti(fun(X_a,X_b),F)
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1)))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
    inference(fof_nnf,[status(thm)],[fact_569_Id__compose]) ).

fof(f_659_2,plain,
    ! [U_2454,U_2453,U_2452,U_2451,U_2450] :
      ( hAPP(fun(U_2454,U_2453),fun(U_2454,U_2453),hAPP(fun(U_2453,U_2453),fun(fun(U_2454,U_2453),fun(U_2454,U_2453)),hAPP(fun(U_2454,bool),fun(fun(U_2453,U_2453),fun(fun(U_2454,U_2453),fun(U_2454,U_2453))),compose(U_2454,U_2453,U_2453),U_2451),hAPP(fun(U_2453,bool),fun(U_2453,U_2453),hAPP(fun(U_2453,U_2453),fun(fun(U_2453,bool),fun(U_2453,U_2453)),restrict(U_2453,U_2453),combi(U_2453)),U_2450)),U_2452) = ti(fun(U_2454,U_2453),U_2452)
      | ~ hBOOL(hAPP(fun(fun(U_2454,U_2453),bool),bool,hAPP(fun(U_2454,U_2453),fun(fun(fun(U_2454,U_2453),bool),bool),member(fun(U_2454,U_2453)),U_2452),hAPP(fun(U_2454,bool),fun(fun(U_2454,U_2453),bool),extensional(U_2454,U_2453),U_2451)))
      | ~ hBOOL(hAPP(fun(fun(U_2454,U_2453),bool),bool,hAPP(fun(U_2454,U_2453),fun(fun(fun(U_2454,U_2453),bool),bool),member(fun(U_2454,U_2453)),U_2452),hAPP(fun(U_2454,fun(U_2453,bool)),fun(fun(U_2454,U_2453),bool),hAPP(fun(U_2454,bool),fun(fun(U_2454,fun(U_2453,bool)),fun(fun(U_2454,U_2453),bool)),pi(U_2454,U_2453),U_2451),hAPP(fun(U_2453,bool),fun(U_2454,fun(U_2453,bool)),combk(fun(U_2453,bool),U_2454),U_2450)))) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

cnf(f_659_3,plain,
    ( hAPP(fun(U_2454,U_2453),fun(U_2454,U_2453),hAPP(fun(U_2453,U_2453),fun(fun(U_2454,U_2453),fun(U_2454,U_2453)),hAPP(fun(U_2454,bool),fun(fun(U_2453,U_2453),fun(fun(U_2454,U_2453),fun(U_2454,U_2453))),compose(U_2454,U_2453,U_2453),U_2451),hAPP(fun(U_2453,bool),fun(U_2453,U_2453),hAPP(fun(U_2453,U_2453),fun(fun(U_2453,bool),fun(U_2453,U_2453)),restrict(U_2453,U_2453),combi(U_2453)),U_2450)),U_2452) = ti(fun(U_2454,U_2453),U_2452)
    | ~ hBOOL(hAPP(fun(fun(U_2454,U_2453),bool),bool,hAPP(fun(U_2454,U_2453),fun(fun(fun(U_2454,U_2453),bool),bool),member(fun(U_2454,U_2453)),U_2452),hAPP(fun(U_2454,bool),fun(fun(U_2454,U_2453),bool),extensional(U_2454,U_2453),U_2451)))
    | ~ hBOOL(hAPP(fun(fun(U_2454,U_2453),bool),bool,hAPP(fun(U_2454,U_2453),fun(fun(fun(U_2454,U_2453),bool),bool),member(fun(U_2454,U_2453)),U_2452),hAPP(fun(U_2454,fun(U_2453,bool)),fun(fun(U_2454,U_2453),bool),hAPP(fun(U_2454,bool),fun(fun(U_2454,fun(U_2453,bool)),fun(fun(U_2454,U_2453),bool)),pi(U_2454,U_2453),U_2451),hAPP(fun(U_2453,bool),fun(U_2454,fun(U_2453,bool)),combk(fun(U_2453,bool),U_2454),U_2450)))) ),
    inference(clausify,[status(thm)],[f_659_2]) ).

fof(f_660_1,plain,
    ! [X_a] :
      ( ! [V_2,U_1,Y,X,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V_2),Y))),A_2))
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V_2) != one_one(X_a)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_2)) )
      | ~ linord626643107strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_570_convex__bound__lt]) ).

fof(f_660_2,plain,
    ! [U_2460] :
      ( ! [U_2459,U_2458,U_2457,U_2456,U_2455] :
          ( hBOOL(hAPP(U_2460,bool,hAPP(U_2460,fun(U_2460,bool),ord_less(U_2460),hAPP(U_2460,U_2460,hAPP(U_2460,fun(U_2460,U_2460),plus_plus(U_2460),hAPP(U_2460,U_2460,hAPP(U_2460,fun(U_2460,U_2460),times_times(U_2460),U_2458),U_2456)),hAPP(U_2460,U_2460,hAPP(U_2460,fun(U_2460,U_2460),times_times(U_2460),U_2459),U_2457))),U_2455))
          | hAPP(U_2460,U_2460,hAPP(U_2460,fun(U_2460,U_2460),plus_plus(U_2460),U_2458),U_2459) != one_one(U_2460)
          | ~ hBOOL(hAPP(U_2460,bool,hAPP(U_2460,fun(U_2460,bool),ord_less_eq(U_2460),zero_zero(U_2460)),U_2459))
          | ~ hBOOL(hAPP(U_2460,bool,hAPP(U_2460,fun(U_2460,bool),ord_less_eq(U_2460),zero_zero(U_2460)),U_2458))
          | ~ hBOOL(hAPP(U_2460,bool,hAPP(U_2460,fun(U_2460,bool),ord_less(U_2460),U_2457),U_2455))
          | ~ hBOOL(hAPP(U_2460,bool,hAPP(U_2460,fun(U_2460,bool),ord_less(U_2460),U_2456),U_2455)) )
      | ~ linord626643107strict(U_2460) ),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

cnf(f_660_3,plain,
    ( hBOOL(hAPP(U_2460,bool,hAPP(U_2460,fun(U_2460,bool),ord_less(U_2460),hAPP(U_2460,U_2460,hAPP(U_2460,fun(U_2460,U_2460),plus_plus(U_2460),hAPP(U_2460,U_2460,hAPP(U_2460,fun(U_2460,U_2460),times_times(U_2460),U_2458),U_2456)),hAPP(U_2460,U_2460,hAPP(U_2460,fun(U_2460,U_2460),times_times(U_2460),U_2459),U_2457))),U_2455))
    | hAPP(U_2460,U_2460,hAPP(U_2460,fun(U_2460,U_2460),plus_plus(U_2460),U_2458),U_2459) != one_one(U_2460)
    | ~ hBOOL(hAPP(U_2460,bool,hAPP(U_2460,fun(U_2460,bool),ord_less_eq(U_2460),zero_zero(U_2460)),U_2459))
    | ~ hBOOL(hAPP(U_2460,bool,hAPP(U_2460,fun(U_2460,bool),ord_less_eq(U_2460),zero_zero(U_2460)),U_2458))
    | ~ hBOOL(hAPP(U_2460,bool,hAPP(U_2460,fun(U_2460,bool),ord_less(U_2460),U_2457),U_2455))
    | ~ hBOOL(hAPP(U_2460,bool,hAPP(U_2460,fun(U_2460,bool),ord_less(U_2460),U_2456),U_2455))
    | ~ linord626643107strict(U_2460) ),
    inference(clausify,[status(thm)],[f_660_2]) ).

fof(f_661_1,plain,
    ! [X_a] :
      ( ! [Ba,Aa] :
          ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),ring_1_Ints(X_a)))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) )
      | ~ ring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_571_Ints__mult]) ).

fof(f_661_2,plain,
    ! [U_2463] :
      ( ! [U_2462,U_2461] :
          ( hBOOL(hAPP(fun(U_2463,bool),bool,hAPP(U_2463,fun(fun(U_2463,bool),bool),member(U_2463),hAPP(U_2463,U_2463,hAPP(U_2463,fun(U_2463,U_2463),times_times(U_2463),U_2461),U_2462)),ring_1_Ints(U_2463)))
          | ~ hBOOL(hAPP(fun(U_2463,bool),bool,hAPP(U_2463,fun(fun(U_2463,bool),bool),member(U_2463),U_2462),ring_1_Ints(U_2463)))
          | ~ hBOOL(hAPP(fun(U_2463,bool),bool,hAPP(U_2463,fun(fun(U_2463,bool),bool),member(U_2463),U_2461),ring_1_Ints(U_2463))) )
      | ~ ring_1(U_2463) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

cnf(f_661_3,plain,
    ( hBOOL(hAPP(fun(U_2463,bool),bool,hAPP(U_2463,fun(fun(U_2463,bool),bool),member(U_2463),hAPP(U_2463,U_2463,hAPP(U_2463,fun(U_2463,U_2463),times_times(U_2463),U_2461),U_2462)),ring_1_Ints(U_2463)))
    | ~ hBOOL(hAPP(fun(U_2463,bool),bool,hAPP(U_2463,fun(fun(U_2463,bool),bool),member(U_2463),U_2462),ring_1_Ints(U_2463)))
    | ~ hBOOL(hAPP(fun(U_2463,bool),bool,hAPP(U_2463,fun(fun(U_2463,bool),bool),member(U_2463),U_2461),ring_1_Ints(U_2463)))
    | ~ ring_1(U_2463) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

fof(f_662_1,plain,
    ! [M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),M_3))),
    inference(fof_nnf,[status(thm)],[fact_572_le__square]) ).

fof(f_662_2,plain,
    ! [U_2464] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2464),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2464),U_2464))),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

cnf(f_662_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2464),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2464),U_2464))),
    inference(clausify,[status(thm)],[f_662_2]) ).

fof(f_663_1,plain,
    ! [M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),M_3)))),
    inference(fof_nnf,[status(thm)],[fact_573_le__cube]) ).

fof(f_663_2,plain,
    ! [U_2465] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2465),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2465),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2465),U_2465)))),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

cnf(f_663_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2465),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2465),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2465),U_2465)))),
    inference(clausify,[status(thm)],[f_663_2]) ).

fof(f_664_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),K_2)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_574_mult__le__mono1]) ).

fof(f_664_2,plain,
    ! [U_2468,U_2467,U_2466] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2467),U_2468)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2466),U_2468)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2467),U_2466)) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

cnf(f_664_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2467),U_2468)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2466),U_2468)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2467),U_2466)) ),
    inference(clausify,[status(thm)],[f_664_2]) ).

fof(f_665_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),J_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_575_mult__le__mono2]) ).

fof(f_665_2,plain,
    ! [U_2471,U_2470,U_2469] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2471),U_2470)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2471),U_2469)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2470),U_2469)) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

cnf(f_665_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2471),U_2470)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2471),U_2469)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2470),U_2469)) ),
    inference(clausify,[status(thm)],[f_665_2]) ).

fof(f_666_1,plain,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),L_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),L_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_576_mult__le__mono]) ).

fof(f_666_2,plain,
    ! [U_2475,U_2474,U_2473,U_2472] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2473),U_2475)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2472),U_2474)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2475),U_2474))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2473),U_2472)) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

cnf(f_666_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2473),U_2475)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2472),U_2474)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2475),U_2474))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2473),U_2472)) ),
    inference(clausify,[status(thm)],[f_666_2]) ).

fof(f_667_1,plain,
    ! [X_a] :
      ( ! [W,Y_1,X_2,Z_1] :
          ( ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y_1))
            | ( ti(X_a,Y_1) != ti(X_a,Z_1)
              & ti(X_a,W) != ti(X_a,X_2) ) )
          & ( ti(X_a,Y_1) = ti(X_a,Z_1)
            | ti(X_a,W) = ti(X_a,X_2)
            | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Z_1)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y_1)) ) )
      | ~ semiri456707255roduct(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_577_crossproduct__eq]) ).

fof(f_667_2,plain,
    ! [U_2480] :
      ( ! [U_2479,U_2478,U_2477,U_2476] :
          ( ( hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2479),U_2478)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2477),U_2476)) = hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2479),U_2476)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2477),U_2478))
            | ( ti(U_2480,U_2478) != ti(U_2480,U_2476)
              & ti(U_2480,U_2479) != ti(U_2480,U_2477) ) )
          & ( ti(U_2480,U_2478) = ti(U_2480,U_2476)
            | ti(U_2480,U_2479) = ti(U_2480,U_2477)
            | hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2479),U_2478)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2477),U_2476)) != hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2479),U_2476)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2477),U_2478)) ) )
      | ~ semiri456707255roduct(U_2480) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

fof(f_667_3,plain,
    ! [U_2480] :
      ( ( ! [U_2488,U_2486,U_2484,U_2482] :
            ( hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2488),U_2486)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2484),U_2482)) = hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2488),U_2482)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2484),U_2486))
            | ( ti(U_2480,U_2486) != ti(U_2480,U_2482)
              & ti(U_2480,U_2488) != ti(U_2480,U_2484) ) )
        & ! [U_2487,U_2485,U_2483,U_2481] :
            ( ti(U_2480,U_2485) = ti(U_2480,U_2481)
            | ti(U_2480,U_2487) = ti(U_2480,U_2483)
            | hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2487),U_2485)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2483),U_2481)) != hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2487),U_2481)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2483),U_2485)) ) )
      | ~ semiri456707255roduct(U_2480) ),
    inference(miniscope,[status(thm)],[f_667_2]) ).

cnf(f_667_4,plain,
    ( ti(U_2480,U_2485) = ti(U_2480,U_2481)
    | ti(U_2480,U_2487) = ti(U_2480,U_2483)
    | hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2487),U_2485)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2483),U_2481)) != hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2487),U_2481)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2483),U_2485))
    | ~ semiri456707255roduct(U_2480) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

cnf(f_667_5,plain,
    ( ti(U_2480,U_2488) != ti(U_2480,U_2484)
    | hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2488),U_2486)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2484),U_2482)) = hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2488),U_2482)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2484),U_2486))
    | ~ semiri456707255roduct(U_2480) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

cnf(f_667_6,plain,
    ( ti(U_2480,U_2486) != ti(U_2480,U_2482)
    | hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2488),U_2486)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2484),U_2482)) = hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),plus_plus(U_2480),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2488),U_2482)),hAPP(U_2480,U_2480,hAPP(U_2480,fun(U_2480,U_2480),times_times(U_2480),U_2484),U_2486))
    | ~ semiri456707255roduct(U_2480) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

fof(f_668_1,plain,
    ! [X_a] :
      ( ! [A_2,M_3,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),M_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),M_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),M_3)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_578_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).

fof(f_668_2,plain,
    ! [U_2492] :
      ( ! [U_2491,U_2490,U_2489] : hAPP(U_2492,U_2492,hAPP(U_2492,fun(U_2492,U_2492),plus_plus(U_2492),hAPP(U_2492,U_2492,hAPP(U_2492,fun(U_2492,U_2492),times_times(U_2492),U_2491),U_2490)),hAPP(U_2492,U_2492,hAPP(U_2492,fun(U_2492,U_2492),times_times(U_2492),U_2489),U_2490)) = hAPP(U_2492,U_2492,hAPP(U_2492,fun(U_2492,U_2492),times_times(U_2492),hAPP(U_2492,U_2492,hAPP(U_2492,fun(U_2492,U_2492),plus_plus(U_2492),U_2491),U_2489)),U_2490)
      | ~ comm_semiring_1(U_2492) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

cnf(f_668_3,plain,
    ( hAPP(U_2492,U_2492,hAPP(U_2492,fun(U_2492,U_2492),plus_plus(U_2492),hAPP(U_2492,U_2492,hAPP(U_2492,fun(U_2492,U_2492),times_times(U_2492),U_2491),U_2490)),hAPP(U_2492,U_2492,hAPP(U_2492,fun(U_2492,U_2492),times_times(U_2492),U_2489),U_2490)) = hAPP(U_2492,U_2492,hAPP(U_2492,fun(U_2492,U_2492),times_times(U_2492),hAPP(U_2492,U_2492,hAPP(U_2492,fun(U_2492,U_2492),plus_plus(U_2492),U_2491),U_2489)),U_2490)
    | ~ comm_semiring_1(U_2492) ),
    inference(clausify,[status(thm)],[f_668_2]) ).

fof(f_669_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_579_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).

fof(f_669_2,plain,
    ! [U_2496] :
      ( ! [U_2495,U_2494,U_2493] : hAPP(U_2496,U_2496,hAPP(U_2496,fun(U_2496,U_2496),times_times(U_2496),hAPP(U_2496,U_2496,hAPP(U_2496,fun(U_2496,U_2496),plus_plus(U_2496),U_2495),U_2494)),U_2493) = hAPP(U_2496,U_2496,hAPP(U_2496,fun(U_2496,U_2496),plus_plus(U_2496),hAPP(U_2496,U_2496,hAPP(U_2496,fun(U_2496,U_2496),times_times(U_2496),U_2495),U_2493)),hAPP(U_2496,U_2496,hAPP(U_2496,fun(U_2496,U_2496),times_times(U_2496),U_2494),U_2493))
      | ~ comm_semiring_1(U_2496) ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

cnf(f_669_3,plain,
    ( hAPP(U_2496,U_2496,hAPP(U_2496,fun(U_2496,U_2496),times_times(U_2496),hAPP(U_2496,U_2496,hAPP(U_2496,fun(U_2496,U_2496),plus_plus(U_2496),U_2495),U_2494)),U_2493) = hAPP(U_2496,U_2496,hAPP(U_2496,fun(U_2496,U_2496),plus_plus(U_2496),hAPP(U_2496,U_2496,hAPP(U_2496,fun(U_2496,U_2496),times_times(U_2496),U_2495),U_2493)),hAPP(U_2496,U_2496,hAPP(U_2496,fun(U_2496,U_2496),times_times(U_2496),U_2494),U_2493))
    | ~ comm_semiring_1(U_2496) ),
    inference(clausify,[status(thm)],[f_669_2]) ).

fof(f_670_1,plain,
    ! [X_a] :
      ( ! [Ca,Da,Aa,Ba] :
          ( ( ( ti(X_a,Ca) != ti(X_a,Da)
              & ti(X_a,Aa) != ti(X_a,Ba) )
            | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),Da)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Da)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),Ca)) )
          & ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),Da)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Da)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),Ca))
            | ti(X_a,Ca) = ti(X_a,Da)
            | ti(X_a,Aa) = ti(X_a,Ba) ) )
      | ~ semiri456707255roduct(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_580_crossproduct__noteq]) ).

fof(f_670_2,plain,
    ! [U_2501] :
      ( ! [U_2500,U_2499,U_2498,U_2497] :
          ( ( ( ti(U_2501,U_2500) != ti(U_2501,U_2499)
              & ti(U_2501,U_2498) != ti(U_2501,U_2497) )
            | hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2498),U_2500)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2497),U_2499)) = hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2498),U_2499)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2497),U_2500)) )
          & ( hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2498),U_2500)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2497),U_2499)) != hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2498),U_2499)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2497),U_2500))
            | ti(U_2501,U_2500) = ti(U_2501,U_2499)
            | ti(U_2501,U_2498) = ti(U_2501,U_2497) ) )
      | ~ semiri456707255roduct(U_2501) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ! [U_2501] :
      ( ( ! [U_2509,U_2507,U_2505,U_2503] :
            ( ( ti(U_2501,U_2509) != ti(U_2501,U_2507)
              & ti(U_2501,U_2505) != ti(U_2501,U_2503) )
            | hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2505),U_2509)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2503),U_2507)) = hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2505),U_2507)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2503),U_2509)) )
        & ! [U_2508,U_2506,U_2504,U_2502] :
            ( hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2504),U_2508)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2502),U_2506)) != hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2504),U_2506)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2502),U_2508))
            | ti(U_2501,U_2508) = ti(U_2501,U_2506)
            | ti(U_2501,U_2504) = ti(U_2501,U_2502) ) )
      | ~ semiri456707255roduct(U_2501) ),
    inference(miniscope,[status(thm)],[f_670_2]) ).

cnf(f_670_4,plain,
    ( hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2504),U_2508)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2502),U_2506)) != hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2504),U_2506)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2502),U_2508))
    | ti(U_2501,U_2508) = ti(U_2501,U_2506)
    | ti(U_2501,U_2504) = ti(U_2501,U_2502)
    | ~ semiri456707255roduct(U_2501) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

cnf(f_670_5,plain,
    ( ti(U_2501,U_2505) != ti(U_2501,U_2503)
    | hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2505),U_2509)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2503),U_2507)) = hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2505),U_2507)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2503),U_2509))
    | ~ semiri456707255roduct(U_2501) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

cnf(f_670_6,plain,
    ( ti(U_2501,U_2509) != ti(U_2501,U_2507)
    | hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2505),U_2509)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2503),U_2507)) = hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),plus_plus(U_2501),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2505),U_2507)),hAPP(U_2501,U_2501,hAPP(U_2501,fun(U_2501,U_2501),times_times(U_2501),U_2503),U_2509))
    | ~ semiri456707255roduct(U_2501) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

fof(f_671_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_581_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).

fof(f_671_2,plain,
    ! [U_2513] :
      ( ! [U_2512,U_2511,U_2510] : hAPP(U_2513,U_2513,hAPP(U_2513,fun(U_2513,U_2513),times_times(U_2513),U_2512),hAPP(U_2513,U_2513,hAPP(U_2513,fun(U_2513,U_2513),plus_plus(U_2513),U_2511),U_2510)) = hAPP(U_2513,U_2513,hAPP(U_2513,fun(U_2513,U_2513),plus_plus(U_2513),hAPP(U_2513,U_2513,hAPP(U_2513,fun(U_2513,U_2513),times_times(U_2513),U_2512),U_2511)),hAPP(U_2513,U_2513,hAPP(U_2513,fun(U_2513,U_2513),times_times(U_2513),U_2512),U_2510))
      | ~ comm_semiring_1(U_2513) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

cnf(f_671_3,plain,
    ( hAPP(U_2513,U_2513,hAPP(U_2513,fun(U_2513,U_2513),times_times(U_2513),U_2512),hAPP(U_2513,U_2513,hAPP(U_2513,fun(U_2513,U_2513),plus_plus(U_2513),U_2511),U_2510)) = hAPP(U_2513,U_2513,hAPP(U_2513,fun(U_2513,U_2513),plus_plus(U_2513),hAPP(U_2513,U_2513,hAPP(U_2513,fun(U_2513,U_2513),times_times(U_2513),U_2512),U_2511)),hAPP(U_2513,U_2513,hAPP(U_2513,fun(U_2513,U_2513),times_times(U_2513),U_2512),U_2510))
    | ~ comm_semiring_1(U_2513) ),
    inference(clausify,[status(thm)],[f_671_2]) ).

fof(f_672_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),one_one(X_a)) = ti(X_a,A_2)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_582_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).

fof(f_672_2,plain,
    ! [U_2515] :
      ( ! [U_2514] : hAPP(U_2515,U_2515,hAPP(U_2515,fun(U_2515,U_2515),times_times(U_2515),U_2514),one_one(U_2515)) = ti(U_2515,U_2514)
      | ~ comm_semiring_1(U_2515) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

cnf(f_672_3,plain,
    ( hAPP(U_2515,U_2515,hAPP(U_2515,fun(U_2515,U_2515),times_times(U_2515),U_2514),one_one(U_2515)) = ti(U_2515,U_2514)
    | ~ comm_semiring_1(U_2515) ),
    inference(clausify,[status(thm)],[f_672_2]) ).

fof(f_673_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_2) = ti(X_a,A_2)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_583_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).

fof(f_673_2,plain,
    ! [U_2517] :
      ( ! [U_2516] : hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),one_one(U_2517)),U_2516) = ti(U_2517,U_2516)
      | ~ comm_semiring_1(U_2517) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

cnf(f_673_3,plain,
    ( hAPP(U_2517,U_2517,hAPP(U_2517,fun(U_2517,U_2517),times_times(U_2517),one_one(U_2517)),U_2516) = ti(U_2517,U_2516)
    | ~ comm_semiring_1(U_2517) ),
    inference(clausify,[status(thm)],[f_673_2]) ).

fof(f_674_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),A_2)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_584_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).

fof(f_674_2,plain,
    ! [U_2520] :
      ( ! [U_2519,U_2518] : hAPP(U_2520,U_2520,hAPP(U_2520,fun(U_2520,U_2520),times_times(U_2520),U_2519),U_2518) = hAPP(U_2520,U_2520,hAPP(U_2520,fun(U_2520,U_2520),times_times(U_2520),U_2518),U_2519)
      | ~ comm_semiring_1(U_2520) ),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

cnf(f_674_3,plain,
    ( hAPP(U_2520,U_2520,hAPP(U_2520,fun(U_2520,U_2520),times_times(U_2520),U_2519),U_2518) = hAPP(U_2520,U_2520,hAPP(U_2520,fun(U_2520,U_2520),times_times(U_2520),U_2518),U_2519)
    | ~ comm_semiring_1(U_2520) ),
    inference(clausify,[status(thm)],[f_674_2]) ).

fof(f_675_1,plain,
    ! [X_a] :
      ( ! [Lx,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_585_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).

fof(f_675_2,plain,
    ! [U_2524] :
      ( ! [U_2523,U_2522,U_2521] : hAPP(U_2524,U_2524,hAPP(U_2524,fun(U_2524,U_2524),times_times(U_2524),U_2523),hAPP(U_2524,U_2524,hAPP(U_2524,fun(U_2524,U_2524),times_times(U_2524),U_2522),U_2521)) = hAPP(U_2524,U_2524,hAPP(U_2524,fun(U_2524,U_2524),times_times(U_2524),U_2522),hAPP(U_2524,U_2524,hAPP(U_2524,fun(U_2524,U_2524),times_times(U_2524),U_2523),U_2521))
      | ~ comm_semiring_1(U_2524) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

cnf(f_675_3,plain,
    ( hAPP(U_2524,U_2524,hAPP(U_2524,fun(U_2524,U_2524),times_times(U_2524),U_2523),hAPP(U_2524,U_2524,hAPP(U_2524,fun(U_2524,U_2524),times_times(U_2524),U_2522),U_2521)) = hAPP(U_2524,U_2524,hAPP(U_2524,fun(U_2524,U_2524),times_times(U_2524),U_2522),hAPP(U_2524,U_2524,hAPP(U_2524,fun(U_2524,U_2524),times_times(U_2524),U_2523),U_2521))
    | ~ comm_semiring_1(U_2524) ),
    inference(clausify,[status(thm)],[f_675_2]) ).

fof(f_676_1,plain,
    ! [X_a] :
      ( ! [Lx,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_586_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).

fof(f_676_2,plain,
    ! [U_2528] :
      ( ! [U_2527,U_2526,U_2525] : hAPP(U_2528,U_2528,hAPP(U_2528,fun(U_2528,U_2528),times_times(U_2528),U_2527),hAPP(U_2528,U_2528,hAPP(U_2528,fun(U_2528,U_2528),times_times(U_2528),U_2526),U_2525)) = hAPP(U_2528,U_2528,hAPP(U_2528,fun(U_2528,U_2528),times_times(U_2528),hAPP(U_2528,U_2528,hAPP(U_2528,fun(U_2528,U_2528),times_times(U_2528),U_2527),U_2526)),U_2525)
      | ~ comm_semiring_1(U_2528) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

cnf(f_676_3,plain,
    ( hAPP(U_2528,U_2528,hAPP(U_2528,fun(U_2528,U_2528),times_times(U_2528),U_2527),hAPP(U_2528,U_2528,hAPP(U_2528,fun(U_2528,U_2528),times_times(U_2528),U_2526),U_2525)) = hAPP(U_2528,U_2528,hAPP(U_2528,fun(U_2528,U_2528),times_times(U_2528),hAPP(U_2528,U_2528,hAPP(U_2528,fun(U_2528,U_2528),times_times(U_2528),U_2527),U_2526)),U_2525)
    | ~ comm_semiring_1(U_2528) ),
    inference(clausify,[status(thm)],[f_676_2]) ).

fof(f_677_1,plain,
    ! [X_a] :
      ( ! [Lx,Ly,Rx] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_587_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).

fof(f_677_2,plain,
    ! [U_2532] :
      ( ! [U_2531,U_2530,U_2529] : hAPP(U_2532,U_2532,hAPP(U_2532,fun(U_2532,U_2532),times_times(U_2532),hAPP(U_2532,U_2532,hAPP(U_2532,fun(U_2532,U_2532),times_times(U_2532),U_2531),U_2530)),U_2529) = hAPP(U_2532,U_2532,hAPP(U_2532,fun(U_2532,U_2532),times_times(U_2532),U_2531),hAPP(U_2532,U_2532,hAPP(U_2532,fun(U_2532,U_2532),times_times(U_2532),U_2530),U_2529))
      | ~ comm_semiring_1(U_2532) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

cnf(f_677_3,plain,
    ( hAPP(U_2532,U_2532,hAPP(U_2532,fun(U_2532,U_2532),times_times(U_2532),hAPP(U_2532,U_2532,hAPP(U_2532,fun(U_2532,U_2532),times_times(U_2532),U_2531),U_2530)),U_2529) = hAPP(U_2532,U_2532,hAPP(U_2532,fun(U_2532,U_2532),times_times(U_2532),U_2531),hAPP(U_2532,U_2532,hAPP(U_2532,fun(U_2532,U_2532),times_times(U_2532),U_2530),U_2529))
    | ~ comm_semiring_1(U_2532) ),
    inference(clausify,[status(thm)],[f_677_2]) ).

fof(f_678_1,plain,
    ! [X_a] :
      ( ! [Lx,Ly,Rx] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_588_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).

fof(f_678_2,plain,
    ! [U_2536] :
      ( ! [U_2535,U_2534,U_2533] : hAPP(U_2536,U_2536,hAPP(U_2536,fun(U_2536,U_2536),times_times(U_2536),hAPP(U_2536,U_2536,hAPP(U_2536,fun(U_2536,U_2536),times_times(U_2536),U_2535),U_2534)),U_2533) = hAPP(U_2536,U_2536,hAPP(U_2536,fun(U_2536,U_2536),times_times(U_2536),hAPP(U_2536,U_2536,hAPP(U_2536,fun(U_2536,U_2536),times_times(U_2536),U_2535),U_2533)),U_2534)
      | ~ comm_semiring_1(U_2536) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

cnf(f_678_3,plain,
    ( hAPP(U_2536,U_2536,hAPP(U_2536,fun(U_2536,U_2536),times_times(U_2536),hAPP(U_2536,U_2536,hAPP(U_2536,fun(U_2536,U_2536),times_times(U_2536),U_2535),U_2534)),U_2533) = hAPP(U_2536,U_2536,hAPP(U_2536,fun(U_2536,U_2536),times_times(U_2536),hAPP(U_2536,U_2536,hAPP(U_2536,fun(U_2536,U_2536),times_times(U_2536),U_2535),U_2533)),U_2534)
    | ~ comm_semiring_1(U_2536) ),
    inference(clausify,[status(thm)],[f_678_2]) ).

fof(f_679_1,plain,
    ! [X_a] :
      ( ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_589_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).

fof(f_679_2,plain,
    ! [U_2541] :
      ( ! [U_2540,U_2539,U_2538,U_2537] : hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),U_2540),U_2539)),hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),U_2538),U_2537)) = hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),U_2540),hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),U_2539),hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),U_2538),U_2537)))
      | ~ comm_semiring_1(U_2541) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

cnf(f_679_3,plain,
    ( hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),U_2540),U_2539)),hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),U_2538),U_2537)) = hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),U_2540),hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),U_2539),hAPP(U_2541,U_2541,hAPP(U_2541,fun(U_2541,U_2541),times_times(U_2541),U_2538),U_2537)))
    | ~ comm_semiring_1(U_2541) ),
    inference(clausify,[status(thm)],[f_679_2]) ).

fof(f_680_1,plain,
    ! [X_a] :
      ( ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).

fof(f_680_2,plain,
    ! [U_2546] :
      ( ! [U_2545,U_2544,U_2543,U_2542] : hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),U_2545),U_2544)),hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),U_2543),U_2542)) = hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),U_2543),hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),U_2545),U_2544)),U_2542))
      | ~ comm_semiring_1(U_2546) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

cnf(f_680_3,plain,
    ( hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),U_2545),U_2544)),hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),U_2543),U_2542)) = hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),U_2543),hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),hAPP(U_2546,U_2546,hAPP(U_2546,fun(U_2546,U_2546),times_times(U_2546),U_2545),U_2544)),U_2542))
    | ~ comm_semiring_1(U_2546) ),
    inference(clausify,[status(thm)],[f_680_2]) ).

fof(f_681_1,plain,
    ! [X_a] :
      ( ! [Lx,Ly,Rx,Ry] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry))
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_591_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).

fof(f_681_2,plain,
    ! [U_2551] :
      ( ! [U_2550,U_2549,U_2548,U_2547] : hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),U_2550),U_2549)),hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),U_2548),U_2547)) = hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),U_2550),U_2548)),hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),U_2549),U_2547))
      | ~ comm_semiring_1(U_2551) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

cnf(f_681_3,plain,
    ( hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),U_2550),U_2549)),hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),U_2548),U_2547)) = hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),U_2550),U_2548)),hAPP(U_2551,U_2551,hAPP(U_2551,fun(U_2551,U_2551),times_times(U_2551),U_2549),U_2547))
    | ~ comm_semiring_1(U_2551) ),
    inference(clausify,[status(thm)],[f_681_2]) ).

fof(f_682_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_2) = zero_zero(X_a)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).

fof(f_682_2,plain,
    ! [U_2553] :
      ( ! [U_2552] : hAPP(U_2553,U_2553,hAPP(U_2553,fun(U_2553,U_2553),times_times(U_2553),zero_zero(U_2553)),U_2552) = zero_zero(U_2553)
      | ~ comm_semiring_1(U_2553) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

cnf(f_682_3,plain,
    ( hAPP(U_2553,U_2553,hAPP(U_2553,fun(U_2553,U_2553),times_times(U_2553),zero_zero(U_2553)),U_2552) = zero_zero(U_2553)
    | ~ comm_semiring_1(U_2553) ),
    inference(clausify,[status(thm)],[f_682_2]) ).

fof(f_683_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),zero_zero(X_a)) = zero_zero(X_a)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).

fof(f_683_2,plain,
    ! [U_2555] :
      ( ! [U_2554] : hAPP(U_2555,U_2555,hAPP(U_2555,fun(U_2555,U_2555),times_times(U_2555),U_2554),zero_zero(U_2555)) = zero_zero(U_2555)
      | ~ comm_semiring_1(U_2555) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

cnf(f_683_3,plain,
    ( hAPP(U_2555,U_2555,hAPP(U_2555,fun(U_2555,U_2555),times_times(U_2555),U_2554),zero_zero(U_2555)) = zero_zero(U_2555)
    | ~ comm_semiring_1(U_2555) ),
    inference(clausify,[status(thm)],[f_683_2]) ).

fof(f_684_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] :
          ( ti(X_a,B_1) = zero_zero(X_a)
          | ti(X_a,A_2) = zero_zero(X_a)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1) != zero_zero(X_a) )
      | ~ no_zero_divisors(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_594_divisors__zero]) ).

fof(f_684_2,plain,
    ! [U_2558] :
      ( ! [U_2557,U_2556] :
          ( ti(U_2558,U_2556) = zero_zero(U_2558)
          | ti(U_2558,U_2557) = zero_zero(U_2558)
          | hAPP(U_2558,U_2558,hAPP(U_2558,fun(U_2558,U_2558),times_times(U_2558),U_2557),U_2556) != zero_zero(U_2558) )
      | ~ no_zero_divisors(U_2558) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

cnf(f_684_3,plain,
    ( ti(U_2558,U_2556) = zero_zero(U_2558)
    | ti(U_2558,U_2557) = zero_zero(U_2558)
    | hAPP(U_2558,U_2558,hAPP(U_2558,fun(U_2558,U_2558),times_times(U_2558),U_2557),U_2556) != zero_zero(U_2558)
    | ~ no_zero_divisors(U_2558) ),
    inference(clausify,[status(thm)],[f_684_2]) ).

fof(f_685_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1) != zero_zero(X_a)
          | ti(X_a,B_1) = zero_zero(X_a)
          | ti(X_a,A_2) = zero_zero(X_a) )
      | ~ no_zero_divisors(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_595_no__zero__divisors]) ).

fof(f_685_2,plain,
    ! [U_2561] :
      ( ! [U_2560,U_2559] :
          ( hAPP(U_2561,U_2561,hAPP(U_2561,fun(U_2561,U_2561),times_times(U_2561),U_2559),U_2560) != zero_zero(U_2561)
          | ti(U_2561,U_2560) = zero_zero(U_2561)
          | ti(U_2561,U_2559) = zero_zero(U_2561) )
      | ~ no_zero_divisors(U_2561) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

cnf(f_685_3,plain,
    ( hAPP(U_2561,U_2561,hAPP(U_2561,fun(U_2561,U_2561),times_times(U_2561),U_2559),U_2560) != zero_zero(U_2561)
    | ti(U_2561,U_2560) = zero_zero(U_2561)
    | ti(U_2561,U_2559) = zero_zero(U_2561)
    | ~ no_zero_divisors(U_2561) ),
    inference(clausify,[status(thm)],[f_685_2]) ).

fof(f_686_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba] :
          ( ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba) = zero_zero(X_a)
            | ( ti(X_a,Ba) != zero_zero(X_a)
              & ti(X_a,Aa) != zero_zero(X_a) ) )
          & ( ti(X_a,Ba) = zero_zero(X_a)
            | ti(X_a,Aa) = zero_zero(X_a)
            | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba) != zero_zero(X_a) ) )
      | ~ ring_n68954251visors(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_596_mult__eq__0__iff]) ).

fof(f_686_2,plain,
    ! [U_2564] :
      ( ! [U_2563,U_2562] :
          ( ( hAPP(U_2564,U_2564,hAPP(U_2564,fun(U_2564,U_2564),times_times(U_2564),U_2563),U_2562) = zero_zero(U_2564)
            | ( ti(U_2564,U_2562) != zero_zero(U_2564)
              & ti(U_2564,U_2563) != zero_zero(U_2564) ) )
          & ( ti(U_2564,U_2562) = zero_zero(U_2564)
            | ti(U_2564,U_2563) = zero_zero(U_2564)
            | hAPP(U_2564,U_2564,hAPP(U_2564,fun(U_2564,U_2564),times_times(U_2564),U_2563),U_2562) != zero_zero(U_2564) ) )
      | ~ ring_n68954251visors(U_2564) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

fof(f_686_3,plain,
    ! [U_2564] :
      ( ( ! [U_2568,U_2566] :
            ( hAPP(U_2564,U_2564,hAPP(U_2564,fun(U_2564,U_2564),times_times(U_2564),U_2568),U_2566) = zero_zero(U_2564)
            | ( ti(U_2564,U_2566) != zero_zero(U_2564)
              & ti(U_2564,U_2568) != zero_zero(U_2564) ) )
        & ! [U_2567,U_2565] :
            ( ti(U_2564,U_2565) = zero_zero(U_2564)
            | ti(U_2564,U_2567) = zero_zero(U_2564)
            | hAPP(U_2564,U_2564,hAPP(U_2564,fun(U_2564,U_2564),times_times(U_2564),U_2567),U_2565) != zero_zero(U_2564) ) )
      | ~ ring_n68954251visors(U_2564) ),
    inference(miniscope,[status(thm)],[f_686_2]) ).

cnf(f_686_4,plain,
    ( ti(U_2564,U_2565) = zero_zero(U_2564)
    | ti(U_2564,U_2567) = zero_zero(U_2564)
    | hAPP(U_2564,U_2564,hAPP(U_2564,fun(U_2564,U_2564),times_times(U_2564),U_2567),U_2565) != zero_zero(U_2564)
    | ~ ring_n68954251visors(U_2564) ),
    inference(clausify,[status(thm)],[f_686_3]) ).

cnf(f_686_5,plain,
    ( ti(U_2564,U_2568) != zero_zero(U_2564)
    | hAPP(U_2564,U_2564,hAPP(U_2564,fun(U_2564,U_2564),times_times(U_2564),U_2568),U_2566) = zero_zero(U_2564)
    | ~ ring_n68954251visors(U_2564) ),
    inference(clausify,[status(thm)],[f_686_3]) ).

cnf(f_686_6,plain,
    ( ti(U_2564,U_2566) != zero_zero(U_2564)
    | hAPP(U_2564,U_2564,hAPP(U_2564,fun(U_2564,U_2564),times_times(U_2564),U_2568),U_2566) = zero_zero(U_2564)
    | ~ ring_n68954251visors(U_2564) ),
    inference(clausify,[status(thm)],[f_686_3]) ).

fof(f_687_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),zero_zero(X_a)) = zero_zero(X_a)
      | ~ mult_zero(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_597_mult__zero__right]) ).

fof(f_687_2,plain,
    ! [U_2570] :
      ( ! [U_2569] : hAPP(U_2570,U_2570,hAPP(U_2570,fun(U_2570,U_2570),times_times(U_2570),U_2569),zero_zero(U_2570)) = zero_zero(U_2570)
      | ~ mult_zero(U_2570) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

cnf(f_687_3,plain,
    ( hAPP(U_2570,U_2570,hAPP(U_2570,fun(U_2570,U_2570),times_times(U_2570),U_2569),zero_zero(U_2570)) = zero_zero(U_2570)
    | ~ mult_zero(U_2570) ),
    inference(clausify,[status(thm)],[f_687_2]) ).

fof(f_688_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_2) = zero_zero(X_a)
      | ~ mult_zero(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_598_mult__zero__left]) ).

fof(f_688_2,plain,
    ! [U_2572] :
      ( ! [U_2571] : hAPP(U_2572,U_2572,hAPP(U_2572,fun(U_2572,U_2572),times_times(U_2572),zero_zero(U_2572)),U_2571) = zero_zero(U_2572)
      | ~ mult_zero(U_2572) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

cnf(f_688_3,plain,
    ( hAPP(U_2572,U_2572,hAPP(U_2572,fun(U_2572,U_2572),times_times(U_2572),zero_zero(U_2572)),U_2571) = zero_zero(U_2572)
    | ~ mult_zero(U_2572) ),
    inference(clausify,[status(thm)],[f_688_2]) ).

fof(f_689_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))
      | ~ ab_semigroup_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_599_ab__semigroup__mult__class_Omult__ac_I1_J]) ).

fof(f_689_2,plain,
    ! [U_2576] :
      ( ! [U_2575,U_2574,U_2573] : hAPP(U_2576,U_2576,hAPP(U_2576,fun(U_2576,U_2576),times_times(U_2576),hAPP(U_2576,U_2576,hAPP(U_2576,fun(U_2576,U_2576),times_times(U_2576),U_2575),U_2574)),U_2573) = hAPP(U_2576,U_2576,hAPP(U_2576,fun(U_2576,U_2576),times_times(U_2576),U_2575),hAPP(U_2576,U_2576,hAPP(U_2576,fun(U_2576,U_2576),times_times(U_2576),U_2574),U_2573))
      | ~ ab_semigroup_mult(U_2576) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

cnf(f_689_3,plain,
    ( hAPP(U_2576,U_2576,hAPP(U_2576,fun(U_2576,U_2576),times_times(U_2576),hAPP(U_2576,U_2576,hAPP(U_2576,fun(U_2576,U_2576),times_times(U_2576),U_2575),U_2574)),U_2573) = hAPP(U_2576,U_2576,hAPP(U_2576,fun(U_2576,U_2576),times_times(U_2576),U_2575),hAPP(U_2576,U_2576,hAPP(U_2576,fun(U_2576,U_2576),times_times(U_2576),U_2574),U_2573))
    | ~ ab_semigroup_mult(U_2576) ),
    inference(clausify,[status(thm)],[f_689_2]) ).

fof(f_690_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = one_one(nat)
        | Na != one_one(nat)
        | M != one_one(nat) )
      & ( ( Na = one_one(nat)
          & M = one_one(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) != one_one(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_600_nat__mult__eq__1__iff]) ).

fof(f_690_2,plain,
    ! [U_2578,U_2577] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2578),U_2577) = one_one(nat)
        | U_2577 != one_one(nat)
        | U_2578 != one_one(nat) )
      & ( ( U_2577 = one_one(nat)
          & U_2578 = one_one(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2578),U_2577) != one_one(nat) ) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

fof(f_690_3,plain,
    ( ! [U_2582,U_2580] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2582),U_2580) = one_one(nat)
        | U_2580 != one_one(nat)
        | U_2582 != one_one(nat) )
    & ! [U_2581,U_2579] :
        ( ( U_2579 = one_one(nat)
          & U_2581 = one_one(nat) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2581),U_2579) != one_one(nat) ) ),
    inference(miniscope,[status(thm)],[f_690_2]) ).

cnf(f_690_4,plain,
    ( U_2581 = one_one(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2581),U_2579) != one_one(nat) ),
    inference(clausify,[status(thm)],[f_690_3]) ).

cnf(f_690_5,plain,
    ( U_2579 = one_one(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2581),U_2579) != one_one(nat) ),
    inference(clausify,[status(thm)],[f_690_3]) ).

cnf(f_690_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2582),U_2580) = one_one(nat)
    | U_2580 != one_one(nat)
    | U_2582 != one_one(nat) ),
    inference(clausify,[status(thm)],[f_690_3]) ).

fof(f_691_1,plain,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat)) = N,
    inference(fof_nnf,[status(thm)],[fact_601_nat__mult__1__right]) ).

fof(f_691_2,plain,
    ! [U_2583] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2583),one_one(nat)) = U_2583,
    inference(variable_rename,[status(thm)],[f_691_1]) ).

cnf(f_691_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2583),one_one(nat)) = U_2583,
    inference(clausify,[status(thm)],[f_691_2]) ).

fof(f_692_1,plain,
    ! [M,Na] :
      ( ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)
        | Na != one_one(nat)
        | M != one_one(nat) )
      & ( ( Na = one_one(nat)
          & M = one_one(nat) )
        | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_602_nat__1__eq__mult__iff]) ).

fof(f_692_2,plain,
    ! [U_2585,U_2584] :
      ( ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2585),U_2584)
        | U_2584 != one_one(nat)
        | U_2585 != one_one(nat) )
      & ( ( U_2584 = one_one(nat)
          & U_2585 = one_one(nat) )
        | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2585),U_2584) ) ),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

fof(f_692_3,plain,
    ( ! [U_2589,U_2587] :
        ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2589),U_2587)
        | U_2587 != one_one(nat)
        | U_2589 != one_one(nat) )
    & ! [U_2588,U_2586] :
        ( ( U_2586 = one_one(nat)
          & U_2588 = one_one(nat) )
        | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2588),U_2586) ) ),
    inference(miniscope,[status(thm)],[f_692_2]) ).

cnf(f_692_4,plain,
    ( U_2588 = one_one(nat)
    | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2588),U_2586) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

cnf(f_692_5,plain,
    ( U_2586 = one_one(nat)
    | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2588),U_2586) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

cnf(f_692_6,plain,
    ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2589),U_2587)
    | U_2587 != one_one(nat)
    | U_2589 != one_one(nat) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

fof(f_693_1,plain,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N) = N,
    inference(fof_nnf,[status(thm)],[fact_603_nat__mult__1]) ).

fof(f_693_2,plain,
    ! [U_2590] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),U_2590) = U_2590,
    inference(variable_rename,[status(thm)],[f_693_1]) ).

cnf(f_693_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),U_2590) = U_2590,
    inference(clausify,[status(thm)],[f_693_2]) ).

fof(f_694_1,plain,
    ! [M_3,N,K_2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_2)),
    inference(fof_nnf,[status(thm)],[fact_604_add__mult__distrib]) ).

fof(f_694_2,plain,
    ! [U_2593,U_2592,U_2591] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2593),U_2592)),U_2591) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2593),U_2591)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2592),U_2591)),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

cnf(f_694_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2593),U_2592)),U_2591) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2593),U_2591)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2592),U_2591)),
    inference(clausify,[status(thm)],[f_694_2]) ).

fof(f_695_1,plain,
    ! [K_2,M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),M_3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),N)),
    inference(fof_nnf,[status(thm)],[fact_605_add__mult__distrib2]) ).

fof(f_695_2,plain,
    ! [U_2596,U_2595,U_2594] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2596),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2595),U_2594)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2596),U_2595)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2596),U_2594)),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

cnf(f_695_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2596),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2595),U_2594)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2596),U_2595)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2596),U_2594)),
    inference(clausify,[status(thm)],[f_695_2]) ).

fof(f_696_1,plain,
    ! [K,M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)
        | M != Na )
      & ( M = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_606_Suc__mult__cancel1]) ).

fof(f_696_2,plain,
    ! [U_2599,U_2598,U_2597] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2599)),U_2598) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2599)),U_2597)
        | U_2598 != U_2597 )
      & ( U_2598 = U_2597
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2599)),U_2598) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2599)),U_2597) ) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

fof(f_696_3,plain,
    ( ! [U_2605,U_2603,U_2601] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2605)),U_2603) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2605)),U_2601)
        | U_2603 != U_2601 )
    & ! [U_2604,U_2602,U_2600] :
        ( U_2602 = U_2600
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2604)),U_2602) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2604)),U_2600) ) ),
    inference(miniscope,[status(thm)],[f_696_2]) ).

cnf(f_696_4,plain,
    ( U_2602 = U_2600
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2604)),U_2602) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2604)),U_2600) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

cnf(f_696_5,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2605)),U_2603) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2605)),U_2601)
    | U_2603 != U_2601 ),
    inference(clausify,[status(thm)],[f_696_3]) ).

fof(f_697_1,plain,
    ! [M,K,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)
        | ( K != zero_zero(nat)
          & M != Na ) )
      & ( K = zero_zero(nat)
        | M = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K) ) ),
    inference(fof_nnf,[status(thm)],[fact_607_mult__cancel2]) ).

fof(f_697_2,plain,
    ! [U_2608,U_2607,U_2606] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2608),U_2607) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2606),U_2607)
        | ( U_2607 != zero_zero(nat)
          & U_2608 != U_2606 ) )
      & ( U_2607 = zero_zero(nat)
        | U_2608 = U_2606
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2608),U_2607) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2606),U_2607) ) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ( ! [U_2614,U_2612,U_2610] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2614),U_2612) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2610),U_2612)
        | ( U_2612 != zero_zero(nat)
          & U_2614 != U_2610 ) )
    & ! [U_2613,U_2611,U_2609] :
        ( U_2611 = zero_zero(nat)
        | U_2613 = U_2609
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2613),U_2611) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2609),U_2611) ) ),
    inference(miniscope,[status(thm)],[f_697_2]) ).

cnf(f_697_4,plain,
    ( U_2611 = zero_zero(nat)
    | U_2613 = U_2609
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2613),U_2611) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2609),U_2611) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

cnf(f_697_5,plain,
    ( U_2614 != U_2610
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2614),U_2612) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2610),U_2612) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

cnf(f_697_6,plain,
    ( U_2612 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2614),U_2612) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2610),U_2612) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

fof(f_698_1,plain,
    ! [K,M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
        | ( K != zero_zero(nat)
          & M != Na ) )
      & ( K = zero_zero(nat)
        | M = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_608_mult__cancel1]) ).

fof(f_698_2,plain,
    ! [U_2617,U_2616,U_2615] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2617),U_2616) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2617),U_2615)
        | ( U_2617 != zero_zero(nat)
          & U_2616 != U_2615 ) )
      & ( U_2617 = zero_zero(nat)
        | U_2616 = U_2615
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2617),U_2616) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2617),U_2615) ) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

fof(f_698_3,plain,
    ( ! [U_2623,U_2621,U_2619] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2623),U_2621) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2623),U_2619)
        | ( U_2623 != zero_zero(nat)
          & U_2621 != U_2619 ) )
    & ! [U_2622,U_2620,U_2618] :
        ( U_2622 = zero_zero(nat)
        | U_2620 = U_2618
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2622),U_2620) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2622),U_2618) ) ),
    inference(miniscope,[status(thm)],[f_698_2]) ).

cnf(f_698_4,plain,
    ( U_2622 = zero_zero(nat)
    | U_2620 = U_2618
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2622),U_2620) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2622),U_2618) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

cnf(f_698_5,plain,
    ( U_2621 != U_2619
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2623),U_2621) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2623),U_2619) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

cnf(f_698_6,plain,
    ( U_2623 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2623),U_2621) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2623),U_2619) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

fof(f_699_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = zero_zero(nat)
        | ( Na != zero_zero(nat)
          & M != zero_zero(nat) ) )
      & ( Na = zero_zero(nat)
        | M = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) != zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_609_mult__is__0]) ).

fof(f_699_2,plain,
    ! [U_2625,U_2624] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2625),U_2624) = zero_zero(nat)
        | ( U_2624 != zero_zero(nat)
          & U_2625 != zero_zero(nat) ) )
      & ( U_2624 = zero_zero(nat)
        | U_2625 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2625),U_2624) != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

fof(f_699_3,plain,
    ( ! [U_2629,U_2627] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2629),U_2627) = zero_zero(nat)
        | ( U_2627 != zero_zero(nat)
          & U_2629 != zero_zero(nat) ) )
    & ! [U_2628,U_2626] :
        ( U_2626 = zero_zero(nat)
        | U_2628 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2628),U_2626) != zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_699_2]) ).

cnf(f_699_4,plain,
    ( U_2626 = zero_zero(nat)
    | U_2628 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2628),U_2626) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

cnf(f_699_5,plain,
    ( U_2629 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2629),U_2627) = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

cnf(f_699_6,plain,
    ( U_2627 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2629),U_2627) = zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

fof(f_700_1,plain,
    ! [M_3] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),zero_zero(nat)) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_610_mult__0__right]) ).

fof(f_700_2,plain,
    ! [U_2630] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2630),zero_zero(nat)) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

cnf(f_700_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2630),zero_zero(nat)) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_700_2]) ).

fof(f_701_1,plain,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_611_mult__0]) ).

fof(f_701_2,plain,
    ! [U_2631] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),U_2631) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

cnf(f_701_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),U_2631) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_701_2]) ).

fof(f_702_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_2) = ti(X_a,A_2)
      | ~ monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_612_mult__1__left]) ).

fof(f_702_2,plain,
    ! [U_2633] :
      ( ! [U_2632] : hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),one_one(U_2633)),U_2632) = ti(U_2633,U_2632)
      | ~ monoid_mult(U_2633) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

cnf(f_702_3,plain,
    ( hAPP(U_2633,U_2633,hAPP(U_2633,fun(U_2633,U_2633),times_times(U_2633),one_one(U_2633)),U_2632) = ti(U_2633,U_2632)
    | ~ monoid_mult(U_2633) ),
    inference(clausify,[status(thm)],[f_702_2]) ).

fof(f_703_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_2) = ti(X_a,A_2)
      | ~ comm_monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_613_mult__1]) ).

fof(f_703_2,plain,
    ! [U_2635] :
      ( ! [U_2634] : hAPP(U_2635,U_2635,hAPP(U_2635,fun(U_2635,U_2635),times_times(U_2635),one_one(U_2635)),U_2634) = ti(U_2635,U_2634)
      | ~ comm_monoid_mult(U_2635) ),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

cnf(f_703_3,plain,
    ( hAPP(U_2635,U_2635,hAPP(U_2635,fun(U_2635,U_2635),times_times(U_2635),one_one(U_2635)),U_2634) = ti(U_2635,U_2634)
    | ~ comm_monoid_mult(U_2635) ),
    inference(clausify,[status(thm)],[f_703_2]) ).

fof(f_704_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),one_one(X_a)) = ti(X_a,A_2)
      | ~ monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_614_mult__1__right]) ).

fof(f_704_2,plain,
    ! [U_2637] :
      ( ! [U_2636] : hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),U_2636),one_one(U_2637)) = ti(U_2637,U_2636)
      | ~ monoid_mult(U_2637) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

cnf(f_704_3,plain,
    ( hAPP(U_2637,U_2637,hAPP(U_2637,fun(U_2637,U_2637),times_times(U_2637),U_2636),one_one(U_2637)) = ti(U_2637,U_2636)
    | ~ monoid_mult(U_2637) ),
    inference(clausify,[status(thm)],[f_704_2]) ).

fof(f_705_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),one_one(X_a)) = ti(X_a,A_2)
      | ~ comm_monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_615_mult_Ocomm__neutral]) ).

fof(f_705_2,plain,
    ! [U_2639] :
      ( ! [U_2638] : hAPP(U_2639,U_2639,hAPP(U_2639,fun(U_2639,U_2639),times_times(U_2639),U_2638),one_one(U_2639)) = ti(U_2639,U_2638)
      | ~ comm_monoid_mult(U_2639) ),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

cnf(f_705_3,plain,
    ( hAPP(U_2639,U_2639,hAPP(U_2639,fun(U_2639,U_2639),times_times(U_2639),U_2638),one_one(U_2639)) = ti(U_2639,U_2638)
    | ~ comm_monoid_mult(U_2639) ),
    inference(clausify,[status(thm)],[f_705_2]) ).

fof(f_706_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))
      | ~ comm_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_616_comm__semiring__class_Odistrib]) ).

fof(f_706_2,plain,
    ! [U_2643] :
      ( ! [U_2642,U_2641,U_2640] : hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),times_times(U_2643),hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),plus_plus(U_2643),U_2642),U_2641)),U_2640) = hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),plus_plus(U_2643),hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),times_times(U_2643),U_2642),U_2640)),hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),times_times(U_2643),U_2641),U_2640))
      | ~ comm_semiring(U_2643) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

cnf(f_706_3,plain,
    ( hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),times_times(U_2643),hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),plus_plus(U_2643),U_2642),U_2641)),U_2640) = hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),plus_plus(U_2643),hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),times_times(U_2643),U_2642),U_2640)),hAPP(U_2643,U_2643,hAPP(U_2643,fun(U_2643,U_2643),times_times(U_2643),U_2641),U_2640))
    | ~ comm_semiring(U_2643) ),
    inference(clausify,[status(thm)],[f_706_2]) ).

fof(f_707_1,plain,
    ! [X_a] :
      ( ! [A_2,E,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E)),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),E)),C_1)
      | ~ semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_617_combine__common__factor]) ).

fof(f_707_2,plain,
    ! [U_2648] :
      ( ! [U_2647,U_2646,U_2645,U_2644] : hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),plus_plus(U_2648),hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),times_times(U_2648),U_2647),U_2646)),hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),plus_plus(U_2648),hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),times_times(U_2648),U_2645),U_2646)),U_2644)) = hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),plus_plus(U_2648),hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),times_times(U_2648),hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),plus_plus(U_2648),U_2647),U_2645)),U_2646)),U_2644)
      | ~ semiring(U_2648) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

cnf(f_707_3,plain,
    ( hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),plus_plus(U_2648),hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),times_times(U_2648),U_2647),U_2646)),hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),plus_plus(U_2648),hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),times_times(U_2648),U_2645),U_2646)),U_2644)) = hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),plus_plus(U_2648),hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),times_times(U_2648),hAPP(U_2648,U_2648,hAPP(U_2648,fun(U_2648,U_2648),plus_plus(U_2648),U_2647),U_2645)),U_2646)),U_2644)
    | ~ semiring(U_2648) ),
    inference(clausify,[status(thm)],[f_707_2]) ).

fof(f_708_1,plain,
    ! [X_a,X_b,B,F,A_1] :
      ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_618_extensional__subset]) ).

fof(f_708_2,plain,
    ! [U_2653,U_2652,U_2651,U_2650,U_2649] :
      ( hBOOL(hAPP(fun(fun(U_2653,U_2652),bool),bool,hAPP(fun(U_2653,U_2652),fun(fun(fun(U_2653,U_2652),bool),bool),member(fun(U_2653,U_2652)),U_2650),hAPP(fun(U_2653,bool),fun(fun(U_2653,U_2652),bool),extensional(U_2653,U_2652),U_2651)))
      | ~ hBOOL(hAPP(fun(U_2653,bool),bool,hAPP(fun(U_2653,bool),fun(fun(U_2653,bool),bool),ord_less_eq(fun(U_2653,bool)),U_2649),U_2651))
      | ~ hBOOL(hAPP(fun(fun(U_2653,U_2652),bool),bool,hAPP(fun(U_2653,U_2652),fun(fun(fun(U_2653,U_2652),bool),bool),member(fun(U_2653,U_2652)),U_2650),hAPP(fun(U_2653,bool),fun(fun(U_2653,U_2652),bool),extensional(U_2653,U_2652),U_2649))) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

cnf(f_708_3,plain,
    ( hBOOL(hAPP(fun(fun(U_2653,U_2652),bool),bool,hAPP(fun(U_2653,U_2652),fun(fun(fun(U_2653,U_2652),bool),bool),member(fun(U_2653,U_2652)),U_2650),hAPP(fun(U_2653,bool),fun(fun(U_2653,U_2652),bool),extensional(U_2653,U_2652),U_2651)))
    | ~ hBOOL(hAPP(fun(U_2653,bool),bool,hAPP(fun(U_2653,bool),fun(fun(U_2653,bool),bool),ord_less_eq(fun(U_2653,bool)),U_2649),U_2651))
    | ~ hBOOL(hAPP(fun(fun(U_2653,U_2652),bool),bool,hAPP(fun(U_2653,U_2652),fun(fun(fun(U_2653,U_2652),bool),bool),member(fun(U_2653,U_2652)),U_2650),hAPP(fun(U_2653,bool),fun(fun(U_2653,U_2652),bool),extensional(U_2653,U_2652),U_2649))) ),
    inference(clausify,[status(thm)],[f_708_2]) ).

fof(f_709_1,plain,
    ! [X_a] :
      ( ! [A_2] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),A_2)))
      | ~ linordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_619_zero__le__square]) ).

fof(f_709_2,plain,
    ! [U_2655] :
      ( ! [U_2654] : hBOOL(hAPP(U_2655,bool,hAPP(U_2655,fun(U_2655,bool),ord_less_eq(U_2655),zero_zero(U_2655)),hAPP(U_2655,U_2655,hAPP(U_2655,fun(U_2655,U_2655),times_times(U_2655),U_2654),U_2654)))
      | ~ linordered_ring(U_2655) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

cnf(f_709_3,plain,
    ( hBOOL(hAPP(U_2655,bool,hAPP(U_2655,fun(U_2655,bool),ord_less_eq(U_2655),zero_zero(U_2655)),hAPP(U_2655,U_2655,hAPP(U_2655,fun(U_2655,U_2655),times_times(U_2655),U_2654),U_2654)))
    | ~ linordered_ring(U_2655) ),
    inference(clausify,[status(thm)],[f_709_2]) ).

fof(f_710_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a)))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) )
              & ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) ) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba))) ) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_620_zero__le__mult__iff]) ).

fof(f_710_2,plain,
    ! [U_2658] :
      ( ! [U_2657,U_2656] :
          ( ( hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2657),U_2656)))
            | ( ( ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2656),zero_zero(U_2658)))
                | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2657),zero_zero(U_2658))) )
              & ( ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2656))
                | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2657)) ) ) )
          & ( ( hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2656),zero_zero(U_2658)))
              & hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2657),zero_zero(U_2658))) )
            | ( hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2656))
              & hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2657)) )
            | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2657),U_2656))) ) )
      | ~ linord581940658strict(U_2658) ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

fof(f_710_3,plain,
    ! [U_2658] :
      ( ( ! [U_2662,U_2660] :
            ( hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2662),U_2660)))
            | ( ( ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2660),zero_zero(U_2658)))
                | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2662),zero_zero(U_2658))) )
              & ( ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2660))
                | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2662)) ) ) )
        & ! [U_2661,U_2659] :
            ( ( hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2659),zero_zero(U_2658)))
              & hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2661),zero_zero(U_2658))) )
            | ( hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2659))
              & hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2661)) )
            | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2661),U_2659))) ) )
      | ~ linord581940658strict(U_2658) ),
    inference(miniscope,[status(thm)],[f_710_2]) ).

cnf(f_710_4,plain,
    ( hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2661),zero_zero(U_2658)))
    | hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2661))
    | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2661),U_2659)))
    | ~ linord581940658strict(U_2658) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

cnf(f_710_5,plain,
    ( hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2659),zero_zero(U_2658)))
    | hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2661))
    | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2661),U_2659)))
    | ~ linord581940658strict(U_2658) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

cnf(f_710_6,plain,
    ( hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2661),zero_zero(U_2658)))
    | hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2659))
    | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2661),U_2659)))
    | ~ linord581940658strict(U_2658) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

cnf(f_710_7,plain,
    ( hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2659),zero_zero(U_2658)))
    | hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2659))
    | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2661),U_2659)))
    | ~ linord581940658strict(U_2658) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

cnf(f_710_8,plain,
    ( ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2660))
    | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),U_2662))
    | hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2662),U_2660)))
    | ~ linord581940658strict(U_2658) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

cnf(f_710_9,plain,
    ( ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2660),zero_zero(U_2658)))
    | ~ hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),U_2662),zero_zero(U_2658)))
    | hBOOL(hAPP(U_2658,bool,hAPP(U_2658,fun(U_2658,bool),ord_less_eq(U_2658),zero_zero(U_2658)),hAPP(U_2658,U_2658,hAPP(U_2658,fun(U_2658,U_2658),times_times(U_2658),U_2662),U_2660)))
    | ~ linord581940658strict(U_2658) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

fof(f_711_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),zero_zero(X_a)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) )
              & ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a)))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) ) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),zero_zero(X_a))) ) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_621_mult__le__0__iff]) ).

fof(f_711_2,plain,
    ! [U_2665] :
      ( ! [U_2664,U_2663] :
          ( ( hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),hAPP(U_2665,U_2665,hAPP(U_2665,fun(U_2665,U_2665),times_times(U_2665),U_2664),U_2663)),zero_zero(U_2665)))
            | ( ( ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2663))
                | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2664),zero_zero(U_2665))) )
              & ( ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2663),zero_zero(U_2665)))
                | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2664)) ) ) )
          & ( ( hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2663))
              & hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2664),zero_zero(U_2665))) )
            | ( hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2663),zero_zero(U_2665)))
              & hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2664)) )
            | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),hAPP(U_2665,U_2665,hAPP(U_2665,fun(U_2665,U_2665),times_times(U_2665),U_2664),U_2663)),zero_zero(U_2665))) ) )
      | ~ linord581940658strict(U_2665) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

fof(f_711_3,plain,
    ! [U_2665] :
      ( ( ! [U_2669,U_2667] :
            ( hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),hAPP(U_2665,U_2665,hAPP(U_2665,fun(U_2665,U_2665),times_times(U_2665),U_2669),U_2667)),zero_zero(U_2665)))
            | ( ( ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2667))
                | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2669),zero_zero(U_2665))) )
              & ( ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2667),zero_zero(U_2665)))
                | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2669)) ) ) )
        & ! [U_2668,U_2666] :
            ( ( hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2666))
              & hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2668),zero_zero(U_2665))) )
            | ( hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2666),zero_zero(U_2665)))
              & hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2668)) )
            | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),hAPP(U_2665,U_2665,hAPP(U_2665,fun(U_2665,U_2665),times_times(U_2665),U_2668),U_2666)),zero_zero(U_2665))) ) )
      | ~ linord581940658strict(U_2665) ),
    inference(miniscope,[status(thm)],[f_711_2]) ).

cnf(f_711_4,plain,
    ( hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2668),zero_zero(U_2665)))
    | hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2668))
    | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),hAPP(U_2665,U_2665,hAPP(U_2665,fun(U_2665,U_2665),times_times(U_2665),U_2668),U_2666)),zero_zero(U_2665)))
    | ~ linord581940658strict(U_2665) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

cnf(f_711_5,plain,
    ( hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2666))
    | hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2668))
    | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),hAPP(U_2665,U_2665,hAPP(U_2665,fun(U_2665,U_2665),times_times(U_2665),U_2668),U_2666)),zero_zero(U_2665)))
    | ~ linord581940658strict(U_2665) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

cnf(f_711_6,plain,
    ( hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2668),zero_zero(U_2665)))
    | hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2666),zero_zero(U_2665)))
    | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),hAPP(U_2665,U_2665,hAPP(U_2665,fun(U_2665,U_2665),times_times(U_2665),U_2668),U_2666)),zero_zero(U_2665)))
    | ~ linord581940658strict(U_2665) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

cnf(f_711_7,plain,
    ( hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2666))
    | hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2666),zero_zero(U_2665)))
    | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),hAPP(U_2665,U_2665,hAPP(U_2665,fun(U_2665,U_2665),times_times(U_2665),U_2668),U_2666)),zero_zero(U_2665)))
    | ~ linord581940658strict(U_2665) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

cnf(f_711_8,plain,
    ( ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2667),zero_zero(U_2665)))
    | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2669))
    | hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),hAPP(U_2665,U_2665,hAPP(U_2665,fun(U_2665,U_2665),times_times(U_2665),U_2669),U_2667)),zero_zero(U_2665)))
    | ~ linord581940658strict(U_2665) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

cnf(f_711_9,plain,
    ( ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),zero_zero(U_2665)),U_2667))
    | ~ hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),U_2669),zero_zero(U_2665)))
    | hBOOL(hAPP(U_2665,bool,hAPP(U_2665,fun(U_2665,bool),ord_less_eq(U_2665),hAPP(U_2665,U_2665,hAPP(U_2665,fun(U_2665,U_2665),times_times(U_2665),U_2669),U_2667)),zero_zero(U_2665)))
    | ~ linord581940658strict(U_2665) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

fof(f_712_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) )
      | ~ ordere453448008miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_622_mult__nonneg__nonneg]) ).

fof(f_712_2,plain,
    ! [U_2672] :
      ( ! [U_2671,U_2670] :
          ( hBOOL(hAPP(U_2672,bool,hAPP(U_2672,fun(U_2672,bool),ord_less_eq(U_2672),zero_zero(U_2672)),hAPP(U_2672,U_2672,hAPP(U_2672,fun(U_2672,U_2672),times_times(U_2672),U_2670),U_2671)))
          | ~ hBOOL(hAPP(U_2672,bool,hAPP(U_2672,fun(U_2672,bool),ord_less_eq(U_2672),zero_zero(U_2672)),U_2671))
          | ~ hBOOL(hAPP(U_2672,bool,hAPP(U_2672,fun(U_2672,bool),ord_less_eq(U_2672),zero_zero(U_2672)),U_2670)) )
      | ~ ordere453448008miring(U_2672) ),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

cnf(f_712_3,plain,
    ( hBOOL(hAPP(U_2672,bool,hAPP(U_2672,fun(U_2672,bool),ord_less_eq(U_2672),zero_zero(U_2672)),hAPP(U_2672,U_2672,hAPP(U_2672,fun(U_2672,U_2672),times_times(U_2672),U_2670),U_2671)))
    | ~ hBOOL(hAPP(U_2672,bool,hAPP(U_2672,fun(U_2672,bool),ord_less_eq(U_2672),zero_zero(U_2672)),U_2671))
    | ~ hBOOL(hAPP(U_2672,bool,hAPP(U_2672,fun(U_2672,bool),ord_less_eq(U_2672),zero_zero(U_2672)),U_2670))
    | ~ ordere453448008miring(U_2672) ),
    inference(clausify,[status(thm)],[f_712_2]) ).

fof(f_713_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) )
      | ~ ordere453448008miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_623_mult__nonneg__nonpos]) ).

fof(f_713_2,plain,
    ! [U_2675] :
      ( ! [U_2674,U_2673] :
          ( hBOOL(hAPP(U_2675,bool,hAPP(U_2675,fun(U_2675,bool),ord_less_eq(U_2675),hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2673),U_2674)),zero_zero(U_2675)))
          | ~ hBOOL(hAPP(U_2675,bool,hAPP(U_2675,fun(U_2675,bool),ord_less_eq(U_2675),U_2674),zero_zero(U_2675)))
          | ~ hBOOL(hAPP(U_2675,bool,hAPP(U_2675,fun(U_2675,bool),ord_less_eq(U_2675),zero_zero(U_2675)),U_2673)) )
      | ~ ordere453448008miring(U_2675) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

cnf(f_713_3,plain,
    ( hBOOL(hAPP(U_2675,bool,hAPP(U_2675,fun(U_2675,bool),ord_less_eq(U_2675),hAPP(U_2675,U_2675,hAPP(U_2675,fun(U_2675,U_2675),times_times(U_2675),U_2673),U_2674)),zero_zero(U_2675)))
    | ~ hBOOL(hAPP(U_2675,bool,hAPP(U_2675,fun(U_2675,bool),ord_less_eq(U_2675),U_2674),zero_zero(U_2675)))
    | ~ hBOOL(hAPP(U_2675,bool,hAPP(U_2675,fun(U_2675,bool),ord_less_eq(U_2675),zero_zero(U_2675)),U_2673))
    | ~ ordere453448008miring(U_2675) ),
    inference(clausify,[status(thm)],[f_713_2]) ).

fof(f_714_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),A_2)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) )
      | ~ ordere453448008miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_624_mult__nonneg__nonpos2]) ).

fof(f_714_2,plain,
    ! [U_2678] :
      ( ! [U_2677,U_2676] :
          ( hBOOL(hAPP(U_2678,bool,hAPP(U_2678,fun(U_2678,bool),ord_less_eq(U_2678),hAPP(U_2678,U_2678,hAPP(U_2678,fun(U_2678,U_2678),times_times(U_2678),U_2677),U_2676)),zero_zero(U_2678)))
          | ~ hBOOL(hAPP(U_2678,bool,hAPP(U_2678,fun(U_2678,bool),ord_less_eq(U_2678),U_2677),zero_zero(U_2678)))
          | ~ hBOOL(hAPP(U_2678,bool,hAPP(U_2678,fun(U_2678,bool),ord_less_eq(U_2678),zero_zero(U_2678)),U_2676)) )
      | ~ ordere453448008miring(U_2678) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

cnf(f_714_3,plain,
    ( hBOOL(hAPP(U_2678,bool,hAPP(U_2678,fun(U_2678,bool),ord_less_eq(U_2678),hAPP(U_2678,U_2678,hAPP(U_2678,fun(U_2678,U_2678),times_times(U_2678),U_2677),U_2676)),zero_zero(U_2678)))
    | ~ hBOOL(hAPP(U_2678,bool,hAPP(U_2678,fun(U_2678,bool),ord_less_eq(U_2678),U_2677),zero_zero(U_2678)))
    | ~ hBOOL(hAPP(U_2678,bool,hAPP(U_2678,fun(U_2678,bool),ord_less_eq(U_2678),zero_zero(U_2678)),U_2676))
    | ~ ordere453448008miring(U_2678) ),
    inference(clausify,[status(thm)],[f_714_2]) ).

fof(f_715_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) )
      | ~ ordere453448008miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_625_mult__nonpos__nonneg]) ).

fof(f_715_2,plain,
    ! [U_2681] :
      ( ! [U_2680,U_2679] :
          ( hBOOL(hAPP(U_2681,bool,hAPP(U_2681,fun(U_2681,bool),ord_less_eq(U_2681),hAPP(U_2681,U_2681,hAPP(U_2681,fun(U_2681,U_2681),times_times(U_2681),U_2679),U_2680)),zero_zero(U_2681)))
          | ~ hBOOL(hAPP(U_2681,bool,hAPP(U_2681,fun(U_2681,bool),ord_less_eq(U_2681),zero_zero(U_2681)),U_2680))
          | ~ hBOOL(hAPP(U_2681,bool,hAPP(U_2681,fun(U_2681,bool),ord_less_eq(U_2681),U_2679),zero_zero(U_2681))) )
      | ~ ordere453448008miring(U_2681) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

cnf(f_715_3,plain,
    ( hBOOL(hAPP(U_2681,bool,hAPP(U_2681,fun(U_2681,bool),ord_less_eq(U_2681),hAPP(U_2681,U_2681,hAPP(U_2681,fun(U_2681,U_2681),times_times(U_2681),U_2679),U_2680)),zero_zero(U_2681)))
    | ~ hBOOL(hAPP(U_2681,bool,hAPP(U_2681,fun(U_2681,bool),ord_less_eq(U_2681),zero_zero(U_2681)),U_2680))
    | ~ hBOOL(hAPP(U_2681,bool,hAPP(U_2681,fun(U_2681,bool),ord_less_eq(U_2681),U_2679),zero_zero(U_2681)))
    | ~ ordere453448008miring(U_2681) ),
    inference(clausify,[status(thm)],[f_715_2]) ).

fof(f_716_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) )
      | ~ ordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_626_mult__nonpos__nonpos]) ).

fof(f_716_2,plain,
    ! [U_2684] :
      ( ! [U_2683,U_2682] :
          ( hBOOL(hAPP(U_2684,bool,hAPP(U_2684,fun(U_2684,bool),ord_less_eq(U_2684),zero_zero(U_2684)),hAPP(U_2684,U_2684,hAPP(U_2684,fun(U_2684,U_2684),times_times(U_2684),U_2682),U_2683)))
          | ~ hBOOL(hAPP(U_2684,bool,hAPP(U_2684,fun(U_2684,bool),ord_less_eq(U_2684),U_2683),zero_zero(U_2684)))
          | ~ hBOOL(hAPP(U_2684,bool,hAPP(U_2684,fun(U_2684,bool),ord_less_eq(U_2684),U_2682),zero_zero(U_2684))) )
      | ~ ordered_ring(U_2684) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

cnf(f_716_3,plain,
    ( hBOOL(hAPP(U_2684,bool,hAPP(U_2684,fun(U_2684,bool),ord_less_eq(U_2684),zero_zero(U_2684)),hAPP(U_2684,U_2684,hAPP(U_2684,fun(U_2684,U_2684),times_times(U_2684),U_2682),U_2683)))
    | ~ hBOOL(hAPP(U_2684,bool,hAPP(U_2684,fun(U_2684,bool),ord_less_eq(U_2684),U_2683),zero_zero(U_2684)))
    | ~ hBOOL(hAPP(U_2684,bool,hAPP(U_2684,fun(U_2684,bool),ord_less_eq(U_2684),U_2682),zero_zero(U_2684)))
    | ~ ordered_ring(U_2684) ),
    inference(clausify,[status(thm)],[f_716_2]) ).

fof(f_717_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ ordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_627_mult__right__mono]) ).

fof(f_717_2,plain,
    ! [U_2688] :
      ( ! [U_2687,U_2686,U_2685] :
          ( hBOOL(hAPP(U_2688,bool,hAPP(U_2688,fun(U_2688,bool),ord_less_eq(U_2688),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2686),U_2687)),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2685),U_2687)))
          | ~ hBOOL(hAPP(U_2688,bool,hAPP(U_2688,fun(U_2688,bool),ord_less_eq(U_2688),zero_zero(U_2688)),U_2687))
          | ~ hBOOL(hAPP(U_2688,bool,hAPP(U_2688,fun(U_2688,bool),ord_less_eq(U_2688),U_2686),U_2685)) )
      | ~ ordered_semiring(U_2688) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

cnf(f_717_3,plain,
    ( hBOOL(hAPP(U_2688,bool,hAPP(U_2688,fun(U_2688,bool),ord_less_eq(U_2688),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2686),U_2687)),hAPP(U_2688,U_2688,hAPP(U_2688,fun(U_2688,U_2688),times_times(U_2688),U_2685),U_2687)))
    | ~ hBOOL(hAPP(U_2688,bool,hAPP(U_2688,fun(U_2688,bool),ord_less_eq(U_2688),zero_zero(U_2688)),U_2687))
    | ~ hBOOL(hAPP(U_2688,bool,hAPP(U_2688,fun(U_2688,bool),ord_less_eq(U_2688),U_2686),U_2685))
    | ~ ordered_semiring(U_2688) ),
    inference(clausify,[status(thm)],[f_717_2]) ).

fof(f_718_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ ordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_628_mult__left__mono]) ).

fof(f_718_2,plain,
    ! [U_2692] :
      ( ! [U_2691,U_2690,U_2689] :
          ( hBOOL(hAPP(U_2692,bool,hAPP(U_2692,fun(U_2692,bool),ord_less_eq(U_2692),hAPP(U_2692,U_2692,hAPP(U_2692,fun(U_2692,U_2692),times_times(U_2692),U_2691),U_2690)),hAPP(U_2692,U_2692,hAPP(U_2692,fun(U_2692,U_2692),times_times(U_2692),U_2691),U_2689)))
          | ~ hBOOL(hAPP(U_2692,bool,hAPP(U_2692,fun(U_2692,bool),ord_less_eq(U_2692),zero_zero(U_2692)),U_2691))
          | ~ hBOOL(hAPP(U_2692,bool,hAPP(U_2692,fun(U_2692,bool),ord_less_eq(U_2692),U_2690),U_2689)) )
      | ~ ordered_semiring(U_2692) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

cnf(f_718_3,plain,
    ( hBOOL(hAPP(U_2692,bool,hAPP(U_2692,fun(U_2692,bool),ord_less_eq(U_2692),hAPP(U_2692,U_2692,hAPP(U_2692,fun(U_2692,U_2692),times_times(U_2692),U_2691),U_2690)),hAPP(U_2692,U_2692,hAPP(U_2692,fun(U_2692,U_2692),times_times(U_2692),U_2691),U_2689)))
    | ~ hBOOL(hAPP(U_2692,bool,hAPP(U_2692,fun(U_2692,bool),ord_less_eq(U_2692),zero_zero(U_2692)),U_2691))
    | ~ hBOOL(hAPP(U_2692,bool,hAPP(U_2692,fun(U_2692,bool),ord_less_eq(U_2692),U_2690),U_2689))
    | ~ ordered_semiring(U_2692) ),
    inference(clausify,[status(thm)],[f_718_2]) ).

fof(f_719_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ ordere1490568538miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_629_comm__mult__left__mono]) ).

fof(f_719_2,plain,
    ! [U_2696] :
      ( ! [U_2695,U_2694,U_2693] :
          ( hBOOL(hAPP(U_2696,bool,hAPP(U_2696,fun(U_2696,bool),ord_less_eq(U_2696),hAPP(U_2696,U_2696,hAPP(U_2696,fun(U_2696,U_2696),times_times(U_2696),U_2695),U_2694)),hAPP(U_2696,U_2696,hAPP(U_2696,fun(U_2696,U_2696),times_times(U_2696),U_2695),U_2693)))
          | ~ hBOOL(hAPP(U_2696,bool,hAPP(U_2696,fun(U_2696,bool),ord_less_eq(U_2696),zero_zero(U_2696)),U_2695))
          | ~ hBOOL(hAPP(U_2696,bool,hAPP(U_2696,fun(U_2696,bool),ord_less_eq(U_2696),U_2694),U_2693)) )
      | ~ ordere1490568538miring(U_2696) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

cnf(f_719_3,plain,
    ( hBOOL(hAPP(U_2696,bool,hAPP(U_2696,fun(U_2696,bool),ord_less_eq(U_2696),hAPP(U_2696,U_2696,hAPP(U_2696,fun(U_2696,U_2696),times_times(U_2696),U_2695),U_2694)),hAPP(U_2696,U_2696,hAPP(U_2696,fun(U_2696,U_2696),times_times(U_2696),U_2695),U_2693)))
    | ~ hBOOL(hAPP(U_2696,bool,hAPP(U_2696,fun(U_2696,bool),ord_less_eq(U_2696),zero_zero(U_2696)),U_2695))
    | ~ hBOOL(hAPP(U_2696,bool,hAPP(U_2696,fun(U_2696,bool),ord_less_eq(U_2696),U_2694),U_2693))
    | ~ ordere1490568538miring(U_2696) ),
    inference(clausify,[status(thm)],[f_719_2]) ).

fof(f_720_1,plain,
    ! [X_a] :
      ( ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) )
      | ~ ordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_630_mult__right__mono__neg]) ).

fof(f_720_2,plain,
    ! [U_2700] :
      ( ! [U_2699,U_2698,U_2697] :
          ( hBOOL(hAPP(U_2700,bool,hAPP(U_2700,fun(U_2700,bool),ord_less_eq(U_2700),hAPP(U_2700,U_2700,hAPP(U_2700,fun(U_2700,U_2700),times_times(U_2700),U_2697),U_2699)),hAPP(U_2700,U_2700,hAPP(U_2700,fun(U_2700,U_2700),times_times(U_2700),U_2698),U_2699)))
          | ~ hBOOL(hAPP(U_2700,bool,hAPP(U_2700,fun(U_2700,bool),ord_less_eq(U_2700),U_2699),zero_zero(U_2700)))
          | ~ hBOOL(hAPP(U_2700,bool,hAPP(U_2700,fun(U_2700,bool),ord_less_eq(U_2700),U_2698),U_2697)) )
      | ~ ordered_ring(U_2700) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

cnf(f_720_3,plain,
    ( hBOOL(hAPP(U_2700,bool,hAPP(U_2700,fun(U_2700,bool),ord_less_eq(U_2700),hAPP(U_2700,U_2700,hAPP(U_2700,fun(U_2700,U_2700),times_times(U_2700),U_2697),U_2699)),hAPP(U_2700,U_2700,hAPP(U_2700,fun(U_2700,U_2700),times_times(U_2700),U_2698),U_2699)))
    | ~ hBOOL(hAPP(U_2700,bool,hAPP(U_2700,fun(U_2700,bool),ord_less_eq(U_2700),U_2699),zero_zero(U_2700)))
    | ~ hBOOL(hAPP(U_2700,bool,hAPP(U_2700,fun(U_2700,bool),ord_less_eq(U_2700),U_2698),U_2697))
    | ~ ordered_ring(U_2700) ),
    inference(clausify,[status(thm)],[f_720_2]) ).

fof(f_721_1,plain,
    ! [X_a] :
      ( ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) )
      | ~ ordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_631_mult__left__mono__neg]) ).

fof(f_721_2,plain,
    ! [U_2704] :
      ( ! [U_2703,U_2702,U_2701] :
          ( hBOOL(hAPP(U_2704,bool,hAPP(U_2704,fun(U_2704,bool),ord_less_eq(U_2704),hAPP(U_2704,U_2704,hAPP(U_2704,fun(U_2704,U_2704),times_times(U_2704),U_2703),U_2701)),hAPP(U_2704,U_2704,hAPP(U_2704,fun(U_2704,U_2704),times_times(U_2704),U_2703),U_2702)))
          | ~ hBOOL(hAPP(U_2704,bool,hAPP(U_2704,fun(U_2704,bool),ord_less_eq(U_2704),U_2703),zero_zero(U_2704)))
          | ~ hBOOL(hAPP(U_2704,bool,hAPP(U_2704,fun(U_2704,bool),ord_less_eq(U_2704),U_2702),U_2701)) )
      | ~ ordered_ring(U_2704) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

cnf(f_721_3,plain,
    ( hBOOL(hAPP(U_2704,bool,hAPP(U_2704,fun(U_2704,bool),ord_less_eq(U_2704),hAPP(U_2704,U_2704,hAPP(U_2704,fun(U_2704,U_2704),times_times(U_2704),U_2703),U_2701)),hAPP(U_2704,U_2704,hAPP(U_2704,fun(U_2704,U_2704),times_times(U_2704),U_2703),U_2702)))
    | ~ hBOOL(hAPP(U_2704,bool,hAPP(U_2704,fun(U_2704,bool),ord_less_eq(U_2704),U_2703),zero_zero(U_2704)))
    | ~ hBOOL(hAPP(U_2704,bool,hAPP(U_2704,fun(U_2704,bool),ord_less_eq(U_2704),U_2702),U_2701))
    | ~ ordered_ring(U_2704) ),
    inference(clausify,[status(thm)],[f_721_2]) ).

fof(f_722_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ ordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_632_mult__mono_H]) ).

fof(f_722_2,plain,
    ! [U_2709] :
      ( ! [U_2708,U_2707,U_2706,U_2705] :
          ( hBOOL(hAPP(U_2709,bool,hAPP(U_2709,fun(U_2709,bool),ord_less_eq(U_2709),hAPP(U_2709,U_2709,hAPP(U_2709,fun(U_2709,U_2709),times_times(U_2709),U_2706),U_2708)),hAPP(U_2709,U_2709,hAPP(U_2709,fun(U_2709,U_2709),times_times(U_2709),U_2705),U_2707)))
          | ~ hBOOL(hAPP(U_2709,bool,hAPP(U_2709,fun(U_2709,bool),ord_less_eq(U_2709),zero_zero(U_2709)),U_2708))
          | ~ hBOOL(hAPP(U_2709,bool,hAPP(U_2709,fun(U_2709,bool),ord_less_eq(U_2709),zero_zero(U_2709)),U_2706))
          | ~ hBOOL(hAPP(U_2709,bool,hAPP(U_2709,fun(U_2709,bool),ord_less_eq(U_2709),U_2708),U_2707))
          | ~ hBOOL(hAPP(U_2709,bool,hAPP(U_2709,fun(U_2709,bool),ord_less_eq(U_2709),U_2706),U_2705)) )
      | ~ ordered_semiring(U_2709) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

cnf(f_722_3,plain,
    ( hBOOL(hAPP(U_2709,bool,hAPP(U_2709,fun(U_2709,bool),ord_less_eq(U_2709),hAPP(U_2709,U_2709,hAPP(U_2709,fun(U_2709,U_2709),times_times(U_2709),U_2706),U_2708)),hAPP(U_2709,U_2709,hAPP(U_2709,fun(U_2709,U_2709),times_times(U_2709),U_2705),U_2707)))
    | ~ hBOOL(hAPP(U_2709,bool,hAPP(U_2709,fun(U_2709,bool),ord_less_eq(U_2709),zero_zero(U_2709)),U_2708))
    | ~ hBOOL(hAPP(U_2709,bool,hAPP(U_2709,fun(U_2709,bool),ord_less_eq(U_2709),zero_zero(U_2709)),U_2706))
    | ~ hBOOL(hAPP(U_2709,bool,hAPP(U_2709,fun(U_2709,bool),ord_less_eq(U_2709),U_2708),U_2707))
    | ~ hBOOL(hAPP(U_2709,bool,hAPP(U_2709,fun(U_2709,bool),ord_less_eq(U_2709),U_2706),U_2705))
    | ~ ordered_semiring(U_2709) ),
    inference(clausify,[status(thm)],[f_722_2]) ).

fof(f_723_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ ordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_633_mult__mono]) ).

fof(f_723_2,plain,
    ! [U_2714] :
      ( ! [U_2713,U_2712,U_2711,U_2710] :
          ( hBOOL(hAPP(U_2714,bool,hAPP(U_2714,fun(U_2714,bool),ord_less_eq(U_2714),hAPP(U_2714,U_2714,hAPP(U_2714,fun(U_2714,U_2714),times_times(U_2714),U_2711),U_2713)),hAPP(U_2714,U_2714,hAPP(U_2714,fun(U_2714,U_2714),times_times(U_2714),U_2710),U_2712)))
          | ~ hBOOL(hAPP(U_2714,bool,hAPP(U_2714,fun(U_2714,bool),ord_less_eq(U_2714),zero_zero(U_2714)),U_2713))
          | ~ hBOOL(hAPP(U_2714,bool,hAPP(U_2714,fun(U_2714,bool),ord_less_eq(U_2714),zero_zero(U_2714)),U_2710))
          | ~ hBOOL(hAPP(U_2714,bool,hAPP(U_2714,fun(U_2714,bool),ord_less_eq(U_2714),U_2713),U_2712))
          | ~ hBOOL(hAPP(U_2714,bool,hAPP(U_2714,fun(U_2714,bool),ord_less_eq(U_2714),U_2711),U_2710)) )
      | ~ ordered_semiring(U_2714) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

cnf(f_723_3,plain,
    ( hBOOL(hAPP(U_2714,bool,hAPP(U_2714,fun(U_2714,bool),ord_less_eq(U_2714),hAPP(U_2714,U_2714,hAPP(U_2714,fun(U_2714,U_2714),times_times(U_2714),U_2711),U_2713)),hAPP(U_2714,U_2714,hAPP(U_2714,fun(U_2714,U_2714),times_times(U_2714),U_2710),U_2712)))
    | ~ hBOOL(hAPP(U_2714,bool,hAPP(U_2714,fun(U_2714,bool),ord_less_eq(U_2714),zero_zero(U_2714)),U_2713))
    | ~ hBOOL(hAPP(U_2714,bool,hAPP(U_2714,fun(U_2714,bool),ord_less_eq(U_2714),zero_zero(U_2714)),U_2710))
    | ~ hBOOL(hAPP(U_2714,bool,hAPP(U_2714,fun(U_2714,bool),ord_less_eq(U_2714),U_2713),U_2712))
    | ~ hBOOL(hAPP(U_2714,bool,hAPP(U_2714,fun(U_2714,bool),ord_less_eq(U_2714),U_2711),U_2710))
    | ~ ordered_semiring(U_2714) ),
    inference(clausify,[status(thm)],[f_723_2]) ).

fof(f_724_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)))
          | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) )
            & ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) ) ) )
      | ~ ordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_634_split__mult__pos__le]) ).

fof(f_724_2,plain,
    ! [U_2717] :
      ( ! [U_2716,U_2715] :
          ( hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),zero_zero(U_2717)),hAPP(U_2717,U_2717,hAPP(U_2717,fun(U_2717,U_2717),times_times(U_2717),U_2715),U_2716)))
          | ( ( ~ hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),U_2716),zero_zero(U_2717)))
              | ~ hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),U_2715),zero_zero(U_2717))) )
            & ( ~ hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),zero_zero(U_2717)),U_2716))
              | ~ hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),zero_zero(U_2717)),U_2715)) ) ) )
      | ~ ordered_ring(U_2717) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

cnf(f_724_3,plain,
    ( ~ hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),zero_zero(U_2717)),U_2716))
    | ~ hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),zero_zero(U_2717)),U_2715))
    | hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),zero_zero(U_2717)),hAPP(U_2717,U_2717,hAPP(U_2717,fun(U_2717,U_2717),times_times(U_2717),U_2715),U_2716)))
    | ~ ordered_ring(U_2717) ),
    inference(clausify,[status(thm)],[f_724_2]) ).

cnf(f_724_4,plain,
    ( ~ hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),U_2716),zero_zero(U_2717)))
    | ~ hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),U_2715),zero_zero(U_2717)))
    | hBOOL(hAPP(U_2717,bool,hAPP(U_2717,fun(U_2717,bool),ord_less_eq(U_2717),zero_zero(U_2717)),hAPP(U_2717,U_2717,hAPP(U_2717,fun(U_2717,U_2717),times_times(U_2717),U_2715),U_2716)))
    | ~ ordered_ring(U_2717) ),
    inference(clausify,[status(thm)],[f_724_2]) ).

fof(f_725_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a)))
          | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) )
            & ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) ) ) )
      | ~ ordere453448008miring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_635_split__mult__neg__le]) ).

fof(f_725_2,plain,
    ! [U_2720] :
      ( ! [U_2719,U_2718] :
          ( hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),hAPP(U_2720,U_2720,hAPP(U_2720,fun(U_2720,U_2720),times_times(U_2720),U_2718),U_2719)),zero_zero(U_2720)))
          | ( ( ~ hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),zero_zero(U_2720)),U_2719))
              | ~ hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),U_2718),zero_zero(U_2720))) )
            & ( ~ hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),U_2719),zero_zero(U_2720)))
              | ~ hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),zero_zero(U_2720)),U_2718)) ) ) )
      | ~ ordere453448008miring(U_2720) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

cnf(f_725_3,plain,
    ( ~ hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),U_2719),zero_zero(U_2720)))
    | ~ hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),zero_zero(U_2720)),U_2718))
    | hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),hAPP(U_2720,U_2720,hAPP(U_2720,fun(U_2720,U_2720),times_times(U_2720),U_2718),U_2719)),zero_zero(U_2720)))
    | ~ ordere453448008miring(U_2720) ),
    inference(clausify,[status(thm)],[f_725_2]) ).

cnf(f_725_4,plain,
    ( ~ hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),zero_zero(U_2720)),U_2719))
    | ~ hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),U_2718),zero_zero(U_2720)))
    | hBOOL(hAPP(U_2720,bool,hAPP(U_2720,fun(U_2720,bool),ord_less_eq(U_2720),hAPP(U_2720,U_2720,hAPP(U_2720,fun(U_2720,U_2720),times_times(U_2720),U_2718),U_2719)),zero_zero(U_2720)))
    | ~ ordere453448008miring(U_2720) ),
    inference(clausify,[status(thm)],[f_725_2]) ).

fof(f_726_1,plain,
    ! [X_a] :
      ( ! [A_2] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),A_2)),zero_zero(X_a)))
      | ~ linordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_636_not__square__less__zero]) ).

fof(f_726_2,plain,
    ! [U_2722] :
      ( ! [U_2721] : ~ hBOOL(hAPP(U_2722,bool,hAPP(U_2722,fun(U_2722,bool),ord_less(U_2722),hAPP(U_2722,U_2722,hAPP(U_2722,fun(U_2722,U_2722),times_times(U_2722),U_2721),U_2721)),zero_zero(U_2722)))
      | ~ linordered_ring(U_2722) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

cnf(f_726_3,plain,
    ( ~ hBOOL(hAPP(U_2722,bool,hAPP(U_2722,fun(U_2722,bool),ord_less(U_2722),hAPP(U_2722,U_2722,hAPP(U_2722,fun(U_2722,U_2722),times_times(U_2722),U_2721),U_2721)),zero_zero(U_2722)))
    | ~ linordered_ring(U_2722) ),
    inference(clausify,[status(thm)],[f_726_2]) ).

fof(f_727_1,plain,
    ! [X_a] :
      ( ! [Aa,Ca,Ba] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),Ca)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),zero_zero(X_a))) )
              & ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ca)) ) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),zero_zero(X_a))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ca)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ca)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),Ca))) ) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_637_mult__less__cancel__right__disj]) ).

fof(f_727_2,plain,
    ! [U_2726] :
      ( ! [U_2725,U_2724,U_2723] :
          ( ( hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2725),U_2724)),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2723),U_2724)))
            | ( ( ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2723),U_2725))
                | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2724),zero_zero(U_2726))) )
              & ( ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2725),U_2723))
                | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),zero_zero(U_2726)),U_2724)) ) ) )
          & ( ( hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2723),U_2725))
              & hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2724),zero_zero(U_2726))) )
            | ( hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2725),U_2723))
              & hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),zero_zero(U_2726)),U_2724)) )
            | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2725),U_2724)),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2723),U_2724))) ) )
      | ~ linord581940658strict(U_2726) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

fof(f_727_3,plain,
    ! [U_2726] :
      ( ( ! [U_2732,U_2730,U_2728] :
            ( hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2732),U_2730)),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2728),U_2730)))
            | ( ( ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2728),U_2732))
                | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2730),zero_zero(U_2726))) )
              & ( ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2732),U_2728))
                | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),zero_zero(U_2726)),U_2730)) ) ) )
        & ! [U_2731,U_2729,U_2727] :
            ( ( hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2727),U_2731))
              & hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2729),zero_zero(U_2726))) )
            | ( hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2731),U_2727))
              & hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),zero_zero(U_2726)),U_2729)) )
            | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2731),U_2729)),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2727),U_2729))) ) )
      | ~ linord581940658strict(U_2726) ),
    inference(miniscope,[status(thm)],[f_727_2]) ).

cnf(f_727_4,plain,
    ( hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2729),zero_zero(U_2726)))
    | hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),zero_zero(U_2726)),U_2729))
    | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2731),U_2729)),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2727),U_2729)))
    | ~ linord581940658strict(U_2726) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

cnf(f_727_5,plain,
    ( hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2727),U_2731))
    | hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),zero_zero(U_2726)),U_2729))
    | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2731),U_2729)),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2727),U_2729)))
    | ~ linord581940658strict(U_2726) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

cnf(f_727_6,plain,
    ( hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2729),zero_zero(U_2726)))
    | hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2731),U_2727))
    | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2731),U_2729)),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2727),U_2729)))
    | ~ linord581940658strict(U_2726) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

cnf(f_727_7,plain,
    ( hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2727),U_2731))
    | hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2731),U_2727))
    | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2731),U_2729)),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2727),U_2729)))
    | ~ linord581940658strict(U_2726) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

cnf(f_727_8,plain,
    ( ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2732),U_2728))
    | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),zero_zero(U_2726)),U_2730))
    | hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2732),U_2730)),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2728),U_2730)))
    | ~ linord581940658strict(U_2726) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

cnf(f_727_9,plain,
    ( ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2728),U_2732))
    | ~ hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),U_2730),zero_zero(U_2726)))
    | hBOOL(hAPP(U_2726,bool,hAPP(U_2726,fun(U_2726,bool),ord_less(U_2726),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2732),U_2730)),hAPP(U_2726,U_2726,hAPP(U_2726,fun(U_2726,U_2726),times_times(U_2726),U_2728),U_2730)))
    | ~ linord581940658strict(U_2726) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

fof(f_728_1,plain,
    ! [X_a] :
      ( ! [Ca,Aa,Ba] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),zero_zero(X_a))) )
              & ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ca)) ) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),zero_zero(X_a))) )
            | ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ca)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba))) ) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_638_mult__less__cancel__left__disj]) ).

fof(f_728_2,plain,
    ! [U_2736] :
      ( ! [U_2735,U_2734,U_2733] :
          ( ( hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2735),U_2734)),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2735),U_2733)))
            | ( ( ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2733),U_2734))
                | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2735),zero_zero(U_2736))) )
              & ( ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2734),U_2733))
                | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),zero_zero(U_2736)),U_2735)) ) ) )
          & ( ( hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2733),U_2734))
              & hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2735),zero_zero(U_2736))) )
            | ( hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2734),U_2733))
              & hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),zero_zero(U_2736)),U_2735)) )
            | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2735),U_2734)),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2735),U_2733))) ) )
      | ~ linord581940658strict(U_2736) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

fof(f_728_3,plain,
    ! [U_2736] :
      ( ( ! [U_2742,U_2740,U_2738] :
            ( hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2742),U_2740)),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2742),U_2738)))
            | ( ( ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2738),U_2740))
                | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2742),zero_zero(U_2736))) )
              & ( ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2740),U_2738))
                | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),zero_zero(U_2736)),U_2742)) ) ) )
        & ! [U_2741,U_2739,U_2737] :
            ( ( hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2737),U_2739))
              & hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2741),zero_zero(U_2736))) )
            | ( hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2739),U_2737))
              & hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),zero_zero(U_2736)),U_2741)) )
            | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2741),U_2739)),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2741),U_2737))) ) )
      | ~ linord581940658strict(U_2736) ),
    inference(miniscope,[status(thm)],[f_728_2]) ).

cnf(f_728_4,plain,
    ( hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2741),zero_zero(U_2736)))
    | hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),zero_zero(U_2736)),U_2741))
    | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2741),U_2739)),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2741),U_2737)))
    | ~ linord581940658strict(U_2736) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

cnf(f_728_5,plain,
    ( hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2737),U_2739))
    | hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),zero_zero(U_2736)),U_2741))
    | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2741),U_2739)),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2741),U_2737)))
    | ~ linord581940658strict(U_2736) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

cnf(f_728_6,plain,
    ( hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2741),zero_zero(U_2736)))
    | hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2739),U_2737))
    | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2741),U_2739)),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2741),U_2737)))
    | ~ linord581940658strict(U_2736) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

cnf(f_728_7,plain,
    ( hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2737),U_2739))
    | hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2739),U_2737))
    | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2741),U_2739)),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2741),U_2737)))
    | ~ linord581940658strict(U_2736) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

cnf(f_728_8,plain,
    ( ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2740),U_2738))
    | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),zero_zero(U_2736)),U_2742))
    | hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2742),U_2740)),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2742),U_2738)))
    | ~ linord581940658strict(U_2736) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

cnf(f_728_9,plain,
    ( ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2738),U_2740))
    | ~ hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),U_2742),zero_zero(U_2736)))
    | hBOOL(hAPP(U_2736,bool,hAPP(U_2736,fun(U_2736,bool),ord_less(U_2736),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2742),U_2740)),hAPP(U_2736,U_2736,hAPP(U_2736,fun(U_2736,U_2736),times_times(U_2736),U_2742),U_2738)))
    | ~ linord581940658strict(U_2736) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

fof(f_729_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba)))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) )
            & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba))) ) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ca)) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_639_mult__less__cancel__left__pos]) ).

fof(f_729_2,plain,
    ! [U_2746] :
      ( ! [U_2745,U_2744,U_2743] :
          ( ( ( hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),hAPP(U_2746,U_2746,hAPP(U_2746,fun(U_2746,U_2746),times_times(U_2746),U_2743),U_2745)),hAPP(U_2746,U_2746,hAPP(U_2746,fun(U_2746,U_2746),times_times(U_2746),U_2743),U_2744)))
              | ~ hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),U_2745),U_2744)) )
            & ( hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),U_2745),U_2744))
              | ~ hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),hAPP(U_2746,U_2746,hAPP(U_2746,fun(U_2746,U_2746),times_times(U_2746),U_2743),U_2745)),hAPP(U_2746,U_2746,hAPP(U_2746,fun(U_2746,U_2746),times_times(U_2746),U_2743),U_2744))) ) )
          | ~ hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),zero_zero(U_2746)),U_2743)) )
      | ~ linord581940658strict(U_2746) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

cnf(f_729_3,plain,
    ( hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),U_2745),U_2744))
    | ~ hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),hAPP(U_2746,U_2746,hAPP(U_2746,fun(U_2746,U_2746),times_times(U_2746),U_2743),U_2745)),hAPP(U_2746,U_2746,hAPP(U_2746,fun(U_2746,U_2746),times_times(U_2746),U_2743),U_2744)))
    | ~ hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),zero_zero(U_2746)),U_2743))
    | ~ linord581940658strict(U_2746) ),
    inference(clausify,[status(thm)],[f_729_2]) ).

cnf(f_729_4,plain,
    ( hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),hAPP(U_2746,U_2746,hAPP(U_2746,fun(U_2746,U_2746),times_times(U_2746),U_2743),U_2745)),hAPP(U_2746,U_2746,hAPP(U_2746,fun(U_2746,U_2746),times_times(U_2746),U_2743),U_2744)))
    | ~ hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),U_2745),U_2744))
    | ~ hBOOL(hAPP(U_2746,bool,hAPP(U_2746,fun(U_2746,bool),ord_less(U_2746),zero_zero(U_2746)),U_2743))
    | ~ linord581940658strict(U_2746) ),
    inference(clausify,[status(thm)],[f_729_2]) ).

fof(f_730_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_640_mult__pos__pos]) ).

fof(f_730_2,plain,
    ! [U_2749] :
      ( ! [U_2748,U_2747] :
          ( hBOOL(hAPP(U_2749,bool,hAPP(U_2749,fun(U_2749,bool),ord_less(U_2749),zero_zero(U_2749)),hAPP(U_2749,U_2749,hAPP(U_2749,fun(U_2749,U_2749),times_times(U_2749),U_2747),U_2748)))
          | ~ hBOOL(hAPP(U_2749,bool,hAPP(U_2749,fun(U_2749,bool),ord_less(U_2749),zero_zero(U_2749)),U_2748))
          | ~ hBOOL(hAPP(U_2749,bool,hAPP(U_2749,fun(U_2749,bool),ord_less(U_2749),zero_zero(U_2749)),U_2747)) )
      | ~ linord20386208strict(U_2749) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

cnf(f_730_3,plain,
    ( hBOOL(hAPP(U_2749,bool,hAPP(U_2749,fun(U_2749,bool),ord_less(U_2749),zero_zero(U_2749)),hAPP(U_2749,U_2749,hAPP(U_2749,fun(U_2749,U_2749),times_times(U_2749),U_2747),U_2748)))
    | ~ hBOOL(hAPP(U_2749,bool,hAPP(U_2749,fun(U_2749,bool),ord_less(U_2749),zero_zero(U_2749)),U_2748))
    | ~ hBOOL(hAPP(U_2749,bool,hAPP(U_2749,fun(U_2749,bool),ord_less(U_2749),zero_zero(U_2749)),U_2747))
    | ~ linord20386208strict(U_2749) ),
    inference(clausify,[status(thm)],[f_730_2]) ).

fof(f_731_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_641_mult__pos__neg]) ).

fof(f_731_2,plain,
    ! [U_2752] :
      ( ! [U_2751,U_2750] :
          ( hBOOL(hAPP(U_2752,bool,hAPP(U_2752,fun(U_2752,bool),ord_less(U_2752),hAPP(U_2752,U_2752,hAPP(U_2752,fun(U_2752,U_2752),times_times(U_2752),U_2750),U_2751)),zero_zero(U_2752)))
          | ~ hBOOL(hAPP(U_2752,bool,hAPP(U_2752,fun(U_2752,bool),ord_less(U_2752),U_2751),zero_zero(U_2752)))
          | ~ hBOOL(hAPP(U_2752,bool,hAPP(U_2752,fun(U_2752,bool),ord_less(U_2752),zero_zero(U_2752)),U_2750)) )
      | ~ linord20386208strict(U_2752) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

cnf(f_731_3,plain,
    ( hBOOL(hAPP(U_2752,bool,hAPP(U_2752,fun(U_2752,bool),ord_less(U_2752),hAPP(U_2752,U_2752,hAPP(U_2752,fun(U_2752,U_2752),times_times(U_2752),U_2750),U_2751)),zero_zero(U_2752)))
    | ~ hBOOL(hAPP(U_2752,bool,hAPP(U_2752,fun(U_2752,bool),ord_less(U_2752),U_2751),zero_zero(U_2752)))
    | ~ hBOOL(hAPP(U_2752,bool,hAPP(U_2752,fun(U_2752,bool),ord_less(U_2752),zero_zero(U_2752)),U_2750))
    | ~ linord20386208strict(U_2752) ),
    inference(clausify,[status(thm)],[f_731_2]) ).

fof(f_732_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),A_2)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_642_mult__pos__neg2]) ).

fof(f_732_2,plain,
    ! [U_2755] :
      ( ! [U_2754,U_2753] :
          ( hBOOL(hAPP(U_2755,bool,hAPP(U_2755,fun(U_2755,bool),ord_less(U_2755),hAPP(U_2755,U_2755,hAPP(U_2755,fun(U_2755,U_2755),times_times(U_2755),U_2754),U_2753)),zero_zero(U_2755)))
          | ~ hBOOL(hAPP(U_2755,bool,hAPP(U_2755,fun(U_2755,bool),ord_less(U_2755),U_2754),zero_zero(U_2755)))
          | ~ hBOOL(hAPP(U_2755,bool,hAPP(U_2755,fun(U_2755,bool),ord_less(U_2755),zero_zero(U_2755)),U_2753)) )
      | ~ linord20386208strict(U_2755) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

cnf(f_732_3,plain,
    ( hBOOL(hAPP(U_2755,bool,hAPP(U_2755,fun(U_2755,bool),ord_less(U_2755),hAPP(U_2755,U_2755,hAPP(U_2755,fun(U_2755,U_2755),times_times(U_2755),U_2754),U_2753)),zero_zero(U_2755)))
    | ~ hBOOL(hAPP(U_2755,bool,hAPP(U_2755,fun(U_2755,bool),ord_less(U_2755),U_2754),zero_zero(U_2755)))
    | ~ hBOOL(hAPP(U_2755,bool,hAPP(U_2755,fun(U_2755,bool),ord_less(U_2755),zero_zero(U_2755)),U_2753))
    | ~ linord20386208strict(U_2755) ),
    inference(clausify,[status(thm)],[f_732_2]) ).

fof(f_733_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_643_zero__less__mult__pos]) ).

fof(f_733_2,plain,
    ! [U_2758] :
      ( ! [U_2757,U_2756] :
          ( hBOOL(hAPP(U_2758,bool,hAPP(U_2758,fun(U_2758,bool),ord_less(U_2758),zero_zero(U_2758)),U_2756))
          | ~ hBOOL(hAPP(U_2758,bool,hAPP(U_2758,fun(U_2758,bool),ord_less(U_2758),zero_zero(U_2758)),U_2757))
          | ~ hBOOL(hAPP(U_2758,bool,hAPP(U_2758,fun(U_2758,bool),ord_less(U_2758),zero_zero(U_2758)),hAPP(U_2758,U_2758,hAPP(U_2758,fun(U_2758,U_2758),times_times(U_2758),U_2757),U_2756))) )
      | ~ linord20386208strict(U_2758) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

cnf(f_733_3,plain,
    ( hBOOL(hAPP(U_2758,bool,hAPP(U_2758,fun(U_2758,bool),ord_less(U_2758),zero_zero(U_2758)),U_2756))
    | ~ hBOOL(hAPP(U_2758,bool,hAPP(U_2758,fun(U_2758,bool),ord_less(U_2758),zero_zero(U_2758)),U_2757))
    | ~ hBOOL(hAPP(U_2758,bool,hAPP(U_2758,fun(U_2758,bool),ord_less(U_2758),zero_zero(U_2758)),hAPP(U_2758,U_2758,hAPP(U_2758,fun(U_2758,U_2758),times_times(U_2758),U_2757),U_2756)))
    | ~ linord20386208strict(U_2758) ),
    inference(clausify,[status(thm)],[f_733_2]) ).

fof(f_734_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),A_2))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_644_zero__less__mult__pos2]) ).

fof(f_734_2,plain,
    ! [U_2761] :
      ( ! [U_2760,U_2759] :
          ( hBOOL(hAPP(U_2761,bool,hAPP(U_2761,fun(U_2761,bool),ord_less(U_2761),zero_zero(U_2761)),U_2760))
          | ~ hBOOL(hAPP(U_2761,bool,hAPP(U_2761,fun(U_2761,bool),ord_less(U_2761),zero_zero(U_2761)),U_2759))
          | ~ hBOOL(hAPP(U_2761,bool,hAPP(U_2761,fun(U_2761,bool),ord_less(U_2761),zero_zero(U_2761)),hAPP(U_2761,U_2761,hAPP(U_2761,fun(U_2761,U_2761),times_times(U_2761),U_2760),U_2759))) )
      | ~ linord20386208strict(U_2761) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

cnf(f_734_3,plain,
    ( hBOOL(hAPP(U_2761,bool,hAPP(U_2761,fun(U_2761,bool),ord_less(U_2761),zero_zero(U_2761)),U_2760))
    | ~ hBOOL(hAPP(U_2761,bool,hAPP(U_2761,fun(U_2761,bool),ord_less(U_2761),zero_zero(U_2761)),U_2759))
    | ~ hBOOL(hAPP(U_2761,bool,hAPP(U_2761,fun(U_2761,bool),ord_less(U_2761),zero_zero(U_2761)),hAPP(U_2761,U_2761,hAPP(U_2761,fun(U_2761,U_2761),times_times(U_2761),U_2760),U_2759)))
    | ~ linord20386208strict(U_2761) ),
    inference(clausify,[status(thm)],[f_734_2]) ).

fof(f_735_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba)))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)) )
            & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba))) ) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),zero_zero(X_a))) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_645_mult__less__cancel__left__neg]) ).

fof(f_735_2,plain,
    ! [U_2765] :
      ( ! [U_2764,U_2763,U_2762] :
          ( ( ( hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),hAPP(U_2765,U_2765,hAPP(U_2765,fun(U_2765,U_2765),times_times(U_2765),U_2762),U_2764)),hAPP(U_2765,U_2765,hAPP(U_2765,fun(U_2765,U_2765),times_times(U_2765),U_2762),U_2763)))
              | ~ hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),U_2763),U_2764)) )
            & ( hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),U_2763),U_2764))
              | ~ hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),hAPP(U_2765,U_2765,hAPP(U_2765,fun(U_2765,U_2765),times_times(U_2765),U_2762),U_2764)),hAPP(U_2765,U_2765,hAPP(U_2765,fun(U_2765,U_2765),times_times(U_2765),U_2762),U_2763))) ) )
          | ~ hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),U_2762),zero_zero(U_2765))) )
      | ~ linord581940658strict(U_2765) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

cnf(f_735_3,plain,
    ( hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),U_2763),U_2764))
    | ~ hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),hAPP(U_2765,U_2765,hAPP(U_2765,fun(U_2765,U_2765),times_times(U_2765),U_2762),U_2764)),hAPP(U_2765,U_2765,hAPP(U_2765,fun(U_2765,U_2765),times_times(U_2765),U_2762),U_2763)))
    | ~ hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),U_2762),zero_zero(U_2765)))
    | ~ linord581940658strict(U_2765) ),
    inference(clausify,[status(thm)],[f_735_2]) ).

cnf(f_735_4,plain,
    ( hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),hAPP(U_2765,U_2765,hAPP(U_2765,fun(U_2765,U_2765),times_times(U_2765),U_2762),U_2764)),hAPP(U_2765,U_2765,hAPP(U_2765,fun(U_2765,U_2765),times_times(U_2765),U_2762),U_2763)))
    | ~ hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),U_2763),U_2764))
    | ~ hBOOL(hAPP(U_2765,bool,hAPP(U_2765,fun(U_2765,bool),ord_less(U_2765),U_2762),zero_zero(U_2765)))
    | ~ linord581940658strict(U_2765) ),
    inference(clausify,[status(thm)],[f_735_2]) ).

fof(f_736_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_646_mult__neg__pos]) ).

fof(f_736_2,plain,
    ! [U_2768] :
      ( ! [U_2767,U_2766] :
          ( hBOOL(hAPP(U_2768,bool,hAPP(U_2768,fun(U_2768,bool),ord_less(U_2768),hAPP(U_2768,U_2768,hAPP(U_2768,fun(U_2768,U_2768),times_times(U_2768),U_2766),U_2767)),zero_zero(U_2768)))
          | ~ hBOOL(hAPP(U_2768,bool,hAPP(U_2768,fun(U_2768,bool),ord_less(U_2768),zero_zero(U_2768)),U_2767))
          | ~ hBOOL(hAPP(U_2768,bool,hAPP(U_2768,fun(U_2768,bool),ord_less(U_2768),U_2766),zero_zero(U_2768))) )
      | ~ linord20386208strict(U_2768) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

cnf(f_736_3,plain,
    ( hBOOL(hAPP(U_2768,bool,hAPP(U_2768,fun(U_2768,bool),ord_less(U_2768),hAPP(U_2768,U_2768,hAPP(U_2768,fun(U_2768,U_2768),times_times(U_2768),U_2766),U_2767)),zero_zero(U_2768)))
    | ~ hBOOL(hAPP(U_2768,bool,hAPP(U_2768,fun(U_2768,bool),ord_less(U_2768),zero_zero(U_2768)),U_2767))
    | ~ hBOOL(hAPP(U_2768,bool,hAPP(U_2768,fun(U_2768,bool),ord_less(U_2768),U_2766),zero_zero(U_2768)))
    | ~ linord20386208strict(U_2768) ),
    inference(clausify,[status(thm)],[f_736_2]) ).

fof(f_737_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_647_mult__neg__neg]) ).

fof(f_737_2,plain,
    ! [U_2771] :
      ( ! [U_2770,U_2769] :
          ( hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less(U_2771),zero_zero(U_2771)),hAPP(U_2771,U_2771,hAPP(U_2771,fun(U_2771,U_2771),times_times(U_2771),U_2769),U_2770)))
          | ~ hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less(U_2771),U_2770),zero_zero(U_2771)))
          | ~ hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less(U_2771),U_2769),zero_zero(U_2771))) )
      | ~ linord581940658strict(U_2771) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

cnf(f_737_3,plain,
    ( hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less(U_2771),zero_zero(U_2771)),hAPP(U_2771,U_2771,hAPP(U_2771,fun(U_2771,U_2771),times_times(U_2771),U_2769),U_2770)))
    | ~ hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less(U_2771),U_2770),zero_zero(U_2771)))
    | ~ hBOOL(hAPP(U_2771,bool,hAPP(U_2771,fun(U_2771,bool),ord_less(U_2771),U_2769),zero_zero(U_2771)))
    | ~ linord581940658strict(U_2771) ),
    inference(clausify,[status(thm)],[f_737_2]) ).

fof(f_738_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_648_mult__strict__right__mono]) ).

fof(f_738_2,plain,
    ! [U_2775] :
      ( ! [U_2774,U_2773,U_2772] :
          ( hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less(U_2775),hAPP(U_2775,U_2775,hAPP(U_2775,fun(U_2775,U_2775),times_times(U_2775),U_2773),U_2774)),hAPP(U_2775,U_2775,hAPP(U_2775,fun(U_2775,U_2775),times_times(U_2775),U_2772),U_2774)))
          | ~ hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less(U_2775),zero_zero(U_2775)),U_2774))
          | ~ hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less(U_2775),U_2773),U_2772)) )
      | ~ linord20386208strict(U_2775) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

cnf(f_738_3,plain,
    ( hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less(U_2775),hAPP(U_2775,U_2775,hAPP(U_2775,fun(U_2775,U_2775),times_times(U_2775),U_2773),U_2774)),hAPP(U_2775,U_2775,hAPP(U_2775,fun(U_2775,U_2775),times_times(U_2775),U_2772),U_2774)))
    | ~ hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less(U_2775),zero_zero(U_2775)),U_2774))
    | ~ hBOOL(hAPP(U_2775,bool,hAPP(U_2775,fun(U_2775,bool),ord_less(U_2775),U_2773),U_2772))
    | ~ linord20386208strict(U_2775) ),
    inference(clausify,[status(thm)],[f_738_2]) ).

fof(f_739_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_649_mult__strict__left__mono]) ).

fof(f_739_2,plain,
    ! [U_2779] :
      ( ! [U_2778,U_2777,U_2776] :
          ( hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less(U_2779),hAPP(U_2779,U_2779,hAPP(U_2779,fun(U_2779,U_2779),times_times(U_2779),U_2778),U_2777)),hAPP(U_2779,U_2779,hAPP(U_2779,fun(U_2779,U_2779),times_times(U_2779),U_2778),U_2776)))
          | ~ hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less(U_2779),zero_zero(U_2779)),U_2778))
          | ~ hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less(U_2779),U_2777),U_2776)) )
      | ~ linord20386208strict(U_2779) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

cnf(f_739_3,plain,
    ( hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less(U_2779),hAPP(U_2779,U_2779,hAPP(U_2779,fun(U_2779,U_2779),times_times(U_2779),U_2778),U_2777)),hAPP(U_2779,U_2779,hAPP(U_2779,fun(U_2779,U_2779),times_times(U_2779),U_2778),U_2776)))
    | ~ hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less(U_2779),zero_zero(U_2779)),U_2778))
    | ~ hBOOL(hAPP(U_2779,bool,hAPP(U_2779,fun(U_2779,bool),ord_less(U_2779),U_2777),U_2776))
    | ~ linord20386208strict(U_2779) ),
    inference(clausify,[status(thm)],[f_739_2]) ).

fof(f_740_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ linord893533164strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_650_comm__mult__strict__left__mono]) ).

fof(f_740_2,plain,
    ! [U_2783] :
      ( ! [U_2782,U_2781,U_2780] :
          ( hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less(U_2783),hAPP(U_2783,U_2783,hAPP(U_2783,fun(U_2783,U_2783),times_times(U_2783),U_2782),U_2781)),hAPP(U_2783,U_2783,hAPP(U_2783,fun(U_2783,U_2783),times_times(U_2783),U_2782),U_2780)))
          | ~ hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less(U_2783),zero_zero(U_2783)),U_2782))
          | ~ hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less(U_2783),U_2781),U_2780)) )
      | ~ linord893533164strict(U_2783) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

cnf(f_740_3,plain,
    ( hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less(U_2783),hAPP(U_2783,U_2783,hAPP(U_2783,fun(U_2783,U_2783),times_times(U_2783),U_2782),U_2781)),hAPP(U_2783,U_2783,hAPP(U_2783,fun(U_2783,U_2783),times_times(U_2783),U_2782),U_2780)))
    | ~ hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less(U_2783),zero_zero(U_2783)),U_2782))
    | ~ hBOOL(hAPP(U_2783,bool,hAPP(U_2783,fun(U_2783,bool),ord_less(U_2783),U_2781),U_2780))
    | ~ linord893533164strict(U_2783) ),
    inference(clausify,[status(thm)],[f_740_2]) ).

fof(f_741_1,plain,
    ! [X_a] :
      ( ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_651_mult__strict__right__mono__neg]) ).

fof(f_741_2,plain,
    ! [U_2787] :
      ( ! [U_2786,U_2785,U_2784] :
          ( hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less(U_2787),hAPP(U_2787,U_2787,hAPP(U_2787,fun(U_2787,U_2787),times_times(U_2787),U_2784),U_2786)),hAPP(U_2787,U_2787,hAPP(U_2787,fun(U_2787,U_2787),times_times(U_2787),U_2785),U_2786)))
          | ~ hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less(U_2787),U_2786),zero_zero(U_2787)))
          | ~ hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less(U_2787),U_2785),U_2784)) )
      | ~ linord581940658strict(U_2787) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

cnf(f_741_3,plain,
    ( hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less(U_2787),hAPP(U_2787,U_2787,hAPP(U_2787,fun(U_2787,U_2787),times_times(U_2787),U_2784),U_2786)),hAPP(U_2787,U_2787,hAPP(U_2787,fun(U_2787,U_2787),times_times(U_2787),U_2785),U_2786)))
    | ~ hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less(U_2787),U_2786),zero_zero(U_2787)))
    | ~ hBOOL(hAPP(U_2787,bool,hAPP(U_2787,fun(U_2787,bool),ord_less(U_2787),U_2785),U_2784))
    | ~ linord581940658strict(U_2787) ),
    inference(clausify,[status(thm)],[f_741_2]) ).

fof(f_742_1,plain,
    ! [X_a] :
      ( ! [C_1,B_1,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_652_mult__strict__left__mono__neg]) ).

fof(f_742_2,plain,
    ! [U_2791] :
      ( ! [U_2790,U_2789,U_2788] :
          ( hBOOL(hAPP(U_2791,bool,hAPP(U_2791,fun(U_2791,bool),ord_less(U_2791),hAPP(U_2791,U_2791,hAPP(U_2791,fun(U_2791,U_2791),times_times(U_2791),U_2790),U_2788)),hAPP(U_2791,U_2791,hAPP(U_2791,fun(U_2791,U_2791),times_times(U_2791),U_2790),U_2789)))
          | ~ hBOOL(hAPP(U_2791,bool,hAPP(U_2791,fun(U_2791,bool),ord_less(U_2791),U_2790),zero_zero(U_2791)))
          | ~ hBOOL(hAPP(U_2791,bool,hAPP(U_2791,fun(U_2791,bool),ord_less(U_2791),U_2789),U_2788)) )
      | ~ linord581940658strict(U_2791) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

cnf(f_742_3,plain,
    ( hBOOL(hAPP(U_2791,bool,hAPP(U_2791,fun(U_2791,bool),ord_less(U_2791),hAPP(U_2791,U_2791,hAPP(U_2791,fun(U_2791,U_2791),times_times(U_2791),U_2790),U_2788)),hAPP(U_2791,U_2791,hAPP(U_2791,fun(U_2791,U_2791),times_times(U_2791),U_2790),U_2789)))
    | ~ hBOOL(hAPP(U_2791,bool,hAPP(U_2791,fun(U_2791,bool),ord_less(U_2791),U_2790),zero_zero(U_2791)))
    | ~ hBOOL(hAPP(U_2791,bool,hAPP(U_2791,fun(U_2791,bool),ord_less(U_2791),U_2789),U_2788))
    | ~ linord581940658strict(U_2791) ),
    inference(clausify,[status(thm)],[f_742_2]) ).

fof(f_743_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)) = zero_zero(X_a)
            | ti(X_a,Y_1) != zero_zero(X_a)
            | ti(X_a,X_2) != zero_zero(X_a) )
          & ( ( ti(X_a,Y_1) = zero_zero(X_a)
              & ti(X_a,X_2) = zero_zero(X_a) )
            | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)) != zero_zero(X_a) ) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_653_sum__squares__eq__zero__iff]) ).

fof(f_743_2,plain,
    ! [U_2794] :
      ( ! [U_2793,U_2792] :
          ( ( hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),plus_plus(U_2794),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2793),U_2793)),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2792),U_2792)) = zero_zero(U_2794)
            | ti(U_2794,U_2792) != zero_zero(U_2794)
            | ti(U_2794,U_2793) != zero_zero(U_2794) )
          & ( ( ti(U_2794,U_2792) = zero_zero(U_2794)
              & ti(U_2794,U_2793) = zero_zero(U_2794) )
            | hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),plus_plus(U_2794),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2793),U_2793)),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2792),U_2792)) != zero_zero(U_2794) ) )
      | ~ linord581940658strict(U_2794) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

fof(f_743_3,plain,
    ! [U_2794] :
      ( ( ! [U_2798,U_2796] :
            ( hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),plus_plus(U_2794),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2798),U_2798)),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2796),U_2796)) = zero_zero(U_2794)
            | ti(U_2794,U_2796) != zero_zero(U_2794)
            | ti(U_2794,U_2798) != zero_zero(U_2794) )
        & ! [U_2797,U_2795] :
            ( ( ti(U_2794,U_2795) = zero_zero(U_2794)
              & ti(U_2794,U_2797) = zero_zero(U_2794) )
            | hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),plus_plus(U_2794),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2797),U_2797)),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2795),U_2795)) != zero_zero(U_2794) ) )
      | ~ linord581940658strict(U_2794) ),
    inference(miniscope,[status(thm)],[f_743_2]) ).

cnf(f_743_4,plain,
    ( ti(U_2794,U_2797) = zero_zero(U_2794)
    | hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),plus_plus(U_2794),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2797),U_2797)),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2795),U_2795)) != zero_zero(U_2794)
    | ~ linord581940658strict(U_2794) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

cnf(f_743_5,plain,
    ( ti(U_2794,U_2795) = zero_zero(U_2794)
    | hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),plus_plus(U_2794),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2797),U_2797)),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2795),U_2795)) != zero_zero(U_2794)
    | ~ linord581940658strict(U_2794) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

cnf(f_743_6,plain,
    ( hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),plus_plus(U_2794),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2798),U_2798)),hAPP(U_2794,U_2794,hAPP(U_2794,fun(U_2794,U_2794),times_times(U_2794),U_2796),U_2796)) = zero_zero(U_2794)
    | ti(U_2794,U_2796) != zero_zero(U_2794)
    | ti(U_2794,U_2798) != zero_zero(U_2794)
    | ~ linord581940658strict(U_2794) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

fof(f_744_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1,R_3] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_3),C_1)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_3),D))
          | ti(X_a,C_1) = ti(X_a,D)
          | ti(X_a,A_2) != ti(X_a,B_1)
          | ti(X_a,R_3) = zero_zero(X_a) )
      | ~ semiri456707255roduct(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_654_add__scale__eq__noteq]) ).

fof(f_744_2,plain,
    ! [U_2804] :
      ( ! [U_2803,U_2802,U_2801,U_2800,U_2799] :
          ( hAPP(U_2804,U_2804,hAPP(U_2804,fun(U_2804,U_2804),plus_plus(U_2804),U_2801),hAPP(U_2804,U_2804,hAPP(U_2804,fun(U_2804,U_2804),times_times(U_2804),U_2799),U_2803)) != hAPP(U_2804,U_2804,hAPP(U_2804,fun(U_2804,U_2804),plus_plus(U_2804),U_2800),hAPP(U_2804,U_2804,hAPP(U_2804,fun(U_2804,U_2804),times_times(U_2804),U_2799),U_2802))
          | ti(U_2804,U_2803) = ti(U_2804,U_2802)
          | ti(U_2804,U_2801) != ti(U_2804,U_2800)
          | ti(U_2804,U_2799) = zero_zero(U_2804) )
      | ~ semiri456707255roduct(U_2804) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

cnf(f_744_3,plain,
    ( hAPP(U_2804,U_2804,hAPP(U_2804,fun(U_2804,U_2804),plus_plus(U_2804),U_2801),hAPP(U_2804,U_2804,hAPP(U_2804,fun(U_2804,U_2804),times_times(U_2804),U_2799),U_2803)) != hAPP(U_2804,U_2804,hAPP(U_2804,fun(U_2804,U_2804),plus_plus(U_2804),U_2800),hAPP(U_2804,U_2804,hAPP(U_2804,fun(U_2804,U_2804),times_times(U_2804),U_2799),U_2802))
    | ti(U_2804,U_2803) = ti(U_2804,U_2802)
    | ti(U_2804,U_2801) != ti(U_2804,U_2800)
    | ti(U_2804,U_2799) = zero_zero(U_2804)
    | ~ semiri456707255roduct(U_2804) ),
    inference(clausify,[status(thm)],[f_744_2]) ).

fof(f_745_1,plain,
    ! [X_a] :
      ( ! [N,M_3] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M_3),N)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M_3)) )
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_655_less__1__mult]) ).

fof(f_745_2,plain,
    ! [U_2807] :
      ( ! [U_2806,U_2805] :
          ( hBOOL(hAPP(U_2807,bool,hAPP(U_2807,fun(U_2807,bool),ord_less(U_2807),one_one(U_2807)),hAPP(U_2807,U_2807,hAPP(U_2807,fun(U_2807,U_2807),times_times(U_2807),U_2805),U_2806)))
          | ~ hBOOL(hAPP(U_2807,bool,hAPP(U_2807,fun(U_2807,bool),ord_less(U_2807),one_one(U_2807)),U_2806))
          | ~ hBOOL(hAPP(U_2807,bool,hAPP(U_2807,fun(U_2807,bool),ord_less(U_2807),one_one(U_2807)),U_2805)) )
      | ~ linordered_semidom(U_2807) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

cnf(f_745_3,plain,
    ( hBOOL(hAPP(U_2807,bool,hAPP(U_2807,fun(U_2807,bool),ord_less(U_2807),one_one(U_2807)),hAPP(U_2807,U_2807,hAPP(U_2807,fun(U_2807,U_2807),times_times(U_2807),U_2805),U_2806)))
    | ~ hBOOL(hAPP(U_2807,bool,hAPP(U_2807,fun(U_2807,bool),ord_less(U_2807),one_one(U_2807)),U_2806))
    | ~ hBOOL(hAPP(U_2807,bool,hAPP(U_2807,fun(U_2807,bool),ord_less(U_2807),one_one(U_2807)),U_2805))
    | ~ linordered_semidom(U_2807) ),
    inference(clausify,[status(thm)],[f_745_2]) ).

fof(f_746_1,plain,
    ! [X_a] :
      ( ! [A_2,M_3] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),M_3)),M_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),one_one(X_a))),M_3)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).

fof(f_746_2,plain,
    ! [U_2810] :
      ( ! [U_2809,U_2808] : hAPP(U_2810,U_2810,hAPP(U_2810,fun(U_2810,U_2810),plus_plus(U_2810),hAPP(U_2810,U_2810,hAPP(U_2810,fun(U_2810,U_2810),times_times(U_2810),U_2809),U_2808)),U_2808) = hAPP(U_2810,U_2810,hAPP(U_2810,fun(U_2810,U_2810),times_times(U_2810),hAPP(U_2810,U_2810,hAPP(U_2810,fun(U_2810,U_2810),plus_plus(U_2810),U_2809),one_one(U_2810))),U_2808)
      | ~ comm_semiring_1(U_2810) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

cnf(f_746_3,plain,
    ( hAPP(U_2810,U_2810,hAPP(U_2810,fun(U_2810,U_2810),plus_plus(U_2810),hAPP(U_2810,U_2810,hAPP(U_2810,fun(U_2810,U_2810),times_times(U_2810),U_2809),U_2808)),U_2808) = hAPP(U_2810,U_2810,hAPP(U_2810,fun(U_2810,U_2810),times_times(U_2810),hAPP(U_2810,U_2810,hAPP(U_2810,fun(U_2810,U_2810),plus_plus(U_2810),U_2809),one_one(U_2810))),U_2808)
    | ~ comm_semiring_1(U_2810) ),
    inference(clausify,[status(thm)],[f_746_2]) ).

fof(f_747_1,plain,
    ! [X_a] :
      ( ! [M_3,A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),M_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),one_one(X_a))),M_3)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).

fof(f_747_2,plain,
    ! [U_2813] :
      ( ! [U_2812,U_2811] : hAPP(U_2813,U_2813,hAPP(U_2813,fun(U_2813,U_2813),plus_plus(U_2813),U_2812),hAPP(U_2813,U_2813,hAPP(U_2813,fun(U_2813,U_2813),times_times(U_2813),U_2811),U_2812)) = hAPP(U_2813,U_2813,hAPP(U_2813,fun(U_2813,U_2813),times_times(U_2813),hAPP(U_2813,U_2813,hAPP(U_2813,fun(U_2813,U_2813),plus_plus(U_2813),U_2811),one_one(U_2813))),U_2812)
      | ~ comm_semiring_1(U_2813) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

cnf(f_747_3,plain,
    ( hAPP(U_2813,U_2813,hAPP(U_2813,fun(U_2813,U_2813),plus_plus(U_2813),U_2812),hAPP(U_2813,U_2813,hAPP(U_2813,fun(U_2813,U_2813),times_times(U_2813),U_2811),U_2812)) = hAPP(U_2813,U_2813,hAPP(U_2813,fun(U_2813,U_2813),times_times(U_2813),hAPP(U_2813,U_2813,hAPP(U_2813,fun(U_2813,U_2813),plus_plus(U_2813),U_2811),one_one(U_2813))),U_2812)
    | ~ comm_semiring_1(U_2813) ),
    inference(clausify,[status(thm)],[f_747_2]) ).

fof(f_748_1,plain,
    ! [X_a] :
      ( ! [M_3] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_3),M_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M_3)
      | ~ comm_semiring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).

fof(f_748_2,plain,
    ! [U_2815] :
      ( ! [U_2814] : hAPP(U_2815,U_2815,hAPP(U_2815,fun(U_2815,U_2815),plus_plus(U_2815),U_2814),U_2814) = hAPP(U_2815,U_2815,hAPP(U_2815,fun(U_2815,U_2815),times_times(U_2815),hAPP(U_2815,U_2815,hAPP(U_2815,fun(U_2815,U_2815),plus_plus(U_2815),one_one(U_2815)),one_one(U_2815))),U_2814)
      | ~ comm_semiring_1(U_2815) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

cnf(f_748_3,plain,
    ( hAPP(U_2815,U_2815,hAPP(U_2815,fun(U_2815,U_2815),plus_plus(U_2815),U_2814),U_2814) = hAPP(U_2815,U_2815,hAPP(U_2815,fun(U_2815,U_2815),times_times(U_2815),hAPP(U_2815,U_2815,hAPP(U_2815,fun(U_2815,U_2815),plus_plus(U_2815),one_one(U_2815)),one_one(U_2815))),U_2814)
    | ~ comm_semiring_1(U_2815) ),
    inference(clausify,[status(thm)],[f_748_2]) ).

fof(f_749_1,plain,
    ! [M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = hAPP(nat,nat,suc,zero_zero(nat))
        | Na != hAPP(nat,nat,suc,zero_zero(nat))
        | M != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_659_mult__eq__1__iff]) ).

fof(f_749_2,plain,
    ! [U_2817,U_2816] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2817),U_2816) = hAPP(nat,nat,suc,zero_zero(nat))
        | U_2816 != hAPP(nat,nat,suc,zero_zero(nat))
        | U_2817 != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( ( U_2816 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2817 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2817),U_2816) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

fof(f_749_3,plain,
    ( ! [U_2821,U_2819] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2821),U_2819) = hAPP(nat,nat,suc,zero_zero(nat))
        | U_2819 != hAPP(nat,nat,suc,zero_zero(nat))
        | U_2821 != hAPP(nat,nat,suc,zero_zero(nat)) )
    & ! [U_2820,U_2818] :
        ( ( U_2818 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2820 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2820),U_2818) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(miniscope,[status(thm)],[f_749_2]) ).

cnf(f_749_4,plain,
    ( U_2820 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2820),U_2818) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_749_3]) ).

cnf(f_749_5,plain,
    ( U_2818 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2820),U_2818) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_749_3]) ).

cnf(f_749_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2821),U_2819) = hAPP(nat,nat,suc,zero_zero(nat))
    | U_2819 != hAPP(nat,nat,suc,zero_zero(nat))
    | U_2821 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_749_3]) ).

fof(f_750_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_2),J_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_660_mult__less__mono2]) ).

fof(f_750_2,plain,
    ! [U_2824,U_2823,U_2822] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2824),U_2823)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2824),U_2822)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2824))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2823),U_2822)) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

cnf(f_750_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2824),U_2823)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2824),U_2822)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2824))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2823),U_2822)) ),
    inference(clausify,[status(thm)],[f_750_2]) ).

fof(f_751_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),K_2)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_661_mult__less__mono1]) ).

fof(f_751_2,plain,
    ! [U_2827,U_2826,U_2825] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2826),U_2827)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2825),U_2827)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2827))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2826),U_2825)) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

cnf(f_751_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2826),U_2827)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2825),U_2827)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2827))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2826),U_2825)) ),
    inference(clausify,[status(thm)],[f_751_2]) ).

fof(f_752_1,plain,
    ! [M,K,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_662_mult__less__cancel2]) ).

fof(f_752_2,plain,
    ! [U_2830,U_2829,U_2828] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2830),U_2829)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2828),U_2829)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2830),U_2828))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2829)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2830),U_2828))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2829)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2830),U_2829)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2828),U_2829))) ) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

fof(f_752_3,plain,
    ( ! [U_2836,U_2834,U_2832] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2836),U_2834)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2832),U_2834)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2836),U_2832))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2834)) )
    & ! [U_2835,U_2833,U_2831] :
        ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2835),U_2831))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2833)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2835),U_2833)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2831),U_2833))) ) ),
    inference(miniscope,[status(thm)],[f_752_2]) ).

cnf(f_752_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2833))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2835),U_2833)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2831),U_2833))) ),
    inference(clausify,[status(thm)],[f_752_3]) ).

cnf(f_752_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2835),U_2831))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2835),U_2833)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2831),U_2833))) ),
    inference(clausify,[status(thm)],[f_752_3]) ).

cnf(f_752_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2836),U_2834)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2832),U_2834)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2836),U_2832))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2834)) ),
    inference(clausify,[status(thm)],[f_752_3]) ).

fof(f_753_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_663_mult__less__cancel1]) ).

fof(f_753_2,plain,
    ! [U_2839,U_2838,U_2837] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2839),U_2838)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2839),U_2837)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2838),U_2837))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2839)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2838),U_2837))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2839)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2839),U_2838)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2839),U_2837))) ) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ( ! [U_2845,U_2843,U_2841] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2845),U_2843)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2845),U_2841)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2843),U_2841))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2845)) )
    & ! [U_2844,U_2842,U_2840] :
        ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2842),U_2840))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2844)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2844),U_2842)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2844),U_2840))) ) ),
    inference(miniscope,[status(thm)],[f_753_2]) ).

cnf(f_753_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2844))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2844),U_2842)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2844),U_2840))) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

cnf(f_753_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2842),U_2840))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2844),U_2842)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2844),U_2840))) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

cnf(f_753_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2845),U_2843)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2845),U_2841)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2843),U_2841))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2845)) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

fof(f_754_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_664_nat__0__less__mult__iff]) ).

fof(f_754_2,plain,
    ! [U_2847,U_2846] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2847),U_2846)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2846))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2847)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2846))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2847)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2847),U_2846))) ) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

fof(f_754_3,plain,
    ( ! [U_2851,U_2849] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2851),U_2849)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2849))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2851)) )
    & ! [U_2850,U_2848] :
        ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2848))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2850)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2850),U_2848))) ) ),
    inference(miniscope,[status(thm)],[f_754_2]) ).

cnf(f_754_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2850))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2850),U_2848))) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

cnf(f_754_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2848))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2850),U_2848))) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

cnf(f_754_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2851),U_2849)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2849))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2851)) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

fof(f_755_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_665_Suc__mult__less__cancel1]) ).

fof(f_755_2,plain,
    ! [U_2854,U_2853,U_2852] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2854)),U_2853)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2854)),U_2852)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2853),U_2852)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2853),U_2852))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2854)),U_2853)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2854)),U_2852))) ) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ( ! [U_2860,U_2858,U_2856] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2860)),U_2858)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2860)),U_2856)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2858),U_2856)) )
    & ! [U_2859,U_2857,U_2855] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2857),U_2855))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2859)),U_2857)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2859)),U_2855))) ) ),
    inference(miniscope,[status(thm)],[f_755_2]) ).

cnf(f_755_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2857),U_2855))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2859)),U_2857)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2859)),U_2855))) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2860)),U_2858)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2860)),U_2856)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2858),U_2856)) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

fof(f_756_1,plain,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N)),
    inference(fof_nnf,[status(thm)],[fact_666_mult__Suc__right]) ).

fof(f_756_2,plain,
    ! [U_2862,U_2861] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2862),hAPP(nat,nat,suc,U_2861)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2862),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2862),U_2861)),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

cnf(f_756_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2862),hAPP(nat,nat,suc,U_2861)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2862),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2862),U_2861)),
    inference(clausify,[status(thm)],[f_756_2]) ).

fof(f_757_1,plain,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M_3)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N)),
    inference(fof_nnf,[status(thm)],[fact_667_mult__Suc]) ).

fof(f_757_2,plain,
    ! [U_2864,U_2863] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2864)),U_2863) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2863),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2864),U_2863)),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

cnf(f_757_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2864)),U_2863) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2863),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2864),U_2863)),
    inference(clausify,[status(thm)],[f_757_2]) ).

fof(f_758_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_668_Suc__mult__le__cancel1]) ).

fof(f_758_2,plain,
    ! [U_2867,U_2866,U_2865] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2867)),U_2866)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2867)),U_2865)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2866),U_2865)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2866),U_2865))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2867)),U_2866)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2867)),U_2865))) ) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ( ! [U_2873,U_2871,U_2869] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2873)),U_2871)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2873)),U_2869)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2871),U_2869)) )
    & ! [U_2872,U_2870,U_2868] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2870),U_2868))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2872)),U_2870)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2872)),U_2868))) ) ),
    inference(miniscope,[status(thm)],[f_758_2]) ).

cnf(f_758_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2870),U_2868))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2872)),U_2870)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2872)),U_2868))) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

cnf(f_758_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2873)),U_2871)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,U_2873)),U_2869)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2871),U_2869)) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

fof(f_759_1,plain,
    ! [M_3,N] :
      ( M_3 = zero_zero(nat)
      | N = one_one(nat)
      | M_3 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N) ),
    inference(fof_nnf,[status(thm)],[fact_669_mult__eq__self__implies__10]) ).

fof(f_759_2,plain,
    ! [U_2875,U_2874] :
      ( U_2875 = zero_zero(nat)
      | U_2874 = one_one(nat)
      | U_2875 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2875),U_2874) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

cnf(f_759_3,plain,
    ( U_2875 = zero_zero(nat)
    | U_2874 = one_one(nat)
    | U_2875 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2875),U_2874) ),
    inference(clausify,[status(thm)],[f_759_2]) ).

fof(f_760_1,plain,
    ! [X_a,X_b,F,A_1] : hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1))),
    inference(fof_nnf,[status(thm)],[fact_670_restrict__extensional]) ).

fof(f_760_2,plain,
    ! [U_2879,U_2878,U_2877,U_2876] : hBOOL(hAPP(fun(fun(U_2879,U_2878),bool),bool,hAPP(fun(U_2879,U_2878),fun(fun(fun(U_2879,U_2878),bool),bool),member(fun(U_2879,U_2878)),hAPP(fun(U_2879,bool),fun(U_2879,U_2878),hAPP(fun(U_2879,U_2878),fun(fun(U_2879,bool),fun(U_2879,U_2878)),restrict(U_2879,U_2878),U_2877),U_2876)),hAPP(fun(U_2879,bool),fun(fun(U_2879,U_2878),bool),extensional(U_2879,U_2878),U_2876))),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

cnf(f_760_3,plain,
    hBOOL(hAPP(fun(fun(U_2879,U_2878),bool),bool,hAPP(fun(U_2879,U_2878),fun(fun(fun(U_2879,U_2878),bool),bool),member(fun(U_2879,U_2878)),hAPP(fun(U_2879,bool),fun(U_2879,U_2878),hAPP(fun(U_2879,U_2878),fun(fun(U_2879,bool),fun(U_2879,U_2878)),restrict(U_2879,U_2878),U_2877),U_2876)),hAPP(fun(U_2879,bool),fun(fun(U_2879,U_2878),bool),extensional(U_2879,U_2878),U_2876))),
    inference(clausify,[status(thm)],[f_760_2]) ).

fof(f_761_1,plain,
    ! [X_a,X_b,F,A_1] :
      ( hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),restrict(X_a,X_b),F),A_1) = ti(fun(X_a,X_b),F)
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_671_extensional__restrict]) ).

fof(f_761_2,plain,
    ! [U_2883,U_2882,U_2881,U_2880] :
      ( hAPP(fun(U_2883,bool),fun(U_2883,U_2882),hAPP(fun(U_2883,U_2882),fun(fun(U_2883,bool),fun(U_2883,U_2882)),restrict(U_2883,U_2882),U_2881),U_2880) = ti(fun(U_2883,U_2882),U_2881)
      | ~ hBOOL(hAPP(fun(fun(U_2883,U_2882),bool),bool,hAPP(fun(U_2883,U_2882),fun(fun(fun(U_2883,U_2882),bool),bool),member(fun(U_2883,U_2882)),U_2881),hAPP(fun(U_2883,bool),fun(fun(U_2883,U_2882),bool),extensional(U_2883,U_2882),U_2880))) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

cnf(f_761_3,plain,
    ( hAPP(fun(U_2883,bool),fun(U_2883,U_2882),hAPP(fun(U_2883,U_2882),fun(fun(U_2883,bool),fun(U_2883,U_2882)),restrict(U_2883,U_2882),U_2881),U_2880) = ti(fun(U_2883,U_2882),U_2881)
    | ~ hBOOL(hAPP(fun(fun(U_2883,U_2882),bool),bool,hAPP(fun(U_2883,U_2882),fun(fun(fun(U_2883,U_2882),bool),bool),member(fun(U_2883,U_2882)),U_2881),hAPP(fun(U_2883,bool),fun(fun(U_2883,U_2882),bool),extensional(U_2883,U_2882),U_2880))) ),
    inference(clausify,[status(thm)],[f_761_2]) ).

fof(f_762_1,plain,
    ! [X_a,X_b,X_c,A_1,F,G] : hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),hAPP(fun(X_a,bool),fun(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b))),compose(X_a,X_c,X_b),A_1),F),G)),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1))),
    inference(fof_nnf,[status(thm)],[fact_672_compose__extensional]) ).

fof(f_762_2,plain,
    ! [U_2889,U_2888,U_2887,U_2886,U_2885,U_2884] : hBOOL(hAPP(fun(fun(U_2889,U_2888),bool),bool,hAPP(fun(U_2889,U_2888),fun(fun(fun(U_2889,U_2888),bool),bool),member(fun(U_2889,U_2888)),hAPP(fun(U_2889,U_2887),fun(U_2889,U_2888),hAPP(fun(U_2887,U_2888),fun(fun(U_2889,U_2887),fun(U_2889,U_2888)),hAPP(fun(U_2889,bool),fun(fun(U_2887,U_2888),fun(fun(U_2889,U_2887),fun(U_2889,U_2888))),compose(U_2889,U_2887,U_2888),U_2886),U_2885),U_2884)),hAPP(fun(U_2889,bool),fun(fun(U_2889,U_2888),bool),extensional(U_2889,U_2888),U_2886))),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

cnf(f_762_3,plain,
    hBOOL(hAPP(fun(fun(U_2889,U_2888),bool),bool,hAPP(fun(U_2889,U_2888),fun(fun(fun(U_2889,U_2888),bool),bool),member(fun(U_2889,U_2888)),hAPP(fun(U_2889,U_2887),fun(U_2889,U_2888),hAPP(fun(U_2887,U_2888),fun(fun(U_2889,U_2887),fun(U_2889,U_2888)),hAPP(fun(U_2889,bool),fun(fun(U_2887,U_2888),fun(fun(U_2889,U_2887),fun(U_2889,U_2888))),compose(U_2889,U_2887,U_2888),U_2886),U_2885),U_2884)),hAPP(fun(U_2889,bool),fun(fun(U_2889,U_2888),bool),extensional(U_2889,U_2888),U_2886))),
    inference(clausify,[status(thm)],[f_762_2]) ).

fof(f_763_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba)))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) )
            & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba))) ) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ca)) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_673_mult__le__cancel__left__pos]) ).

fof(f_763_2,plain,
    ! [U_2893] :
      ( ! [U_2892,U_2891,U_2890] :
          ( ( ( hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less_eq(U_2893),hAPP(U_2893,U_2893,hAPP(U_2893,fun(U_2893,U_2893),times_times(U_2893),U_2890),U_2892)),hAPP(U_2893,U_2893,hAPP(U_2893,fun(U_2893,U_2893),times_times(U_2893),U_2890),U_2891)))
              | ~ hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less_eq(U_2893),U_2892),U_2891)) )
            & ( hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less_eq(U_2893),U_2892),U_2891))
              | ~ hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less_eq(U_2893),hAPP(U_2893,U_2893,hAPP(U_2893,fun(U_2893,U_2893),times_times(U_2893),U_2890),U_2892)),hAPP(U_2893,U_2893,hAPP(U_2893,fun(U_2893,U_2893),times_times(U_2893),U_2890),U_2891))) ) )
          | ~ hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less(U_2893),zero_zero(U_2893)),U_2890)) )
      | ~ linord581940658strict(U_2893) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

cnf(f_763_3,plain,
    ( hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less_eq(U_2893),U_2892),U_2891))
    | ~ hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less_eq(U_2893),hAPP(U_2893,U_2893,hAPP(U_2893,fun(U_2893,U_2893),times_times(U_2893),U_2890),U_2892)),hAPP(U_2893,U_2893,hAPP(U_2893,fun(U_2893,U_2893),times_times(U_2893),U_2890),U_2891)))
    | ~ hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less(U_2893),zero_zero(U_2893)),U_2890))
    | ~ linord581940658strict(U_2893) ),
    inference(clausify,[status(thm)],[f_763_2]) ).

cnf(f_763_4,plain,
    ( hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less_eq(U_2893),hAPP(U_2893,U_2893,hAPP(U_2893,fun(U_2893,U_2893),times_times(U_2893),U_2890),U_2892)),hAPP(U_2893,U_2893,hAPP(U_2893,fun(U_2893,U_2893),times_times(U_2893),U_2890),U_2891)))
    | ~ hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less_eq(U_2893),U_2892),U_2891))
    | ~ hBOOL(hAPP(U_2893,bool,hAPP(U_2893,fun(U_2893,bool),ord_less(U_2893),zero_zero(U_2893)),U_2890))
    | ~ linord581940658strict(U_2893) ),
    inference(clausify,[status(thm)],[f_763_2]) ).

fof(f_764_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca] :
          ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba)))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) )
            & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa))
              | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ca),Ba))) ) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),zero_zero(X_a))) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_674_mult__le__cancel__left__neg]) ).

fof(f_764_2,plain,
    ! [U_2897] :
      ( ! [U_2896,U_2895,U_2894] :
          ( ( ( hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less_eq(U_2897),hAPP(U_2897,U_2897,hAPP(U_2897,fun(U_2897,U_2897),times_times(U_2897),U_2894),U_2896)),hAPP(U_2897,U_2897,hAPP(U_2897,fun(U_2897,U_2897),times_times(U_2897),U_2894),U_2895)))
              | ~ hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less_eq(U_2897),U_2895),U_2896)) )
            & ( hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less_eq(U_2897),U_2895),U_2896))
              | ~ hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less_eq(U_2897),hAPP(U_2897,U_2897,hAPP(U_2897,fun(U_2897,U_2897),times_times(U_2897),U_2894),U_2896)),hAPP(U_2897,U_2897,hAPP(U_2897,fun(U_2897,U_2897),times_times(U_2897),U_2894),U_2895))) ) )
          | ~ hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less(U_2897),U_2894),zero_zero(U_2897))) )
      | ~ linord581940658strict(U_2897) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

cnf(f_764_3,plain,
    ( hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less_eq(U_2897),U_2895),U_2896))
    | ~ hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less_eq(U_2897),hAPP(U_2897,U_2897,hAPP(U_2897,fun(U_2897,U_2897),times_times(U_2897),U_2894),U_2896)),hAPP(U_2897,U_2897,hAPP(U_2897,fun(U_2897,U_2897),times_times(U_2897),U_2894),U_2895)))
    | ~ hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less(U_2897),U_2894),zero_zero(U_2897)))
    | ~ linord581940658strict(U_2897) ),
    inference(clausify,[status(thm)],[f_764_2]) ).

cnf(f_764_4,plain,
    ( hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less_eq(U_2897),hAPP(U_2897,U_2897,hAPP(U_2897,fun(U_2897,U_2897),times_times(U_2897),U_2894),U_2896)),hAPP(U_2897,U_2897,hAPP(U_2897,fun(U_2897,U_2897),times_times(U_2897),U_2894),U_2895)))
    | ~ hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less_eq(U_2897),U_2895),U_2896))
    | ~ hBOOL(hAPP(U_2897,bool,hAPP(U_2897,fun(U_2897,bool),ord_less(U_2897),U_2894),zero_zero(U_2897)))
    | ~ linord581940658strict(U_2897) ),
    inference(clausify,[status(thm)],[f_764_2]) ).

fof(f_765_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_675_mult__strict__mono]) ).

fof(f_765_2,plain,
    ! [U_2902] :
      ( ! [U_2901,U_2900,U_2899,U_2898] :
          ( hBOOL(hAPP(U_2902,bool,hAPP(U_2902,fun(U_2902,bool),ord_less(U_2902),hAPP(U_2902,U_2902,hAPP(U_2902,fun(U_2902,U_2902),times_times(U_2902),U_2899),U_2901)),hAPP(U_2902,U_2902,hAPP(U_2902,fun(U_2902,U_2902),times_times(U_2902),U_2898),U_2900)))
          | ~ hBOOL(hAPP(U_2902,bool,hAPP(U_2902,fun(U_2902,bool),ord_less_eq(U_2902),zero_zero(U_2902)),U_2901))
          | ~ hBOOL(hAPP(U_2902,bool,hAPP(U_2902,fun(U_2902,bool),ord_less(U_2902),zero_zero(U_2902)),U_2898))
          | ~ hBOOL(hAPP(U_2902,bool,hAPP(U_2902,fun(U_2902,bool),ord_less(U_2902),U_2901),U_2900))
          | ~ hBOOL(hAPP(U_2902,bool,hAPP(U_2902,fun(U_2902,bool),ord_less(U_2902),U_2899),U_2898)) )
      | ~ linord20386208strict(U_2902) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

cnf(f_765_3,plain,
    ( hBOOL(hAPP(U_2902,bool,hAPP(U_2902,fun(U_2902,bool),ord_less(U_2902),hAPP(U_2902,U_2902,hAPP(U_2902,fun(U_2902,U_2902),times_times(U_2902),U_2899),U_2901)),hAPP(U_2902,U_2902,hAPP(U_2902,fun(U_2902,U_2902),times_times(U_2902),U_2898),U_2900)))
    | ~ hBOOL(hAPP(U_2902,bool,hAPP(U_2902,fun(U_2902,bool),ord_less_eq(U_2902),zero_zero(U_2902)),U_2901))
    | ~ hBOOL(hAPP(U_2902,bool,hAPP(U_2902,fun(U_2902,bool),ord_less(U_2902),zero_zero(U_2902)),U_2898))
    | ~ hBOOL(hAPP(U_2902,bool,hAPP(U_2902,fun(U_2902,bool),ord_less(U_2902),U_2901),U_2900))
    | ~ hBOOL(hAPP(U_2902,bool,hAPP(U_2902,fun(U_2902,bool),ord_less(U_2902),U_2899),U_2898))
    | ~ linord20386208strict(U_2902) ),
    inference(clausify,[status(thm)],[f_765_2]) ).

fof(f_766_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_676_mult__strict__mono_H]) ).

fof(f_766_2,plain,
    ! [U_2907] :
      ( ! [U_2906,U_2905,U_2904,U_2903] :
          ( hBOOL(hAPP(U_2907,bool,hAPP(U_2907,fun(U_2907,bool),ord_less(U_2907),hAPP(U_2907,U_2907,hAPP(U_2907,fun(U_2907,U_2907),times_times(U_2907),U_2904),U_2906)),hAPP(U_2907,U_2907,hAPP(U_2907,fun(U_2907,U_2907),times_times(U_2907),U_2903),U_2905)))
          | ~ hBOOL(hAPP(U_2907,bool,hAPP(U_2907,fun(U_2907,bool),ord_less_eq(U_2907),zero_zero(U_2907)),U_2906))
          | ~ hBOOL(hAPP(U_2907,bool,hAPP(U_2907,fun(U_2907,bool),ord_less_eq(U_2907),zero_zero(U_2907)),U_2904))
          | ~ hBOOL(hAPP(U_2907,bool,hAPP(U_2907,fun(U_2907,bool),ord_less(U_2907),U_2906),U_2905))
          | ~ hBOOL(hAPP(U_2907,bool,hAPP(U_2907,fun(U_2907,bool),ord_less(U_2907),U_2904),U_2903)) )
      | ~ linord20386208strict(U_2907) ),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

cnf(f_766_3,plain,
    ( hBOOL(hAPP(U_2907,bool,hAPP(U_2907,fun(U_2907,bool),ord_less(U_2907),hAPP(U_2907,U_2907,hAPP(U_2907,fun(U_2907,U_2907),times_times(U_2907),U_2904),U_2906)),hAPP(U_2907,U_2907,hAPP(U_2907,fun(U_2907,U_2907),times_times(U_2907),U_2903),U_2905)))
    | ~ hBOOL(hAPP(U_2907,bool,hAPP(U_2907,fun(U_2907,bool),ord_less_eq(U_2907),zero_zero(U_2907)),U_2906))
    | ~ hBOOL(hAPP(U_2907,bool,hAPP(U_2907,fun(U_2907,bool),ord_less_eq(U_2907),zero_zero(U_2907)),U_2904))
    | ~ hBOOL(hAPP(U_2907,bool,hAPP(U_2907,fun(U_2907,bool),ord_less(U_2907),U_2906),U_2905))
    | ~ hBOOL(hAPP(U_2907,bool,hAPP(U_2907,fun(U_2907,bool),ord_less(U_2907),U_2904),U_2903))
    | ~ linord20386208strict(U_2907) ),
    inference(clausify,[status(thm)],[f_766_2]) ).

fof(f_767_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_677_mult__less__le__imp__less]) ).

fof(f_767_2,plain,
    ! [U_2912] :
      ( ! [U_2911,U_2910,U_2909,U_2908] :
          ( hBOOL(hAPP(U_2912,bool,hAPP(U_2912,fun(U_2912,bool),ord_less(U_2912),hAPP(U_2912,U_2912,hAPP(U_2912,fun(U_2912,U_2912),times_times(U_2912),U_2909),U_2911)),hAPP(U_2912,U_2912,hAPP(U_2912,fun(U_2912,U_2912),times_times(U_2912),U_2908),U_2910)))
          | ~ hBOOL(hAPP(U_2912,bool,hAPP(U_2912,fun(U_2912,bool),ord_less(U_2912),zero_zero(U_2912)),U_2911))
          | ~ hBOOL(hAPP(U_2912,bool,hAPP(U_2912,fun(U_2912,bool),ord_less_eq(U_2912),zero_zero(U_2912)),U_2909))
          | ~ hBOOL(hAPP(U_2912,bool,hAPP(U_2912,fun(U_2912,bool),ord_less_eq(U_2912),U_2911),U_2910))
          | ~ hBOOL(hAPP(U_2912,bool,hAPP(U_2912,fun(U_2912,bool),ord_less(U_2912),U_2909),U_2908)) )
      | ~ linord20386208strict(U_2912) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

cnf(f_767_3,plain,
    ( hBOOL(hAPP(U_2912,bool,hAPP(U_2912,fun(U_2912,bool),ord_less(U_2912),hAPP(U_2912,U_2912,hAPP(U_2912,fun(U_2912,U_2912),times_times(U_2912),U_2909),U_2911)),hAPP(U_2912,U_2912,hAPP(U_2912,fun(U_2912,U_2912),times_times(U_2912),U_2908),U_2910)))
    | ~ hBOOL(hAPP(U_2912,bool,hAPP(U_2912,fun(U_2912,bool),ord_less(U_2912),zero_zero(U_2912)),U_2911))
    | ~ hBOOL(hAPP(U_2912,bool,hAPP(U_2912,fun(U_2912,bool),ord_less_eq(U_2912),zero_zero(U_2912)),U_2909))
    | ~ hBOOL(hAPP(U_2912,bool,hAPP(U_2912,fun(U_2912,bool),ord_less_eq(U_2912),U_2911),U_2910))
    | ~ hBOOL(hAPP(U_2912,bool,hAPP(U_2912,fun(U_2912,bool),ord_less(U_2912),U_2909),U_2908))
    | ~ linord20386208strict(U_2912) ),
    inference(clausify,[status(thm)],[f_767_2]) ).

fof(f_768_1,plain,
    ! [X_a] :
      ( ! [C_1,D,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_678_mult__le__less__imp__less]) ).

fof(f_768_2,plain,
    ! [U_2917] :
      ( ! [U_2916,U_2915,U_2914,U_2913] :
          ( hBOOL(hAPP(U_2917,bool,hAPP(U_2917,fun(U_2917,bool),ord_less(U_2917),hAPP(U_2917,U_2917,hAPP(U_2917,fun(U_2917,U_2917),times_times(U_2917),U_2914),U_2916)),hAPP(U_2917,U_2917,hAPP(U_2917,fun(U_2917,U_2917),times_times(U_2917),U_2913),U_2915)))
          | ~ hBOOL(hAPP(U_2917,bool,hAPP(U_2917,fun(U_2917,bool),ord_less_eq(U_2917),zero_zero(U_2917)),U_2916))
          | ~ hBOOL(hAPP(U_2917,bool,hAPP(U_2917,fun(U_2917,bool),ord_less(U_2917),zero_zero(U_2917)),U_2914))
          | ~ hBOOL(hAPP(U_2917,bool,hAPP(U_2917,fun(U_2917,bool),ord_less(U_2917),U_2916),U_2915))
          | ~ hBOOL(hAPP(U_2917,bool,hAPP(U_2917,fun(U_2917,bool),ord_less_eq(U_2917),U_2914),U_2913)) )
      | ~ linord20386208strict(U_2917) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

cnf(f_768_3,plain,
    ( hBOOL(hAPP(U_2917,bool,hAPP(U_2917,fun(U_2917,bool),ord_less(U_2917),hAPP(U_2917,U_2917,hAPP(U_2917,fun(U_2917,U_2917),times_times(U_2917),U_2914),U_2916)),hAPP(U_2917,U_2917,hAPP(U_2917,fun(U_2917,U_2917),times_times(U_2917),U_2913),U_2915)))
    | ~ hBOOL(hAPP(U_2917,bool,hAPP(U_2917,fun(U_2917,bool),ord_less_eq(U_2917),zero_zero(U_2917)),U_2916))
    | ~ hBOOL(hAPP(U_2917,bool,hAPP(U_2917,fun(U_2917,bool),ord_less(U_2917),zero_zero(U_2917)),U_2914))
    | ~ hBOOL(hAPP(U_2917,bool,hAPP(U_2917,fun(U_2917,bool),ord_less(U_2917),U_2916),U_2915))
    | ~ hBOOL(hAPP(U_2917,bool,hAPP(U_2917,fun(U_2917,bool),ord_less_eq(U_2917),U_2914),U_2913))
    | ~ linord20386208strict(U_2917) ),
    inference(clausify,[status(thm)],[f_768_2]) ).

fof(f_769_1,plain,
    ! [X_a] :
      ( ! [A_2,C_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))) )
      | ~ linordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_679_mult__right__less__imp__less]) ).

fof(f_769_2,plain,
    ! [U_2921] :
      ( ! [U_2920,U_2919,U_2918] :
          ( hBOOL(hAPP(U_2921,bool,hAPP(U_2921,fun(U_2921,bool),ord_less(U_2921),U_2920),U_2918))
          | ~ hBOOL(hAPP(U_2921,bool,hAPP(U_2921,fun(U_2921,bool),ord_less_eq(U_2921),zero_zero(U_2921)),U_2919))
          | ~ hBOOL(hAPP(U_2921,bool,hAPP(U_2921,fun(U_2921,bool),ord_less(U_2921),hAPP(U_2921,U_2921,hAPP(U_2921,fun(U_2921,U_2921),times_times(U_2921),U_2920),U_2919)),hAPP(U_2921,U_2921,hAPP(U_2921,fun(U_2921,U_2921),times_times(U_2921),U_2918),U_2919))) )
      | ~ linordered_semiring(U_2921) ),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

cnf(f_769_3,plain,
    ( hBOOL(hAPP(U_2921,bool,hAPP(U_2921,fun(U_2921,bool),ord_less(U_2921),U_2920),U_2918))
    | ~ hBOOL(hAPP(U_2921,bool,hAPP(U_2921,fun(U_2921,bool),ord_less_eq(U_2921),zero_zero(U_2921)),U_2919))
    | ~ hBOOL(hAPP(U_2921,bool,hAPP(U_2921,fun(U_2921,bool),ord_less(U_2921),hAPP(U_2921,U_2921,hAPP(U_2921,fun(U_2921,U_2921),times_times(U_2921),U_2920),U_2919)),hAPP(U_2921,U_2921,hAPP(U_2921,fun(U_2921,U_2921),times_times(U_2921),U_2918),U_2919)))
    | ~ linordered_semiring(U_2921) ),
    inference(clausify,[status(thm)],[f_769_2]) ).

fof(f_770_1,plain,
    ! [X_a] :
      ( ! [A_2,C_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_680_mult__less__imp__less__right]) ).

fof(f_770_2,plain,
    ! [U_2925] :
      ( ! [U_2924,U_2923,U_2922] :
          ( hBOOL(hAPP(U_2925,bool,hAPP(U_2925,fun(U_2925,bool),ord_less(U_2925),U_2924),U_2922))
          | ~ hBOOL(hAPP(U_2925,bool,hAPP(U_2925,fun(U_2925,bool),ord_less_eq(U_2925),zero_zero(U_2925)),U_2923))
          | ~ hBOOL(hAPP(U_2925,bool,hAPP(U_2925,fun(U_2925,bool),ord_less(U_2925),hAPP(U_2925,U_2925,hAPP(U_2925,fun(U_2925,U_2925),times_times(U_2925),U_2924),U_2923)),hAPP(U_2925,U_2925,hAPP(U_2925,fun(U_2925,U_2925),times_times(U_2925),U_2922),U_2923))) )
      | ~ linord20386208strict(U_2925) ),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

cnf(f_770_3,plain,
    ( hBOOL(hAPP(U_2925,bool,hAPP(U_2925,fun(U_2925,bool),ord_less(U_2925),U_2924),U_2922))
    | ~ hBOOL(hAPP(U_2925,bool,hAPP(U_2925,fun(U_2925,bool),ord_less_eq(U_2925),zero_zero(U_2925)),U_2923))
    | ~ hBOOL(hAPP(U_2925,bool,hAPP(U_2925,fun(U_2925,bool),ord_less(U_2925),hAPP(U_2925,U_2925,hAPP(U_2925,fun(U_2925,U_2925),times_times(U_2925),U_2924),U_2923)),hAPP(U_2925,U_2925,hAPP(U_2925,fun(U_2925,U_2925),times_times(U_2925),U_2922),U_2923)))
    | ~ linord20386208strict(U_2925) ),
    inference(clausify,[status(thm)],[f_770_2]) ).

fof(f_771_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) )
      | ~ linordered_semiring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_681_mult__left__less__imp__less]) ).

fof(f_771_2,plain,
    ! [U_2929] :
      ( ! [U_2928,U_2927,U_2926] :
          ( hBOOL(hAPP(U_2929,bool,hAPP(U_2929,fun(U_2929,bool),ord_less(U_2929),U_2927),U_2926))
          | ~ hBOOL(hAPP(U_2929,bool,hAPP(U_2929,fun(U_2929,bool),ord_less_eq(U_2929),zero_zero(U_2929)),U_2928))
          | ~ hBOOL(hAPP(U_2929,bool,hAPP(U_2929,fun(U_2929,bool),ord_less(U_2929),hAPP(U_2929,U_2929,hAPP(U_2929,fun(U_2929,U_2929),times_times(U_2929),U_2928),U_2927)),hAPP(U_2929,U_2929,hAPP(U_2929,fun(U_2929,U_2929),times_times(U_2929),U_2928),U_2926))) )
      | ~ linordered_semiring(U_2929) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

cnf(f_771_3,plain,
    ( hBOOL(hAPP(U_2929,bool,hAPP(U_2929,fun(U_2929,bool),ord_less(U_2929),U_2927),U_2926))
    | ~ hBOOL(hAPP(U_2929,bool,hAPP(U_2929,fun(U_2929,bool),ord_less_eq(U_2929),zero_zero(U_2929)),U_2928))
    | ~ hBOOL(hAPP(U_2929,bool,hAPP(U_2929,fun(U_2929,bool),ord_less(U_2929),hAPP(U_2929,U_2929,hAPP(U_2929,fun(U_2929,U_2929),times_times(U_2929),U_2928),U_2927)),hAPP(U_2929,U_2929,hAPP(U_2929,fun(U_2929,U_2929),times_times(U_2929),U_2928),U_2926)))
    | ~ linordered_semiring(U_2929) ),
    inference(clausify,[status(thm)],[f_771_2]) ).

fof(f_772_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_682_mult__less__imp__less__left]) ).

fof(f_772_2,plain,
    ! [U_2933] :
      ( ! [U_2932,U_2931,U_2930] :
          ( hBOOL(hAPP(U_2933,bool,hAPP(U_2933,fun(U_2933,bool),ord_less(U_2933),U_2931),U_2930))
          | ~ hBOOL(hAPP(U_2933,bool,hAPP(U_2933,fun(U_2933,bool),ord_less_eq(U_2933),zero_zero(U_2933)),U_2932))
          | ~ hBOOL(hAPP(U_2933,bool,hAPP(U_2933,fun(U_2933,bool),ord_less(U_2933),hAPP(U_2933,U_2933,hAPP(U_2933,fun(U_2933,U_2933),times_times(U_2933),U_2932),U_2931)),hAPP(U_2933,U_2933,hAPP(U_2933,fun(U_2933,U_2933),times_times(U_2933),U_2932),U_2930))) )
      | ~ linord20386208strict(U_2933) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

cnf(f_772_3,plain,
    ( hBOOL(hAPP(U_2933,bool,hAPP(U_2933,fun(U_2933,bool),ord_less(U_2933),U_2931),U_2930))
    | ~ hBOOL(hAPP(U_2933,bool,hAPP(U_2933,fun(U_2933,bool),ord_less_eq(U_2933),zero_zero(U_2933)),U_2932))
    | ~ hBOOL(hAPP(U_2933,bool,hAPP(U_2933,fun(U_2933,bool),ord_less(U_2933),hAPP(U_2933,U_2933,hAPP(U_2933,fun(U_2933,U_2933),times_times(U_2933),U_2932),U_2931)),hAPP(U_2933,U_2933,hAPP(U_2933,fun(U_2933,U_2933),times_times(U_2933),U_2932),U_2930)))
    | ~ linord20386208strict(U_2933) ),
    inference(clausify,[status(thm)],[f_772_2]) ).

fof(f_773_1,plain,
    ! [X_a] :
      ( ! [A_2,C_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_683_mult__right__le__imp__le]) ).

fof(f_773_2,plain,
    ! [U_2937] :
      ( ! [U_2936,U_2935,U_2934] :
          ( hBOOL(hAPP(U_2937,bool,hAPP(U_2937,fun(U_2937,bool),ord_less_eq(U_2937),U_2936),U_2934))
          | ~ hBOOL(hAPP(U_2937,bool,hAPP(U_2937,fun(U_2937,bool),ord_less(U_2937),zero_zero(U_2937)),U_2935))
          | ~ hBOOL(hAPP(U_2937,bool,hAPP(U_2937,fun(U_2937,bool),ord_less_eq(U_2937),hAPP(U_2937,U_2937,hAPP(U_2937,fun(U_2937,U_2937),times_times(U_2937),U_2936),U_2935)),hAPP(U_2937,U_2937,hAPP(U_2937,fun(U_2937,U_2937),times_times(U_2937),U_2934),U_2935))) )
      | ~ linord20386208strict(U_2937) ),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

cnf(f_773_3,plain,
    ( hBOOL(hAPP(U_2937,bool,hAPP(U_2937,fun(U_2937,bool),ord_less_eq(U_2937),U_2936),U_2934))
    | ~ hBOOL(hAPP(U_2937,bool,hAPP(U_2937,fun(U_2937,bool),ord_less(U_2937),zero_zero(U_2937)),U_2935))
    | ~ hBOOL(hAPP(U_2937,bool,hAPP(U_2937,fun(U_2937,bool),ord_less_eq(U_2937),hAPP(U_2937,U_2937,hAPP(U_2937,fun(U_2937,U_2937),times_times(U_2937),U_2936),U_2935)),hAPP(U_2937,U_2937,hAPP(U_2937,fun(U_2937,U_2937),times_times(U_2937),U_2934),U_2935)))
    | ~ linord20386208strict(U_2937) ),
    inference(clausify,[status(thm)],[f_773_2]) ).

fof(f_774_1,plain,
    ! [X_a] :
      ( ! [C_1,A_2,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) )
      | ~ linord20386208strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_684_mult__left__le__imp__le]) ).

fof(f_774_2,plain,
    ! [U_2941] :
      ( ! [U_2940,U_2939,U_2938] :
          ( hBOOL(hAPP(U_2941,bool,hAPP(U_2941,fun(U_2941,bool),ord_less_eq(U_2941),U_2939),U_2938))
          | ~ hBOOL(hAPP(U_2941,bool,hAPP(U_2941,fun(U_2941,bool),ord_less(U_2941),zero_zero(U_2941)),U_2940))
          | ~ hBOOL(hAPP(U_2941,bool,hAPP(U_2941,fun(U_2941,bool),ord_less_eq(U_2941),hAPP(U_2941,U_2941,hAPP(U_2941,fun(U_2941,U_2941),times_times(U_2941),U_2940),U_2939)),hAPP(U_2941,U_2941,hAPP(U_2941,fun(U_2941,U_2941),times_times(U_2941),U_2940),U_2938))) )
      | ~ linord20386208strict(U_2941) ),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

cnf(f_774_3,plain,
    ( hBOOL(hAPP(U_2941,bool,hAPP(U_2941,fun(U_2941,bool),ord_less_eq(U_2941),U_2939),U_2938))
    | ~ hBOOL(hAPP(U_2941,bool,hAPP(U_2941,fun(U_2941,bool),ord_less(U_2941),zero_zero(U_2941)),U_2940))
    | ~ hBOOL(hAPP(U_2941,bool,hAPP(U_2941,fun(U_2941,bool),ord_less_eq(U_2941),hAPP(U_2941,U_2941,hAPP(U_2941,fun(U_2941,U_2941),times_times(U_2941),U_2940),U_2939)),hAPP(U_2941,U_2941,hAPP(U_2941,fun(U_2941,U_2941),times_times(U_2941),U_2940),U_2938)))
    | ~ linord20386208strict(U_2941) ),
    inference(clausify,[status(thm)],[f_774_2]) ).

fof(f_775_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))))
      | ~ linordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_685_sum__squares__ge__zero]) ).

fof(f_775_2,plain,
    ! [U_2944] :
      ( ! [U_2943,U_2942] : hBOOL(hAPP(U_2944,bool,hAPP(U_2944,fun(U_2944,bool),ord_less_eq(U_2944),zero_zero(U_2944)),hAPP(U_2944,U_2944,hAPP(U_2944,fun(U_2944,U_2944),plus_plus(U_2944),hAPP(U_2944,U_2944,hAPP(U_2944,fun(U_2944,U_2944),times_times(U_2944),U_2943),U_2943)),hAPP(U_2944,U_2944,hAPP(U_2944,fun(U_2944,U_2944),times_times(U_2944),U_2942),U_2942))))
      | ~ linordered_ring(U_2944) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

cnf(f_775_3,plain,
    ( hBOOL(hAPP(U_2944,bool,hAPP(U_2944,fun(U_2944,bool),ord_less_eq(U_2944),zero_zero(U_2944)),hAPP(U_2944,U_2944,hAPP(U_2944,fun(U_2944,U_2944),plus_plus(U_2944),hAPP(U_2944,U_2944,hAPP(U_2944,fun(U_2944,U_2944),times_times(U_2944),U_2943),U_2943)),hAPP(U_2944,U_2944,hAPP(U_2944,fun(U_2944,U_2944),times_times(U_2944),U_2942),U_2942))))
    | ~ linordered_ring(U_2944) ),
    inference(clausify,[status(thm)],[f_775_2]) ).

fof(f_776_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a)))
            | ti(X_a,Y_1) != zero_zero(X_a)
            | ti(X_a,X_2) != zero_zero(X_a) )
          & ( ( ti(X_a,Y_1) = zero_zero(X_a)
              & ti(X_a,X_2) = zero_zero(X_a) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a))) ) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_686_sum__squares__le__zero__iff]) ).

fof(f_776_2,plain,
    ! [U_2947] :
      ( ! [U_2946,U_2945] :
          ( ( hBOOL(hAPP(U_2947,bool,hAPP(U_2947,fun(U_2947,bool),ord_less_eq(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),plus_plus(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2946),U_2946)),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2945),U_2945))),zero_zero(U_2947)))
            | ti(U_2947,U_2945) != zero_zero(U_2947)
            | ti(U_2947,U_2946) != zero_zero(U_2947) )
          & ( ( ti(U_2947,U_2945) = zero_zero(U_2947)
              & ti(U_2947,U_2946) = zero_zero(U_2947) )
            | ~ hBOOL(hAPP(U_2947,bool,hAPP(U_2947,fun(U_2947,bool),ord_less_eq(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),plus_plus(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2946),U_2946)),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2945),U_2945))),zero_zero(U_2947))) ) )
      | ~ linord581940658strict(U_2947) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

fof(f_776_3,plain,
    ! [U_2947] :
      ( ( ! [U_2951,U_2949] :
            ( hBOOL(hAPP(U_2947,bool,hAPP(U_2947,fun(U_2947,bool),ord_less_eq(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),plus_plus(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2951),U_2951)),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2949),U_2949))),zero_zero(U_2947)))
            | ti(U_2947,U_2949) != zero_zero(U_2947)
            | ti(U_2947,U_2951) != zero_zero(U_2947) )
        & ! [U_2950,U_2948] :
            ( ( ti(U_2947,U_2948) = zero_zero(U_2947)
              & ti(U_2947,U_2950) = zero_zero(U_2947) )
            | ~ hBOOL(hAPP(U_2947,bool,hAPP(U_2947,fun(U_2947,bool),ord_less_eq(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),plus_plus(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2950),U_2950)),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2948),U_2948))),zero_zero(U_2947))) ) )
      | ~ linord581940658strict(U_2947) ),
    inference(miniscope,[status(thm)],[f_776_2]) ).

cnf(f_776_4,plain,
    ( ti(U_2947,U_2950) = zero_zero(U_2947)
    | ~ hBOOL(hAPP(U_2947,bool,hAPP(U_2947,fun(U_2947,bool),ord_less_eq(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),plus_plus(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2950),U_2950)),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2948),U_2948))),zero_zero(U_2947)))
    | ~ linord581940658strict(U_2947) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

cnf(f_776_5,plain,
    ( ti(U_2947,U_2948) = zero_zero(U_2947)
    | ~ hBOOL(hAPP(U_2947,bool,hAPP(U_2947,fun(U_2947,bool),ord_less_eq(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),plus_plus(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2950),U_2950)),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2948),U_2948))),zero_zero(U_2947)))
    | ~ linord581940658strict(U_2947) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

cnf(f_776_6,plain,
    ( hBOOL(hAPP(U_2947,bool,hAPP(U_2947,fun(U_2947,bool),ord_less_eq(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),plus_plus(U_2947),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2951),U_2951)),hAPP(U_2947,U_2947,hAPP(U_2947,fun(U_2947,U_2947),times_times(U_2947),U_2949),U_2949))),zero_zero(U_2947)))
    | ti(U_2947,U_2949) != zero_zero(U_2947)
    | ti(U_2947,U_2951) != zero_zero(U_2947)
    | ~ linord581940658strict(U_2947) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

fof(f_777_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))))
            | ( ti(X_a,Y_1) = zero_zero(X_a)
              & ti(X_a,X_2) = zero_zero(X_a) ) )
          & ( ti(X_a,Y_1) != zero_zero(X_a)
            | ti(X_a,X_2) != zero_zero(X_a)
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)))) ) )
      | ~ linord581940658strict(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_687_sum__squares__gt__zero__iff]) ).

fof(f_777_2,plain,
    ! [U_2954] :
      ( ! [U_2953,U_2952] :
          ( ( hBOOL(hAPP(U_2954,bool,hAPP(U_2954,fun(U_2954,bool),ord_less(U_2954),zero_zero(U_2954)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),plus_plus(U_2954),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2953),U_2953)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2952),U_2952))))
            | ( ti(U_2954,U_2952) = zero_zero(U_2954)
              & ti(U_2954,U_2953) = zero_zero(U_2954) ) )
          & ( ti(U_2954,U_2952) != zero_zero(U_2954)
            | ti(U_2954,U_2953) != zero_zero(U_2954)
            | ~ hBOOL(hAPP(U_2954,bool,hAPP(U_2954,fun(U_2954,bool),ord_less(U_2954),zero_zero(U_2954)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),plus_plus(U_2954),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2953),U_2953)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2952),U_2952)))) ) )
      | ~ linord581940658strict(U_2954) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

fof(f_777_3,plain,
    ! [U_2954] :
      ( ( ! [U_2958,U_2956] :
            ( hBOOL(hAPP(U_2954,bool,hAPP(U_2954,fun(U_2954,bool),ord_less(U_2954),zero_zero(U_2954)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),plus_plus(U_2954),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2958),U_2958)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2956),U_2956))))
            | ( ti(U_2954,U_2956) = zero_zero(U_2954)
              & ti(U_2954,U_2958) = zero_zero(U_2954) ) )
        & ! [U_2957,U_2955] :
            ( ti(U_2954,U_2955) != zero_zero(U_2954)
            | ti(U_2954,U_2957) != zero_zero(U_2954)
            | ~ hBOOL(hAPP(U_2954,bool,hAPP(U_2954,fun(U_2954,bool),ord_less(U_2954),zero_zero(U_2954)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),plus_plus(U_2954),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2957),U_2957)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2955),U_2955)))) ) )
      | ~ linord581940658strict(U_2954) ),
    inference(miniscope,[status(thm)],[f_777_2]) ).

cnf(f_777_4,plain,
    ( ti(U_2954,U_2955) != zero_zero(U_2954)
    | ti(U_2954,U_2957) != zero_zero(U_2954)
    | ~ hBOOL(hAPP(U_2954,bool,hAPP(U_2954,fun(U_2954,bool),ord_less(U_2954),zero_zero(U_2954)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),plus_plus(U_2954),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2957),U_2957)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2955),U_2955))))
    | ~ linord581940658strict(U_2954) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

cnf(f_777_5,plain,
    ( ti(U_2954,U_2958) = zero_zero(U_2954)
    | hBOOL(hAPP(U_2954,bool,hAPP(U_2954,fun(U_2954,bool),ord_less(U_2954),zero_zero(U_2954)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),plus_plus(U_2954),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2958),U_2958)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2956),U_2956))))
    | ~ linord581940658strict(U_2954) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

cnf(f_777_6,plain,
    ( ti(U_2954,U_2956) = zero_zero(U_2954)
    | hBOOL(hAPP(U_2954,bool,hAPP(U_2954,fun(U_2954,bool),ord_less(U_2954),zero_zero(U_2954)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),plus_plus(U_2954),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2958),U_2958)),hAPP(U_2954,U_2954,hAPP(U_2954,fun(U_2954,U_2954),times_times(U_2954),U_2956),U_2956))))
    | ~ linord581940658strict(U_2954) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

fof(f_778_1,plain,
    ! [X_a] :
      ( ! [X,Y] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))),zero_zero(X_a)))
      | ~ linordered_ring(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_688_not__sum__squares__lt__zero]) ).

fof(f_778_2,plain,
    ! [U_2961] :
      ( ! [U_2960,U_2959] : ~ hBOOL(hAPP(U_2961,bool,hAPP(U_2961,fun(U_2961,bool),ord_less(U_2961),hAPP(U_2961,U_2961,hAPP(U_2961,fun(U_2961,U_2961),plus_plus(U_2961),hAPP(U_2961,U_2961,hAPP(U_2961,fun(U_2961,U_2961),times_times(U_2961),U_2960),U_2960)),hAPP(U_2961,U_2961,hAPP(U_2961,fun(U_2961,U_2961),times_times(U_2961),U_2959),U_2959))),zero_zero(U_2961)))
      | ~ linordered_ring(U_2961) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

cnf(f_778_3,plain,
    ( ~ hBOOL(hAPP(U_2961,bool,hAPP(U_2961,fun(U_2961,bool),ord_less(U_2961),hAPP(U_2961,U_2961,hAPP(U_2961,fun(U_2961,U_2961),plus_plus(U_2961),hAPP(U_2961,U_2961,hAPP(U_2961,fun(U_2961,U_2961),times_times(U_2961),U_2960),U_2960)),hAPP(U_2961,U_2961,hAPP(U_2961,fun(U_2961,U_2961),times_times(U_2961),U_2959),U_2959))),zero_zero(U_2961)))
    | ~ linordered_ring(U_2961) ),
    inference(clausify,[status(thm)],[f_778_2]) ).

fof(f_779_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) )
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_689_mult__left__le__one__le]) ).

fof(f_779_2,plain,
    ! [U_2964] :
      ( ! [U_2963,U_2962] :
          ( hBOOL(hAPP(U_2964,bool,hAPP(U_2964,fun(U_2964,bool),ord_less_eq(U_2964),hAPP(U_2964,U_2964,hAPP(U_2964,fun(U_2964,U_2964),times_times(U_2964),U_2963),U_2962)),U_2962))
          | ~ hBOOL(hAPP(U_2964,bool,hAPP(U_2964,fun(U_2964,bool),ord_less_eq(U_2964),U_2963),one_one(U_2964)))
          | ~ hBOOL(hAPP(U_2964,bool,hAPP(U_2964,fun(U_2964,bool),ord_less_eq(U_2964),zero_zero(U_2964)),U_2963))
          | ~ hBOOL(hAPP(U_2964,bool,hAPP(U_2964,fun(U_2964,bool),ord_less_eq(U_2964),zero_zero(U_2964)),U_2962)) )
      | ~ linordered_idom(U_2964) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

cnf(f_779_3,plain,
    ( hBOOL(hAPP(U_2964,bool,hAPP(U_2964,fun(U_2964,bool),ord_less_eq(U_2964),hAPP(U_2964,U_2964,hAPP(U_2964,fun(U_2964,U_2964),times_times(U_2964),U_2963),U_2962)),U_2962))
    | ~ hBOOL(hAPP(U_2964,bool,hAPP(U_2964,fun(U_2964,bool),ord_less_eq(U_2964),U_2963),one_one(U_2964)))
    | ~ hBOOL(hAPP(U_2964,bool,hAPP(U_2964,fun(U_2964,bool),ord_less_eq(U_2964),zero_zero(U_2964)),U_2963))
    | ~ hBOOL(hAPP(U_2964,bool,hAPP(U_2964,fun(U_2964,bool),ord_less_eq(U_2964),zero_zero(U_2964)),U_2962))
    | ~ linordered_idom(U_2964) ),
    inference(clausify,[status(thm)],[f_779_2]) ).

fof(f_780_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) )
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_690_mult__right__le__one__le]) ).

fof(f_780_2,plain,
    ! [U_2967] :
      ( ! [U_2966,U_2965] :
          ( hBOOL(hAPP(U_2967,bool,hAPP(U_2967,fun(U_2967,bool),ord_less_eq(U_2967),hAPP(U_2967,U_2967,hAPP(U_2967,fun(U_2967,U_2967),times_times(U_2967),U_2965),U_2966)),U_2965))
          | ~ hBOOL(hAPP(U_2967,bool,hAPP(U_2967,fun(U_2967,bool),ord_less_eq(U_2967),U_2966),one_one(U_2967)))
          | ~ hBOOL(hAPP(U_2967,bool,hAPP(U_2967,fun(U_2967,bool),ord_less_eq(U_2967),zero_zero(U_2967)),U_2966))
          | ~ hBOOL(hAPP(U_2967,bool,hAPP(U_2967,fun(U_2967,bool),ord_less_eq(U_2967),zero_zero(U_2967)),U_2965)) )
      | ~ linordered_idom(U_2967) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

cnf(f_780_3,plain,
    ( hBOOL(hAPP(U_2967,bool,hAPP(U_2967,fun(U_2967,bool),ord_less_eq(U_2967),hAPP(U_2967,U_2967,hAPP(U_2967,fun(U_2967,U_2967),times_times(U_2967),U_2965),U_2966)),U_2965))
    | ~ hBOOL(hAPP(U_2967,bool,hAPP(U_2967,fun(U_2967,bool),ord_less_eq(U_2967),U_2966),one_one(U_2967)))
    | ~ hBOOL(hAPP(U_2967,bool,hAPP(U_2967,fun(U_2967,bool),ord_less_eq(U_2967),zero_zero(U_2967)),U_2966))
    | ~ hBOOL(hAPP(U_2967,bool,hAPP(U_2967,fun(U_2967,bool),ord_less_eq(U_2967),zero_zero(U_2967)),U_2965))
    | ~ linordered_idom(U_2967) ),
    inference(clausify,[status(thm)],[f_780_2]) ).

fof(f_781_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_3))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) ),
    inference(fof_nnf,[status(thm)],[fact_691_n__less__m__mult__n]) ).

fof(f_781_2,plain,
    ! [U_2969,U_2968] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2968),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2969),U_2968)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2969))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2968)) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

cnf(f_781_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2968),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2969),U_2968)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2969))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2968)) ),
    inference(clausify,[status(thm)],[f_781_2]) ).

fof(f_782_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_3)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_3))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) ),
    inference(fof_nnf,[status(thm)],[fact_692_n__less__n__mult__m]) ).

fof(f_782_2,plain,
    ! [U_2971,U_2970] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2970),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2970),U_2971)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2971))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2970)) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

cnf(f_782_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_2970),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2970),U_2971)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2971))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2970)) ),
    inference(clausify,[status(thm)],[f_782_2]) ).

fof(f_783_1,plain,
    ! [M_3,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_3))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) ),
    inference(fof_nnf,[status(thm)],[fact_693_one__less__mult]) ).

fof(f_783_2,plain,
    ! [U_2973,U_2972] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2973),U_2972)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2973))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2972)) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

cnf(f_783_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2973),U_2972)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2973))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2972)) ),
    inference(clausify,[status(thm)],[f_783_2]) ).

fof(f_784_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_694_one__le__mult__iff]) ).

fof(f_784_2,plain,
    ! [U_2975,U_2974] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2975),U_2974)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2974))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2975)) )
      & ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2974))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2975)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2975),U_2974))) ) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

fof(f_784_3,plain,
    ( ! [U_2979,U_2977] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2979),U_2977)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2977))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2979)) )
    & ! [U_2978,U_2976] :
        ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2976))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2978)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2978),U_2976))) ) ),
    inference(miniscope,[status(thm)],[f_784_2]) ).

cnf(f_784_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2978))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2978),U_2976))) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

cnf(f_784_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2976))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2978),U_2976))) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

cnf(f_784_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2979),U_2977)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2977))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_2979)) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

fof(f_785_1,plain,
    ! [M,K,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_695_mult__le__cancel2]) ).

fof(f_785_2,plain,
    ! [U_2982,U_2981,U_2980] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2982),U_2981)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2980),U_2981)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2982),U_2980))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2981)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2982),U_2980))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2981))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2982),U_2981)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2980),U_2981))) ) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

fof(f_785_3,plain,
    ( ! [U_2988,U_2986,U_2984] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2988),U_2986)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2984),U_2986)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2988),U_2984))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2986)) ) )
    & ! [U_2987,U_2985,U_2983] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2987),U_2983))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2985))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2987),U_2985)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2983),U_2985))) ) ),
    inference(miniscope,[status(thm)],[f_785_2]) ).

cnf(f_785_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2987),U_2983))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2985))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2987),U_2985)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2983),U_2985))) ),
    inference(clausify,[status(thm)],[f_785_3]) ).

cnf(f_785_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2986))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2988),U_2986)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2984),U_2986))) ),
    inference(clausify,[status(thm)],[f_785_3]) ).

cnf(f_785_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2988),U_2984))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2988),U_2986)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2984),U_2986))) ),
    inference(clausify,[status(thm)],[f_785_3]) ).

fof(f_786_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_696_mult__le__cancel1]) ).

fof(f_786_2,plain,
    ! [U_2991,U_2990,U_2989] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2991),U_2990)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2991),U_2989)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2990),U_2989))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2991)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2990),U_2989))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2991))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2991),U_2990)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2991),U_2989))) ) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

fof(f_786_3,plain,
    ( ! [U_2997,U_2995,U_2993] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2997),U_2995)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2997),U_2993)))
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2995),U_2993))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2997)) ) )
    & ! [U_2996,U_2994,U_2992] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2994),U_2992))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2996))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2996),U_2994)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2996),U_2992))) ) ),
    inference(miniscope,[status(thm)],[f_786_2]) ).

cnf(f_786_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2994),U_2992))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2996))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2996),U_2994)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2996),U_2992))) ),
    inference(clausify,[status(thm)],[f_786_3]) ).

cnf(f_786_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_2997))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2997),U_2995)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2997),U_2993))) ),
    inference(clausify,[status(thm)],[f_786_3]) ).

cnf(f_786_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2995),U_2993))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2997),U_2995)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_2997),U_2993))) ),
    inference(clausify,[status(thm)],[f_786_3]) ).

fof(f_787_1,plain,
    ! [X_a,X_b] :
      ( ! [G,Ha,A_1] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Ha)),one_one(X_b)),A_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),one_one(X_b)),A_1)),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),Ha),one_one(X_b)),A_1))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_mult(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_697_fold__image__distrib]) ).

fof(f_787_2,plain,
    ! [U_3002,U_3001] :
      ( ! [U_3000,U_2999,U_2998] :
          ( hAPP(fun(U_3002,bool),U_3001,hAPP(U_3001,fun(fun(U_3002,bool),U_3001),hAPP(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001)),hAPP(fun(U_3001,fun(U_3001,U_3001)),fun(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001))),finite_fold_image(U_3001,U_3002),times_times(U_3001)),hAPP(fun(U_3002,U_3001),fun(U_3002,U_3001),hAPP(fun(U_3002,fun(U_3001,U_3001)),fun(fun(U_3002,U_3001),fun(U_3002,U_3001)),combs(U_3002,U_3001,U_3001),hAPP(fun(U_3002,U_3001),fun(U_3002,fun(U_3001,U_3001)),hAPP(fun(U_3001,fun(U_3001,U_3001)),fun(fun(U_3002,U_3001),fun(U_3002,fun(U_3001,U_3001))),combb(U_3001,fun(U_3001,U_3001),U_3002),times_times(U_3001)),U_3000)),U_2999)),one_one(U_3001)),U_2998) = hAPP(U_3001,U_3001,hAPP(U_3001,fun(U_3001,U_3001),times_times(U_3001),hAPP(fun(U_3002,bool),U_3001,hAPP(U_3001,fun(fun(U_3002,bool),U_3001),hAPP(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001)),hAPP(fun(U_3001,fun(U_3001,U_3001)),fun(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001))),finite_fold_image(U_3001,U_3002),times_times(U_3001)),U_3000),one_one(U_3001)),U_2998)),hAPP(fun(U_3002,bool),U_3001,hAPP(U_3001,fun(fun(U_3002,bool),U_3001),hAPP(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001)),hAPP(fun(U_3001,fun(U_3001,U_3001)),fun(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001))),finite_fold_image(U_3001,U_3002),times_times(U_3001)),U_2999),one_one(U_3001)),U_2998))
          | ~ hBOOL(hAPP(fun(U_3002,bool),bool,finite_finite_1(U_3002),U_2998)) )
      | ~ comm_monoid_mult(U_3001) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

cnf(f_787_3,plain,
    ( hAPP(fun(U_3002,bool),U_3001,hAPP(U_3001,fun(fun(U_3002,bool),U_3001),hAPP(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001)),hAPP(fun(U_3001,fun(U_3001,U_3001)),fun(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001))),finite_fold_image(U_3001,U_3002),times_times(U_3001)),hAPP(fun(U_3002,U_3001),fun(U_3002,U_3001),hAPP(fun(U_3002,fun(U_3001,U_3001)),fun(fun(U_3002,U_3001),fun(U_3002,U_3001)),combs(U_3002,U_3001,U_3001),hAPP(fun(U_3002,U_3001),fun(U_3002,fun(U_3001,U_3001)),hAPP(fun(U_3001,fun(U_3001,U_3001)),fun(fun(U_3002,U_3001),fun(U_3002,fun(U_3001,U_3001))),combb(U_3001,fun(U_3001,U_3001),U_3002),times_times(U_3001)),U_3000)),U_2999)),one_one(U_3001)),U_2998) = hAPP(U_3001,U_3001,hAPP(U_3001,fun(U_3001,U_3001),times_times(U_3001),hAPP(fun(U_3002,bool),U_3001,hAPP(U_3001,fun(fun(U_3002,bool),U_3001),hAPP(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001)),hAPP(fun(U_3001,fun(U_3001,U_3001)),fun(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001))),finite_fold_image(U_3001,U_3002),times_times(U_3001)),U_3000),one_one(U_3001)),U_2998)),hAPP(fun(U_3002,bool),U_3001,hAPP(U_3001,fun(fun(U_3002,bool),U_3001),hAPP(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001)),hAPP(fun(U_3001,fun(U_3001,U_3001)),fun(fun(U_3002,U_3001),fun(U_3001,fun(fun(U_3002,bool),U_3001))),finite_fold_image(U_3001,U_3002),times_times(U_3001)),U_2999),one_one(U_3001)),U_2998))
    | ~ hBOOL(hAPP(fun(U_3002,bool),bool,finite_finite_1(U_3002),U_2998))
    | ~ comm_monoid_mult(U_3001) ),
    inference(clausify,[status(thm)],[f_787_2]) ).

fof(f_788_1,plain,
    ! [X_a] :
      ( ! [V_2,U_1,Y,X,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V_2),Y))),A_2))
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V_2) != one_one(X_a)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),A_2))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2)) )
      | ~ linord1278240602ring_1(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_698_convex__bound__le]) ).

fof(f_788_2,plain,
    ! [U_3008] :
      ( ! [U_3007,U_3006,U_3005,U_3004,U_3003] :
          ( hBOOL(hAPP(U_3008,bool,hAPP(U_3008,fun(U_3008,bool),ord_less_eq(U_3008),hAPP(U_3008,U_3008,hAPP(U_3008,fun(U_3008,U_3008),plus_plus(U_3008),hAPP(U_3008,U_3008,hAPP(U_3008,fun(U_3008,U_3008),times_times(U_3008),U_3006),U_3004)),hAPP(U_3008,U_3008,hAPP(U_3008,fun(U_3008,U_3008),times_times(U_3008),U_3007),U_3005))),U_3003))
          | hAPP(U_3008,U_3008,hAPP(U_3008,fun(U_3008,U_3008),plus_plus(U_3008),U_3006),U_3007) != one_one(U_3008)
          | ~ hBOOL(hAPP(U_3008,bool,hAPP(U_3008,fun(U_3008,bool),ord_less_eq(U_3008),zero_zero(U_3008)),U_3007))
          | ~ hBOOL(hAPP(U_3008,bool,hAPP(U_3008,fun(U_3008,bool),ord_less_eq(U_3008),zero_zero(U_3008)),U_3006))
          | ~ hBOOL(hAPP(U_3008,bool,hAPP(U_3008,fun(U_3008,bool),ord_less_eq(U_3008),U_3005),U_3003))
          | ~ hBOOL(hAPP(U_3008,bool,hAPP(U_3008,fun(U_3008,bool),ord_less_eq(U_3008),U_3004),U_3003)) )
      | ~ linord1278240602ring_1(U_3008) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

cnf(f_788_3,plain,
    ( hBOOL(hAPP(U_3008,bool,hAPP(U_3008,fun(U_3008,bool),ord_less_eq(U_3008),hAPP(U_3008,U_3008,hAPP(U_3008,fun(U_3008,U_3008),plus_plus(U_3008),hAPP(U_3008,U_3008,hAPP(U_3008,fun(U_3008,U_3008),times_times(U_3008),U_3006),U_3004)),hAPP(U_3008,U_3008,hAPP(U_3008,fun(U_3008,U_3008),times_times(U_3008),U_3007),U_3005))),U_3003))
    | hAPP(U_3008,U_3008,hAPP(U_3008,fun(U_3008,U_3008),plus_plus(U_3008),U_3006),U_3007) != one_one(U_3008)
    | ~ hBOOL(hAPP(U_3008,bool,hAPP(U_3008,fun(U_3008,bool),ord_less_eq(U_3008),zero_zero(U_3008)),U_3007))
    | ~ hBOOL(hAPP(U_3008,bool,hAPP(U_3008,fun(U_3008,bool),ord_less_eq(U_3008),zero_zero(U_3008)),U_3006))
    | ~ hBOOL(hAPP(U_3008,bool,hAPP(U_3008,fun(U_3008,bool),ord_less_eq(U_3008),U_3005),U_3003))
    | ~ hBOOL(hAPP(U_3008,bool,hAPP(U_3008,fun(U_3008,bool),ord_less_eq(U_3008),U_3004),U_3003))
    | ~ linord1278240602ring_1(U_3008) ),
    inference(clausify,[status(thm)],[f_788_2]) ).

fof(f_789_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
          | ? [Z_2] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_2),X)),Y))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),one_one(X_a)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_2)) ) )
      | ~ linord1117847801e_zero(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_699_field__le__mult__one__interval]) ).

fof(f_789_2,plain,
    ! [U_3012] :
      ( ! [U_3011,U_3010] :
          ( hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less_eq(U_3012),U_3011),U_3010))
          | ? [U_3009] :
              ( ~ hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less_eq(U_3012),hAPP(U_3012,U_3012,hAPP(U_3012,fun(U_3012,U_3012),times_times(U_3012),U_3009),U_3011)),U_3010))
              & hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less(U_3012),U_3009),one_one(U_3012)))
              & hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less(U_3012),zero_zero(U_3012)),U_3009)) ) )
      | ~ linord1117847801e_zero(U_3012) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ! [U_3012] :
      ( ! [U_3011,U_3010] :
          ( hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less_eq(U_3012),U_3011),U_3010))
          | ( ~ hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less_eq(U_3012),hAPP(U_3012,U_3012,hAPP(U_3012,fun(U_3012,U_3012),times_times(U_3012),sK143(U_3012,U_3011,U_3010)),U_3011)),U_3010))
            & hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less(U_3012),sK143(U_3012,U_3011,U_3010)),one_one(U_3012)))
            & hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less(U_3012),zero_zero(U_3012)),sK143(U_3012,U_3011,U_3010))) ) )
      | ~ linord1117847801e_zero(U_3012) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_3009,sK143(U_3012,U_3011,U_3010))],[f_789_2]) ).

cnf(f_789_4,plain,
    ( hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less(U_3012),zero_zero(U_3012)),sK143(U_3012,U_3011,U_3010)))
    | hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less_eq(U_3012),U_3011),U_3010))
    | ~ linord1117847801e_zero(U_3012) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

cnf(f_789_5,plain,
    ( hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less(U_3012),sK143(U_3012,U_3011,U_3010)),one_one(U_3012)))
    | hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less_eq(U_3012),U_3011),U_3010))
    | ~ linord1117847801e_zero(U_3012) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

cnf(f_789_6,plain,
    ( ~ hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less_eq(U_3012),hAPP(U_3012,U_3012,hAPP(U_3012,fun(U_3012,U_3012),times_times(U_3012),sK143(U_3012,U_3011,U_3010)),U_3011)),U_3010))
    | hBOOL(hAPP(U_3012,bool,hAPP(U_3012,fun(U_3012,bool),ord_less_eq(U_3012),U_3011),U_3010))
    | ~ linord1117847801e_zero(U_3012) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

fof(f_790_1,plain,
    ! [X_a,X_b] :
      ( ! [F,S] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),F),one_one(X_b)),S) = one_one(X_b)
          | ? [X_1] :
              ( hAPP(X_a,X_b,F,X_1) != one_one(X_b)
              & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),S)) )
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) )
      | ~ comm_monoid_mult(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_700_fold__image__1]) ).

fof(f_790_2,plain,
    ! [U_3017,U_3016] :
      ( ! [U_3015,U_3014] :
          ( hAPP(fun(U_3017,bool),U_3016,hAPP(U_3016,fun(fun(U_3017,bool),U_3016),hAPP(fun(U_3017,U_3016),fun(U_3016,fun(fun(U_3017,bool),U_3016)),hAPP(fun(U_3016,fun(U_3016,U_3016)),fun(fun(U_3017,U_3016),fun(U_3016,fun(fun(U_3017,bool),U_3016))),finite_fold_image(U_3016,U_3017),times_times(U_3016)),U_3015),one_one(U_3016)),U_3014) = one_one(U_3016)
          | ? [U_3013] :
              ( hAPP(U_3017,U_3016,U_3015,U_3013) != one_one(U_3016)
              & hBOOL(hAPP(fun(U_3017,bool),bool,hAPP(U_3017,fun(fun(U_3017,bool),bool),member(U_3017),U_3013),U_3014)) )
          | ~ hBOOL(hAPP(fun(U_3017,bool),bool,finite_finite_1(U_3017),U_3014)) )
      | ~ comm_monoid_mult(U_3016) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

fof(f_790_3,plain,
    ! [U_3017,U_3016] :
      ( ! [U_3015,U_3014] :
          ( hAPP(fun(U_3017,bool),U_3016,hAPP(U_3016,fun(fun(U_3017,bool),U_3016),hAPP(fun(U_3017,U_3016),fun(U_3016,fun(fun(U_3017,bool),U_3016)),hAPP(fun(U_3016,fun(U_3016,U_3016)),fun(fun(U_3017,U_3016),fun(U_3016,fun(fun(U_3017,bool),U_3016))),finite_fold_image(U_3016,U_3017),times_times(U_3016)),U_3015),one_one(U_3016)),U_3014) = one_one(U_3016)
          | ( hAPP(U_3017,U_3016,U_3015,sK144(U_3017,U_3016,U_3015,U_3014)) != one_one(U_3016)
            & hBOOL(hAPP(fun(U_3017,bool),bool,hAPP(U_3017,fun(fun(U_3017,bool),bool),member(U_3017),sK144(U_3017,U_3016,U_3015,U_3014)),U_3014)) )
          | ~ hBOOL(hAPP(fun(U_3017,bool),bool,finite_finite_1(U_3017),U_3014)) )
      | ~ comm_monoid_mult(U_3016) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_3013,sK144(U_3017,U_3016,U_3015,U_3014))],[f_790_2]) ).

cnf(f_790_4,plain,
    ( hBOOL(hAPP(fun(U_3017,bool),bool,hAPP(U_3017,fun(fun(U_3017,bool),bool),member(U_3017),sK144(U_3017,U_3016,U_3015,U_3014)),U_3014))
    | hAPP(fun(U_3017,bool),U_3016,hAPP(U_3016,fun(fun(U_3017,bool),U_3016),hAPP(fun(U_3017,U_3016),fun(U_3016,fun(fun(U_3017,bool),U_3016)),hAPP(fun(U_3016,fun(U_3016,U_3016)),fun(fun(U_3017,U_3016),fun(U_3016,fun(fun(U_3017,bool),U_3016))),finite_fold_image(U_3016,U_3017),times_times(U_3016)),U_3015),one_one(U_3016)),U_3014) = one_one(U_3016)
    | ~ hBOOL(hAPP(fun(U_3017,bool),bool,finite_finite_1(U_3017),U_3014))
    | ~ comm_monoid_mult(U_3016) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

cnf(f_790_5,plain,
    ( hAPP(U_3017,U_3016,U_3015,sK144(U_3017,U_3016,U_3015,U_3014)) != one_one(U_3016)
    | hAPP(fun(U_3017,bool),U_3016,hAPP(U_3016,fun(fun(U_3017,bool),U_3016),hAPP(fun(U_3017,U_3016),fun(U_3016,fun(fun(U_3017,bool),U_3016)),hAPP(fun(U_3016,fun(U_3016,U_3016)),fun(fun(U_3017,U_3016),fun(U_3016,fun(fun(U_3017,bool),U_3016))),finite_fold_image(U_3016,U_3017),times_times(U_3016)),U_3015),one_one(U_3016)),U_3014) = one_one(U_3016)
    | ~ hBOOL(hAPP(fun(U_3017,bool),bool,finite_finite_1(U_3017),U_3014))
    | ~ comm_monoid_mult(U_3016) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

fof(f_791_1,plain,
    ! [X_a,X_b] :
      ( ! [Z_1,G,Ha,A_1] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),Z_1),A_1) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),Ha),Z_1),A_1)
          | ? [X_1] :
              ( hAPP(X_a,X_b,G,X_1) != hAPP(X_a,X_b,Ha,X_1)
              & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) )
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ ab_semigroup_mult(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_701_fold__image__cong]) ).

fof(f_791_2,plain,
    ! [U_3024,U_3023] :
      ( ! [U_3022,U_3021,U_3020,U_3019] :
          ( hAPP(fun(U_3024,bool),U_3023,hAPP(U_3023,fun(fun(U_3024,bool),U_3023),hAPP(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023)),hAPP(fun(U_3023,fun(U_3023,U_3023)),fun(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023))),finite_fold_image(U_3023,U_3024),times_times(U_3023)),U_3021),U_3022),U_3019) = hAPP(fun(U_3024,bool),U_3023,hAPP(U_3023,fun(fun(U_3024,bool),U_3023),hAPP(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023)),hAPP(fun(U_3023,fun(U_3023,U_3023)),fun(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023))),finite_fold_image(U_3023,U_3024),times_times(U_3023)),U_3020),U_3022),U_3019)
          | ? [U_3018] :
              ( hAPP(U_3024,U_3023,U_3021,U_3018) != hAPP(U_3024,U_3023,U_3020,U_3018)
              & hBOOL(hAPP(fun(U_3024,bool),bool,hAPP(U_3024,fun(fun(U_3024,bool),bool),member(U_3024),U_3018),U_3019)) )
          | ~ hBOOL(hAPP(fun(U_3024,bool),bool,finite_finite_1(U_3024),U_3019)) )
      | ~ ab_semigroup_mult(U_3023) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

fof(f_791_3,plain,
    ! [U_3024,U_3023] :
      ( ! [U_3022,U_3021,U_3020,U_3019] :
          ( hAPP(fun(U_3024,bool),U_3023,hAPP(U_3023,fun(fun(U_3024,bool),U_3023),hAPP(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023)),hAPP(fun(U_3023,fun(U_3023,U_3023)),fun(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023))),finite_fold_image(U_3023,U_3024),times_times(U_3023)),U_3021),U_3022),U_3019) = hAPP(fun(U_3024,bool),U_3023,hAPP(U_3023,fun(fun(U_3024,bool),U_3023),hAPP(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023)),hAPP(fun(U_3023,fun(U_3023,U_3023)),fun(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023))),finite_fold_image(U_3023,U_3024),times_times(U_3023)),U_3020),U_3022),U_3019)
          | ( hAPP(U_3024,U_3023,U_3021,sK145(U_3024,U_3023,U_3022,U_3021,U_3020,U_3019)) != hAPP(U_3024,U_3023,U_3020,sK145(U_3024,U_3023,U_3022,U_3021,U_3020,U_3019))
            & hBOOL(hAPP(fun(U_3024,bool),bool,hAPP(U_3024,fun(fun(U_3024,bool),bool),member(U_3024),sK145(U_3024,U_3023,U_3022,U_3021,U_3020,U_3019)),U_3019)) )
          | ~ hBOOL(hAPP(fun(U_3024,bool),bool,finite_finite_1(U_3024),U_3019)) )
      | ~ ab_semigroup_mult(U_3023) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_3018,sK145(U_3024,U_3023,U_3022,U_3021,U_3020,U_3019))],[f_791_2]) ).

cnf(f_791_4,plain,
    ( hBOOL(hAPP(fun(U_3024,bool),bool,hAPP(U_3024,fun(fun(U_3024,bool),bool),member(U_3024),sK145(U_3024,U_3023,U_3022,U_3021,U_3020,U_3019)),U_3019))
    | hAPP(fun(U_3024,bool),U_3023,hAPP(U_3023,fun(fun(U_3024,bool),U_3023),hAPP(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023)),hAPP(fun(U_3023,fun(U_3023,U_3023)),fun(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023))),finite_fold_image(U_3023,U_3024),times_times(U_3023)),U_3021),U_3022),U_3019) = hAPP(fun(U_3024,bool),U_3023,hAPP(U_3023,fun(fun(U_3024,bool),U_3023),hAPP(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023)),hAPP(fun(U_3023,fun(U_3023,U_3023)),fun(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023))),finite_fold_image(U_3023,U_3024),times_times(U_3023)),U_3020),U_3022),U_3019)
    | ~ hBOOL(hAPP(fun(U_3024,bool),bool,finite_finite_1(U_3024),U_3019))
    | ~ ab_semigroup_mult(U_3023) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

cnf(f_791_5,plain,
    ( hAPP(U_3024,U_3023,U_3021,sK145(U_3024,U_3023,U_3022,U_3021,U_3020,U_3019)) != hAPP(U_3024,U_3023,U_3020,sK145(U_3024,U_3023,U_3022,U_3021,U_3020,U_3019))
    | hAPP(fun(U_3024,bool),U_3023,hAPP(U_3023,fun(fun(U_3024,bool),U_3023),hAPP(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023)),hAPP(fun(U_3023,fun(U_3023,U_3023)),fun(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023))),finite_fold_image(U_3023,U_3024),times_times(U_3023)),U_3021),U_3022),U_3019) = hAPP(fun(U_3024,bool),U_3023,hAPP(U_3023,fun(fun(U_3024,bool),U_3023),hAPP(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023)),hAPP(fun(U_3023,fun(U_3023,U_3023)),fun(fun(U_3024,U_3023),fun(U_3023,fun(fun(U_3024,bool),U_3023))),finite_fold_image(U_3023,U_3024),times_times(U_3023)),U_3020),U_3022),U_3019)
    | ~ hBOOL(hAPP(fun(U_3024,bool),bool,finite_finite_1(U_3024),U_3019))
    | ~ ab_semigroup_mult(U_3023) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

fof(f_792_1,plain,
    ! [M_3,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_3),
    inference(fof_nnf,[status(thm)],[fact_702_nat__mult__commute]) ).

fof(f_792_2,plain,
    ! [U_3026,U_3025] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3026),U_3025) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3025),U_3026),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

cnf(f_792_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3026),U_3025) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3025),U_3026),
    inference(clausify,[status(thm)],[f_792_2]) ).

fof(f_793_1,plain,
    ! [M_3,N,K_2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),N)),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_2)),
    inference(fof_nnf,[status(thm)],[fact_703_nat__mult__assoc]) ).

fof(f_793_2,plain,
    ! [U_3029,U_3028,U_3027] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3029),U_3028)),U_3027) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3029),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3028),U_3027)),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

cnf(f_793_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3029),U_3028)),U_3027) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3029),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3028),U_3027)),
    inference(clausify,[status(thm)],[f_793_2]) ).

fof(f_794_1,plain,
    ! [M,Na,K] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ),
    inference(fof_nnf,[status(thm)],[fact_704_nat__mult__le__cancel1]) ).

fof(f_794_2,plain,
    ! [U_3032,U_3031,U_3030] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3030),U_3032)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3030),U_3031)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3032),U_3031)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3032),U_3031))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3030),U_3032)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3030),U_3031))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3030)) ),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

cnf(f_794_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3032),U_3031))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3030),U_3032)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3030),U_3031)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3030)) ),
    inference(clausify,[status(thm)],[f_794_2]) ).

cnf(f_794_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3030),U_3032)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3030),U_3031)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3032),U_3031))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3030)) ),
    inference(clausify,[status(thm)],[f_794_2]) ).

fof(f_795_1,plain,
    ! [M,Na,K] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ),
    inference(fof_nnf,[status(thm)],[fact_705_nat__mult__less__cancel1]) ).

fof(f_795_2,plain,
    ! [U_3035,U_3034,U_3033] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3033),U_3035)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3033),U_3034)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3035),U_3034)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3035),U_3034))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3033),U_3035)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3033),U_3034))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3033)) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

cnf(f_795_3,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3035),U_3034))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3033),U_3035)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3033),U_3034)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3033)) ),
    inference(clausify,[status(thm)],[f_795_2]) ).

cnf(f_795_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3033),U_3035)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3033),U_3034)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_3035),U_3034))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3033)) ),
    inference(clausify,[status(thm)],[f_795_2]) ).

fof(f_796_1,plain,
    ! [M,Na,K] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
          | M != Na )
        & ( M = Na
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) ),
    inference(fof_nnf,[status(thm)],[fact_706_nat__mult__eq__cancel1]) ).

fof(f_796_2,plain,
    ! [U_3038,U_3037,U_3036] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3036),U_3038) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3036),U_3037)
          | U_3038 != U_3037 )
        & ( U_3038 = U_3037
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3036),U_3038) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3036),U_3037) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3036)) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

cnf(f_796_3,plain,
    ( U_3038 = U_3037
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3036),U_3038) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3036),U_3037)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3036)) ),
    inference(clausify,[status(thm)],[f_796_2]) ).

cnf(f_796_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3036),U_3038) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3036),U_3037)
    | U_3038 != U_3037
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_3036)) ),
    inference(clausify,[status(thm)],[f_796_2]) ).

fof(f_797_1,plain,
    ! [K,M,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na)
        | ( M != Na
          & K != zero_zero(nat) ) )
      & ( M = Na
        | K = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_707_nat__mult__eq__cancel__disj]) ).

fof(f_797_2,plain,
    ! [U_3041,U_3040,U_3039] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3041),U_3040) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3041),U_3039)
        | ( U_3040 != U_3039
          & U_3041 != zero_zero(nat) ) )
      & ( U_3040 = U_3039
        | U_3041 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3041),U_3040) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3041),U_3039) ) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ( ! [U_3047,U_3045,U_3043] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3047),U_3045) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3047),U_3043)
        | ( U_3045 != U_3043
          & U_3047 != zero_zero(nat) ) )
    & ! [U_3046,U_3044,U_3042] :
        ( U_3044 = U_3042
        | U_3046 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3046),U_3044) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3046),U_3042) ) ),
    inference(miniscope,[status(thm)],[f_797_2]) ).

cnf(f_797_4,plain,
    ( U_3044 = U_3042
    | U_3046 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3046),U_3044) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3046),U_3042) ),
    inference(clausify,[status(thm)],[f_797_3]) ).

cnf(f_797_5,plain,
    ( U_3047 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3047),U_3045) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3047),U_3043) ),
    inference(clausify,[status(thm)],[f_797_3]) ).

cnf(f_797_6,plain,
    ( U_3045 != U_3043
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3047),U_3045) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3047),U_3043) ),
    inference(clausify,[status(thm)],[f_797_3]) ).

fof(f_798_1,plain,
    ! [I_2,U_1,J_1,K_2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(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,hAPP(nat,fun(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_708_left__add__mult__distrib]) ).

fof(f_798_2,plain,
    ! [U_3051,U_3050,U_3049,U_3048] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3051),U_3050)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3049),U_3050)),U_3048)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3051),U_3049)),U_3050)),U_3048),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

cnf(f_798_3,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3051),U_3050)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),U_3049),U_3050)),U_3048)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3051),U_3049)),U_3050)),U_3048),
    inference(clausify,[status(thm)],[f_798_2]) ).

fof(f_799_1,plain,
    ! [X_b,X_a] :
      ( ! [Ha,G,S,R_2,Ea] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold_image(X_a,X_b),times_times(X_a)),Ha),Ea),S)),hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold_image(X_a,X_b),times_times(X_a)),G),Ea),S)))
          | ? [X_1] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(X_b,X_a,Ha,X_1)),hAPP(X_b,X_a,G,X_1)))
              & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),S)) )
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S))
          | ? [X1,Y1,X2,Y2] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X2),Y2)))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,Y1),Y2))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,X1),X2)) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,Ea),Ea)) )
      | ~ comm_monoid_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_709_fold__image__related]) ).

fof(f_799_2,plain,
    ! [U_3063,U_3062] :
      ( ! [U_3061,U_3060,U_3059,U_3058,U_3057] :
          ( hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
          | ? [U_3056] :
              ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3063,U_3062,U_3061,U_3056)),hAPP(U_3063,U_3062,U_3060,U_3056)))
              & hBOOL(hAPP(fun(U_3063,bool),bool,hAPP(U_3063,fun(fun(U_3063,bool),bool),member(U_3063),U_3056),U_3059)) )
          | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
          | ? [U_3055,U_3054,U_3053,U_3052] :
              ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3055),U_3054)),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3053),U_3052)))
              & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3054),U_3052))
              & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3055),U_3053)) )
          | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057)) )
      | ~ comm_monoid_mult(U_3062) ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ! [U_3063,U_3062] :
      ( ! [U_3061,U_3060,U_3059,U_3058,U_3057] :
          ( hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
          | ? [U_3056] :
              ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3063,U_3062,U_3061,U_3056)),hAPP(U_3063,U_3062,U_3060,U_3056)))
              & hBOOL(hAPP(fun(U_3063,bool),bool,hAPP(U_3063,fun(fun(U_3063,bool),bool),member(U_3063),U_3056),U_3059)) )
          | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
          | ? [U_3054,U_3053,U_3052] :
              ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),U_3054)),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3053),U_3052)))
              & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3054),U_3052))
              & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),U_3053)) )
          | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057)) )
      | ~ comm_monoid_mult(U_3062) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_3055,sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))],[f_799_2]) ).

fof(f_799_4,plain,
    ! [U_3063,U_3062] :
      ( ! [U_3061,U_3060,U_3059,U_3058,U_3057] :
          ( hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
          | ? [U_3056] :
              ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3063,U_3062,U_3061,U_3056)),hAPP(U_3063,U_3062,U_3060,U_3056)))
              & hBOOL(hAPP(fun(U_3063,bool),bool,hAPP(U_3063,fun(fun(U_3063,bool),bool),member(U_3063),U_3056),U_3059)) )
          | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
          | ? [U_3053,U_3052] :
              ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),U_3053),U_3052)))
              & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),U_3052))
              & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),U_3053)) )
          | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057)) )
      | ~ comm_monoid_mult(U_3062) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_3054,sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))],[f_799_3]) ).

fof(f_799_5,plain,
    ! [U_3063,U_3062] :
      ( ! [U_3061,U_3060,U_3059,U_3058,U_3057] :
          ( hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
          | ? [U_3056] :
              ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3063,U_3062,U_3061,U_3056)),hAPP(U_3063,U_3062,U_3060,U_3056)))
              & hBOOL(hAPP(fun(U_3063,bool),bool,hAPP(U_3063,fun(fun(U_3063,bool),bool),member(U_3063),U_3056),U_3059)) )
          | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
          | ? [U_3052] :
              ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),U_3052)))
              & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),U_3052))
              & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))) )
          | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057)) )
      | ~ comm_monoid_mult(U_3062) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_3053,sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))],[f_799_4]) ).

fof(f_799_6,plain,
    ! [U_3063,U_3062] :
      ( ! [U_3061,U_3060,U_3059,U_3058,U_3057] :
          ( hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
          | ? [U_3056] :
              ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3063,U_3062,U_3061,U_3056)),hAPP(U_3063,U_3062,U_3060,U_3056)))
              & hBOOL(hAPP(fun(U_3063,bool),bool,hAPP(U_3063,fun(fun(U_3063,bool),bool),member(U_3063),U_3056),U_3059)) )
          | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
          | ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK149(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))))
            & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK149(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)))
            & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))) )
          | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057)) )
      | ~ comm_monoid_mult(U_3062) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_3052,sK149(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))],[f_799_5]) ).

fof(f_799_7,plain,
    ! [U_3063,U_3062] :
      ( ! [U_3061,U_3060,U_3059,U_3058,U_3057] :
          ( hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
          | ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3063,U_3062,U_3061,sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))),hAPP(U_3063,U_3062,U_3060,sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))))
            & hBOOL(hAPP(fun(U_3063,bool),bool,hAPP(U_3063,fun(fun(U_3063,bool),bool),member(U_3063),sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),U_3059)) )
          | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
          | ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK149(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))))
            & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK149(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)))
            & hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))) )
          | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057)) )
      | ~ comm_monoid_mult(U_3062) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_3056,sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))],[f_799_6]) ).

cnf(f_799_8,plain,
    ( hBOOL(hAPP(fun(U_3063,bool),bool,hAPP(U_3063,fun(fun(U_3063,bool),bool),member(U_3063),sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),U_3059))
    | hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
    | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
    | hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)))
    | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057))
    | ~ comm_monoid_mult(U_3062) ),
    inference(clausify,[status(thm)],[f_799_7]) ).

cnf(f_799_9,plain,
    ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3063,U_3062,U_3061,sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))),hAPP(U_3063,U_3062,U_3060,sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))))
    | hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
    | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
    | hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)))
    | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057))
    | ~ comm_monoid_mult(U_3062) ),
    inference(clausify,[status(thm)],[f_799_7]) ).

cnf(f_799_10,plain,
    ( hBOOL(hAPP(fun(U_3063,bool),bool,hAPP(U_3063,fun(fun(U_3063,bool),bool),member(U_3063),sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),U_3059))
    | hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
    | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
    | hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK149(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)))
    | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057))
    | ~ comm_monoid_mult(U_3062) ),
    inference(clausify,[status(thm)],[f_799_7]) ).

cnf(f_799_11,plain,
    ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3063,U_3062,U_3061,sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))),hAPP(U_3063,U_3062,U_3060,sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))))
    | hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
    | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
    | hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK149(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)))
    | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057))
    | ~ comm_monoid_mult(U_3062) ),
    inference(clausify,[status(thm)],[f_799_7]) ).

cnf(f_799_12,plain,
    ( hBOOL(hAPP(fun(U_3063,bool),bool,hAPP(U_3063,fun(fun(U_3063,bool),bool),member(U_3063),sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),U_3059))
    | hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
    | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
    | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK149(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))))
    | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057))
    | ~ comm_monoid_mult(U_3062) ),
    inference(clausify,[status(thm)],[f_799_7]) ).

cnf(f_799_13,plain,
    ( ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3063,U_3062,U_3061,sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))),hAPP(U_3063,U_3062,U_3060,sK150(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))))
    | hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3061),U_3057),U_3059)),hAPP(fun(U_3063,bool),U_3062,hAPP(U_3062,fun(fun(U_3063,bool),U_3062),hAPP(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062)),hAPP(fun(U_3062,fun(U_3062,U_3062)),fun(fun(U_3063,U_3062),fun(U_3062,fun(fun(U_3063,bool),U_3062))),finite_fold_image(U_3062,U_3063),times_times(U_3062)),U_3060),U_3057),U_3059)))
    | ~ hBOOL(hAPP(fun(U_3063,bool),bool,finite_finite_1(U_3063),U_3059))
    | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK146(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK147(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))),hAPP(U_3062,U_3062,hAPP(U_3062,fun(U_3062,U_3062),times_times(U_3062),sK148(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057)),sK149(U_3063,U_3062,U_3061,U_3060,U_3059,U_3058,U_3057))))
    | ~ hBOOL(hAPP(U_3062,bool,hAPP(U_3062,fun(U_3062,bool),U_3058,U_3057),U_3057))
    | ~ comm_monoid_mult(U_3062) ),
    inference(clausify,[status(thm)],[f_799_7]) ).

fof(f_800_1,plain,
    ! [X_b,X_a,X_c] :
      ( ! [Ea,G,F,Ha,K,T_3,S] :
          ( hAPP(fun(X_a,bool),X_c,hAPP(X_c,fun(fun(X_a,bool),X_c),hAPP(fun(X_a,X_c),fun(X_c,fun(fun(X_a,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_a,X_c),fun(X_c,fun(fun(X_a,bool),X_c))),finite_fold_image(X_c,X_a),times_times(X_c)),F),Ea),S) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Ea),T_3)
          | ? [X_1] :
              ( ( hAPP(X_b,X_c,G,hAPP(X_a,X_b,Ha,X_1)) != hAPP(X_a,X_c,F,X_1)
                | hAPP(X_b,X_a,K,hAPP(X_a,X_b,Ha,X_1)) != ti(X_a,X_1)
                | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,Ha,X_1)),T_3)) )
              & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),S)) )
          | ? [Y_2] :
              ( ( hAPP(X_a,X_b,Ha,hAPP(X_b,X_a,K,Y_2)) != ti(X_b,Y_2)
                | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_b,X_a,K,Y_2)),S)) )
              & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),T_3)) )
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) )
      | ~ comm_monoid_mult(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_710_fold__image__eq__general__inverses]) ).

fof(f_800_2,plain,
    ! [U_3075,U_3074,U_3073] :
      ( ! [U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066] :
          ( hAPP(fun(U_3074,bool),U_3073,hAPP(U_3073,fun(fun(U_3074,bool),U_3073),hAPP(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073))),finite_fold_image(U_3073,U_3074),times_times(U_3073)),U_3070),U_3072),U_3066) = hAPP(fun(U_3075,bool),U_3073,hAPP(U_3073,fun(fun(U_3075,bool),U_3073),hAPP(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073))),finite_fold_image(U_3073,U_3075),times_times(U_3073)),U_3071),U_3072),U_3067)
          | ? [U_3065] :
              ( ( hAPP(U_3075,U_3073,U_3071,hAPP(U_3074,U_3075,U_3069,U_3065)) != hAPP(U_3074,U_3073,U_3070,U_3065)
                | hAPP(U_3075,U_3074,U_3068,hAPP(U_3074,U_3075,U_3069,U_3065)) != ti(U_3074,U_3065)
                | ~ hBOOL(hAPP(fun(U_3075,bool),bool,hAPP(U_3075,fun(fun(U_3075,bool),bool),member(U_3075),hAPP(U_3074,U_3075,U_3069,U_3065)),U_3067)) )
              & hBOOL(hAPP(fun(U_3074,bool),bool,hAPP(U_3074,fun(fun(U_3074,bool),bool),member(U_3074),U_3065),U_3066)) )
          | ? [U_3064] :
              ( ( hAPP(U_3074,U_3075,U_3069,hAPP(U_3075,U_3074,U_3068,U_3064)) != ti(U_3075,U_3064)
                | ~ hBOOL(hAPP(fun(U_3074,bool),bool,hAPP(U_3074,fun(fun(U_3074,bool),bool),member(U_3074),hAPP(U_3075,U_3074,U_3068,U_3064)),U_3066)) )
              & hBOOL(hAPP(fun(U_3075,bool),bool,hAPP(U_3075,fun(fun(U_3075,bool),bool),member(U_3075),U_3064),U_3067)) )
          | ~ hBOOL(hAPP(fun(U_3074,bool),bool,finite_finite_1(U_3074),U_3066)) )
      | ~ comm_monoid_mult(U_3073) ),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ! [U_3075,U_3074,U_3073] :
      ( ! [U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066] :
          ( hAPP(fun(U_3074,bool),U_3073,hAPP(U_3073,fun(fun(U_3074,bool),U_3073),hAPP(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073))),finite_fold_image(U_3073,U_3074),times_times(U_3073)),U_3070),U_3072),U_3066) = hAPP(fun(U_3075,bool),U_3073,hAPP(U_3073,fun(fun(U_3075,bool),U_3073),hAPP(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073))),finite_fold_image(U_3073,U_3075),times_times(U_3073)),U_3071),U_3072),U_3067)
          | ? [U_3065] :
              ( ( hAPP(U_3075,U_3073,U_3071,hAPP(U_3074,U_3075,U_3069,U_3065)) != hAPP(U_3074,U_3073,U_3070,U_3065)
                | hAPP(U_3075,U_3074,U_3068,hAPP(U_3074,U_3075,U_3069,U_3065)) != ti(U_3074,U_3065)
                | ~ hBOOL(hAPP(fun(U_3075,bool),bool,hAPP(U_3075,fun(fun(U_3075,bool),bool),member(U_3075),hAPP(U_3074,U_3075,U_3069,U_3065)),U_3067)) )
              & hBOOL(hAPP(fun(U_3074,bool),bool,hAPP(U_3074,fun(fun(U_3074,bool),bool),member(U_3074),U_3065),U_3066)) )
          | ( ( hAPP(U_3074,U_3075,U_3069,hAPP(U_3075,U_3074,U_3068,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))) != ti(U_3075,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))
              | ~ hBOOL(hAPP(fun(U_3074,bool),bool,hAPP(U_3074,fun(fun(U_3074,bool),bool),member(U_3074),hAPP(U_3075,U_3074,U_3068,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))),U_3066)) )
            & hBOOL(hAPP(fun(U_3075,bool),bool,hAPP(U_3075,fun(fun(U_3075,bool),bool),member(U_3075),sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066)),U_3067)) )
          | ~ hBOOL(hAPP(fun(U_3074,bool),bool,finite_finite_1(U_3074),U_3066)) )
      | ~ comm_monoid_mult(U_3073) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_3064,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))],[f_800_2]) ).

fof(f_800_4,plain,
    ! [U_3075,U_3074,U_3073] :
      ( ! [U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066] :
          ( hAPP(fun(U_3074,bool),U_3073,hAPP(U_3073,fun(fun(U_3074,bool),U_3073),hAPP(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073))),finite_fold_image(U_3073,U_3074),times_times(U_3073)),U_3070),U_3072),U_3066) = hAPP(fun(U_3075,bool),U_3073,hAPP(U_3073,fun(fun(U_3075,bool),U_3073),hAPP(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073))),finite_fold_image(U_3073,U_3075),times_times(U_3073)),U_3071),U_3072),U_3067)
          | ( ( hAPP(U_3075,U_3073,U_3071,hAPP(U_3074,U_3075,U_3069,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))) != hAPP(U_3074,U_3073,U_3070,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))
              | hAPP(U_3075,U_3074,U_3068,hAPP(U_3074,U_3075,U_3069,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))) != ti(U_3074,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))
              | ~ hBOOL(hAPP(fun(U_3075,bool),bool,hAPP(U_3075,fun(fun(U_3075,bool),bool),member(U_3075),hAPP(U_3074,U_3075,U_3069,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))),U_3067)) )
            & hBOOL(hAPP(fun(U_3074,bool),bool,hAPP(U_3074,fun(fun(U_3074,bool),bool),member(U_3074),sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066)),U_3066)) )
          | ( ( hAPP(U_3074,U_3075,U_3069,hAPP(U_3075,U_3074,U_3068,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))) != ti(U_3075,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))
              | ~ hBOOL(hAPP(fun(U_3074,bool),bool,hAPP(U_3074,fun(fun(U_3074,bool),bool),member(U_3074),hAPP(U_3075,U_3074,U_3068,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))),U_3066)) )
            & hBOOL(hAPP(fun(U_3075,bool),bool,hAPP(U_3075,fun(fun(U_3075,bool),bool),member(U_3075),sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066)),U_3067)) )
          | ~ hBOOL(hAPP(fun(U_3074,bool),bool,finite_finite_1(U_3074),U_3066)) )
      | ~ comm_monoid_mult(U_3073) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_3065,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))],[f_800_3]) ).

cnf(f_800_5,plain,
    ( hBOOL(hAPP(fun(U_3074,bool),bool,hAPP(U_3074,fun(fun(U_3074,bool),bool),member(U_3074),sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066)),U_3066))
    | hAPP(fun(U_3074,bool),U_3073,hAPP(U_3073,fun(fun(U_3074,bool),U_3073),hAPP(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073))),finite_fold_image(U_3073,U_3074),times_times(U_3073)),U_3070),U_3072),U_3066) = hAPP(fun(U_3075,bool),U_3073,hAPP(U_3073,fun(fun(U_3075,bool),U_3073),hAPP(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073))),finite_fold_image(U_3073,U_3075),times_times(U_3073)),U_3071),U_3072),U_3067)
    | hBOOL(hAPP(fun(U_3075,bool),bool,hAPP(U_3075,fun(fun(U_3075,bool),bool),member(U_3075),sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066)),U_3067))
    | ~ hBOOL(hAPP(fun(U_3074,bool),bool,finite_finite_1(U_3074),U_3066))
    | ~ comm_monoid_mult(U_3073) ),
    inference(clausify,[status(thm)],[f_800_4]) ).

cnf(f_800_6,plain,
    ( hAPP(U_3075,U_3073,U_3071,hAPP(U_3074,U_3075,U_3069,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))) != hAPP(U_3074,U_3073,U_3070,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))
    | hAPP(U_3075,U_3074,U_3068,hAPP(U_3074,U_3075,U_3069,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))) != ti(U_3074,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))
    | ~ hBOOL(hAPP(fun(U_3075,bool),bool,hAPP(U_3075,fun(fun(U_3075,bool),bool),member(U_3075),hAPP(U_3074,U_3075,U_3069,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))),U_3067))
    | hAPP(fun(U_3074,bool),U_3073,hAPP(U_3073,fun(fun(U_3074,bool),U_3073),hAPP(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073))),finite_fold_image(U_3073,U_3074),times_times(U_3073)),U_3070),U_3072),U_3066) = hAPP(fun(U_3075,bool),U_3073,hAPP(U_3073,fun(fun(U_3075,bool),U_3073),hAPP(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073))),finite_fold_image(U_3073,U_3075),times_times(U_3073)),U_3071),U_3072),U_3067)
    | hBOOL(hAPP(fun(U_3075,bool),bool,hAPP(U_3075,fun(fun(U_3075,bool),bool),member(U_3075),sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066)),U_3067))
    | ~ hBOOL(hAPP(fun(U_3074,bool),bool,finite_finite_1(U_3074),U_3066))
    | ~ comm_monoid_mult(U_3073) ),
    inference(clausify,[status(thm)],[f_800_4]) ).

cnf(f_800_7,plain,
    ( hBOOL(hAPP(fun(U_3074,bool),bool,hAPP(U_3074,fun(fun(U_3074,bool),bool),member(U_3074),sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066)),U_3066))
    | hAPP(fun(U_3074,bool),U_3073,hAPP(U_3073,fun(fun(U_3074,bool),U_3073),hAPP(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073))),finite_fold_image(U_3073,U_3074),times_times(U_3073)),U_3070),U_3072),U_3066) = hAPP(fun(U_3075,bool),U_3073,hAPP(U_3073,fun(fun(U_3075,bool),U_3073),hAPP(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073))),finite_fold_image(U_3073,U_3075),times_times(U_3073)),U_3071),U_3072),U_3067)
    | hAPP(U_3074,U_3075,U_3069,hAPP(U_3075,U_3074,U_3068,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))) != ti(U_3075,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))
    | ~ hBOOL(hAPP(fun(U_3074,bool),bool,hAPP(U_3074,fun(fun(U_3074,bool),bool),member(U_3074),hAPP(U_3075,U_3074,U_3068,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))),U_3066))
    | ~ hBOOL(hAPP(fun(U_3074,bool),bool,finite_finite_1(U_3074),U_3066))
    | ~ comm_monoid_mult(U_3073) ),
    inference(clausify,[status(thm)],[f_800_4]) ).

cnf(f_800_8,plain,
    ( hAPP(U_3075,U_3073,U_3071,hAPP(U_3074,U_3075,U_3069,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))) != hAPP(U_3074,U_3073,U_3070,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))
    | hAPP(U_3075,U_3074,U_3068,hAPP(U_3074,U_3075,U_3069,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))) != ti(U_3074,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))
    | ~ hBOOL(hAPP(fun(U_3075,bool),bool,hAPP(U_3075,fun(fun(U_3075,bool),bool),member(U_3075),hAPP(U_3074,U_3075,U_3069,sK152(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))),U_3067))
    | hAPP(fun(U_3074,bool),U_3073,hAPP(U_3073,fun(fun(U_3074,bool),U_3073),hAPP(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3074,U_3073),fun(U_3073,fun(fun(U_3074,bool),U_3073))),finite_fold_image(U_3073,U_3074),times_times(U_3073)),U_3070),U_3072),U_3066) = hAPP(fun(U_3075,bool),U_3073,hAPP(U_3073,fun(fun(U_3075,bool),U_3073),hAPP(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073)),hAPP(fun(U_3073,fun(U_3073,U_3073)),fun(fun(U_3075,U_3073),fun(U_3073,fun(fun(U_3075,bool),U_3073))),finite_fold_image(U_3073,U_3075),times_times(U_3073)),U_3071),U_3072),U_3067)
    | hAPP(U_3074,U_3075,U_3069,hAPP(U_3075,U_3074,U_3068,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))) != ti(U_3075,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))
    | ~ hBOOL(hAPP(fun(U_3074,bool),bool,hAPP(U_3074,fun(fun(U_3074,bool),bool),member(U_3074),hAPP(U_3075,U_3074,U_3068,sK151(U_3075,U_3074,U_3073,U_3072,U_3071,U_3070,U_3069,U_3068,U_3067,U_3066))),U_3066))
    | ~ hBOOL(hAPP(fun(U_3074,bool),bool,finite_finite_1(U_3074),U_3066))
    | ~ comm_monoid_mult(U_3073) ),
    inference(clausify,[status(thm)],[f_800_4]) ).

fof(f_801_1,plain,
    ! [X_a,X_b,G,F,A_1] :
      ( ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G)
      | ? [X_1] :
          ( hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,G,X_1)
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) )
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1)))
      | ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),bool),extensional(X_a,X_b),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_711_extensionalityI]) ).

fof(f_801_2,plain,
    ! [U_3081,U_3080,U_3079,U_3078,U_3077] :
      ( ti(fun(U_3081,U_3080),U_3078) = ti(fun(U_3081,U_3080),U_3079)
      | ? [U_3076] :
          ( hAPP(U_3081,U_3080,U_3078,U_3076) != hAPP(U_3081,U_3080,U_3079,U_3076)
          & hBOOL(hAPP(fun(U_3081,bool),bool,hAPP(U_3081,fun(fun(U_3081,bool),bool),member(U_3081),U_3076),U_3077)) )
      | ~ hBOOL(hAPP(fun(fun(U_3081,U_3080),bool),bool,hAPP(fun(U_3081,U_3080),fun(fun(fun(U_3081,U_3080),bool),bool),member(fun(U_3081,U_3080)),U_3079),hAPP(fun(U_3081,bool),fun(fun(U_3081,U_3080),bool),extensional(U_3081,U_3080),U_3077)))
      | ~ hBOOL(hAPP(fun(fun(U_3081,U_3080),bool),bool,hAPP(fun(U_3081,U_3080),fun(fun(fun(U_3081,U_3080),bool),bool),member(fun(U_3081,U_3080)),U_3078),hAPP(fun(U_3081,bool),fun(fun(U_3081,U_3080),bool),extensional(U_3081,U_3080),U_3077))) ),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

fof(f_801_3,plain,
    ! [U_3081,U_3080,U_3079,U_3078,U_3077] :
      ( ti(fun(U_3081,U_3080),U_3078) = ti(fun(U_3081,U_3080),U_3079)
      | ( hAPP(U_3081,U_3080,U_3078,sK153(U_3081,U_3080,U_3079,U_3078,U_3077)) != hAPP(U_3081,U_3080,U_3079,sK153(U_3081,U_3080,U_3079,U_3078,U_3077))
        & hBOOL(hAPP(fun(U_3081,bool),bool,hAPP(U_3081,fun(fun(U_3081,bool),bool),member(U_3081),sK153(U_3081,U_3080,U_3079,U_3078,U_3077)),U_3077)) )
      | ~ hBOOL(hAPP(fun(fun(U_3081,U_3080),bool),bool,hAPP(fun(U_3081,U_3080),fun(fun(fun(U_3081,U_3080),bool),bool),member(fun(U_3081,U_3080)),U_3079),hAPP(fun(U_3081,bool),fun(fun(U_3081,U_3080),bool),extensional(U_3081,U_3080),U_3077)))
      | ~ hBOOL(hAPP(fun(fun(U_3081,U_3080),bool),bool,hAPP(fun(U_3081,U_3080),fun(fun(fun(U_3081,U_3080),bool),bool),member(fun(U_3081,U_3080)),U_3078),hAPP(fun(U_3081,bool),fun(fun(U_3081,U_3080),bool),extensional(U_3081,U_3080),U_3077))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_3076,sK153(U_3081,U_3080,U_3079,U_3078,U_3077))],[f_801_2]) ).

cnf(f_801_4,plain,
    ( hBOOL(hAPP(fun(U_3081,bool),bool,hAPP(U_3081,fun(fun(U_3081,bool),bool),member(U_3081),sK153(U_3081,U_3080,U_3079,U_3078,U_3077)),U_3077))
    | ti(fun(U_3081,U_3080),U_3078) = ti(fun(U_3081,U_3080),U_3079)
    | ~ hBOOL(hAPP(fun(fun(U_3081,U_3080),bool),bool,hAPP(fun(U_3081,U_3080),fun(fun(fun(U_3081,U_3080),bool),bool),member(fun(U_3081,U_3080)),U_3079),hAPP(fun(U_3081,bool),fun(fun(U_3081,U_3080),bool),extensional(U_3081,U_3080),U_3077)))
    | ~ hBOOL(hAPP(fun(fun(U_3081,U_3080),bool),bool,hAPP(fun(U_3081,U_3080),fun(fun(fun(U_3081,U_3080),bool),bool),member(fun(U_3081,U_3080)),U_3078),hAPP(fun(U_3081,bool),fun(fun(U_3081,U_3080),bool),extensional(U_3081,U_3080),U_3077))) ),
    inference(clausify,[status(thm)],[f_801_3]) ).

cnf(f_801_5,plain,
    ( hAPP(U_3081,U_3080,U_3078,sK153(U_3081,U_3080,U_3079,U_3078,U_3077)) != hAPP(U_3081,U_3080,U_3079,sK153(U_3081,U_3080,U_3079,U_3078,U_3077))
    | ti(fun(U_3081,U_3080),U_3078) = ti(fun(U_3081,U_3080),U_3079)
    | ~ hBOOL(hAPP(fun(fun(U_3081,U_3080),bool),bool,hAPP(fun(U_3081,U_3080),fun(fun(fun(U_3081,U_3080),bool),bool),member(fun(U_3081,U_3080)),U_3079),hAPP(fun(U_3081,bool),fun(fun(U_3081,U_3080),bool),extensional(U_3081,U_3080),U_3077)))
    | ~ hBOOL(hAPP(fun(fun(U_3081,U_3080),bool),bool,hAPP(fun(U_3081,U_3080),fun(fun(fun(U_3081,U_3080),bool),bool),member(fun(U_3081,U_3080)),U_3078),hAPP(fun(U_3081,bool),fun(fun(U_3081,U_3080),bool),extensional(U_3081,U_3080),U_3077))) ),
    inference(clausify,[status(thm)],[f_801_3]) ).

fof(f_802_1,plain,
    ! [X_a,M,Pa,K] :
      ( ? [X_1] :
          ( ! [Y_2] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X_a,nat,M,X_1)),hAPP(X_a,nat,M,Y_2)))
              | ~ hBOOL(hAPP(X_a,bool,Pa,Y_2)) )
          & hBOOL(hAPP(X_a,bool,Pa,X_1)) )
      | ~ hBOOL(hAPP(X_a,bool,Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_712_ex__has__least__nat]) ).

fof(f_802_2,plain,
    ! [U_3087,U_3086,U_3085,U_3084] :
      ( ? [U_3083] :
          ( ! [U_3082] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(U_3087,nat,U_3086,U_3083)),hAPP(U_3087,nat,U_3086,U_3082)))
              | ~ hBOOL(hAPP(U_3087,bool,U_3085,U_3082)) )
          & hBOOL(hAPP(U_3087,bool,U_3085,U_3083)) )
      | ~ hBOOL(hAPP(U_3087,bool,U_3085,U_3084)) ),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

fof(f_802_3,plain,
    ! [U_3087,U_3086,U_3085] :
      ( ! [U_3084] : ~ hBOOL(hAPP(U_3087,bool,U_3085,U_3084))
      | ? [U_3083] :
          ( ! [U_3082] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(U_3087,nat,U_3086,U_3083)),hAPP(U_3087,nat,U_3086,U_3082)))
              | ~ hBOOL(hAPP(U_3087,bool,U_3085,U_3082)) )
          & hBOOL(hAPP(U_3087,bool,U_3085,U_3083)) ) ),
    inference(miniscope,[status(thm)],[f_802_2]) ).

fof(f_802_4,plain,
    ! [U_3087,U_3086,U_3085] :
      ( ! [U_3084] : ~ hBOOL(hAPP(U_3087,bool,U_3085,U_3084))
      | ( ! [U_3082] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(U_3087,nat,U_3086,sK154(U_3087,U_3086,U_3085))),hAPP(U_3087,nat,U_3086,U_3082)))
            | ~ hBOOL(hAPP(U_3087,bool,U_3085,U_3082)) )
        & hBOOL(hAPP(U_3087,bool,U_3085,sK154(U_3087,U_3086,U_3085))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_3083,sK154(U_3087,U_3086,U_3085))],[f_802_3]) ).

cnf(f_802_5,plain,
    ( hBOOL(hAPP(U_3087,bool,U_3085,sK154(U_3087,U_3086,U_3085)))
    | ~ hBOOL(hAPP(U_3087,bool,U_3085,U_3084)) ),
    inference(clausify,[status(thm)],[f_802_4]) ).

cnf(f_802_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(U_3087,nat,U_3086,sK154(U_3087,U_3086,U_3085))),hAPP(U_3087,nat,U_3086,U_3082)))
    | ~ hBOOL(hAPP(U_3087,bool,U_3085,U_3082))
    | ~ hBOOL(hAPP(U_3087,bool,U_3085,U_3084)) ),
    inference(clausify,[status(thm)],[f_802_4]) ).

fof(f_803_1,plain,
    ! [X_b,X_a,F,G,M_2,N_1] :
      ( hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),M_2) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),G),N_1)
      | ? [X_1] :
          ( hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,G,X_1)
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),N_1)) )
      | ti(fun(X_a,bool),M_2) != ti(fun(X_a,bool),N_1) ),
    inference(fof_nnf,[status(thm)],[fact_713_image__cong]) ).

fof(f_803_2,plain,
    ! [U_3094,U_3093,U_3092,U_3091,U_3090,U_3089] :
      ( hAPP(fun(U_3093,bool),fun(U_3094,bool),hAPP(fun(U_3093,U_3094),fun(fun(U_3093,bool),fun(U_3094,bool)),image(U_3093,U_3094),U_3092),U_3090) = hAPP(fun(U_3093,bool),fun(U_3094,bool),hAPP(fun(U_3093,U_3094),fun(fun(U_3093,bool),fun(U_3094,bool)),image(U_3093,U_3094),U_3091),U_3089)
      | ? [U_3088] :
          ( hAPP(U_3093,U_3094,U_3092,U_3088) != hAPP(U_3093,U_3094,U_3091,U_3088)
          & hBOOL(hAPP(fun(U_3093,bool),bool,hAPP(U_3093,fun(fun(U_3093,bool),bool),member(U_3093),U_3088),U_3089)) )
      | ti(fun(U_3093,bool),U_3090) != ti(fun(U_3093,bool),U_3089) ),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ! [U_3094,U_3093,U_3092,U_3091,U_3090,U_3089] :
      ( hAPP(fun(U_3093,bool),fun(U_3094,bool),hAPP(fun(U_3093,U_3094),fun(fun(U_3093,bool),fun(U_3094,bool)),image(U_3093,U_3094),U_3092),U_3090) = hAPP(fun(U_3093,bool),fun(U_3094,bool),hAPP(fun(U_3093,U_3094),fun(fun(U_3093,bool),fun(U_3094,bool)),image(U_3093,U_3094),U_3091),U_3089)
      | ( hAPP(U_3093,U_3094,U_3092,sK155(U_3094,U_3093,U_3092,U_3091,U_3090,U_3089)) != hAPP(U_3093,U_3094,U_3091,sK155(U_3094,U_3093,U_3092,U_3091,U_3090,U_3089))
        & hBOOL(hAPP(fun(U_3093,bool),bool,hAPP(U_3093,fun(fun(U_3093,bool),bool),member(U_3093),sK155(U_3094,U_3093,U_3092,U_3091,U_3090,U_3089)),U_3089)) )
      | ti(fun(U_3093,bool),U_3090) != ti(fun(U_3093,bool),U_3089) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_3088,sK155(U_3094,U_3093,U_3092,U_3091,U_3090,U_3089))],[f_803_2]) ).

cnf(f_803_4,plain,
    ( hBOOL(hAPP(fun(U_3093,bool),bool,hAPP(U_3093,fun(fun(U_3093,bool),bool),member(U_3093),sK155(U_3094,U_3093,U_3092,U_3091,U_3090,U_3089)),U_3089))
    | hAPP(fun(U_3093,bool),fun(U_3094,bool),hAPP(fun(U_3093,U_3094),fun(fun(U_3093,bool),fun(U_3094,bool)),image(U_3093,U_3094),U_3092),U_3090) = hAPP(fun(U_3093,bool),fun(U_3094,bool),hAPP(fun(U_3093,U_3094),fun(fun(U_3093,bool),fun(U_3094,bool)),image(U_3093,U_3094),U_3091),U_3089)
    | ti(fun(U_3093,bool),U_3090) != ti(fun(U_3093,bool),U_3089) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

cnf(f_803_5,plain,
    ( hAPP(U_3093,U_3094,U_3092,sK155(U_3094,U_3093,U_3092,U_3091,U_3090,U_3089)) != hAPP(U_3093,U_3094,U_3091,sK155(U_3094,U_3093,U_3092,U_3091,U_3090,U_3089))
    | hAPP(fun(U_3093,bool),fun(U_3094,bool),hAPP(fun(U_3093,U_3094),fun(fun(U_3093,bool),fun(U_3094,bool)),image(U_3093,U_3094),U_3092),U_3090) = hAPP(fun(U_3093,bool),fun(U_3094,bool),hAPP(fun(U_3093,U_3094),fun(fun(U_3093,bool),fun(U_3094,bool)),image(U_3093,U_3094),U_3091),U_3089)
    | ti(fun(U_3093,bool),U_3090) != ti(fun(U_3093,bool),U_3089) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

fof(f_804_1,plain,
    ! [X_a] :
    ? [X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool)))),
    inference(fof_nnf,[status(thm)],[fact_714_UNIV__witness]) ).

fof(f_804_2,plain,
    ! [U_3096] :
    ? [U_3095] : hBOOL(hAPP(fun(U_3096,bool),bool,hAPP(U_3096,fun(fun(U_3096,bool),bool),member(U_3096),U_3095),top_top(fun(U_3096,bool)))),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ! [U_3096] : hBOOL(hAPP(fun(U_3096,bool),bool,hAPP(U_3096,fun(fun(U_3096,bool),bool),member(U_3096),sK156(U_3096)),top_top(fun(U_3096,bool)))),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_3095,sK156(U_3096))],[f_804_2]) ).

cnf(f_804_4,plain,
    hBOOL(hAPP(fun(U_3096,bool),bool,hAPP(U_3096,fun(fun(U_3096,bool),bool),member(U_3096),sK156(U_3096)),top_top(fun(U_3096,bool)))),
    inference(clausify,[status(thm)],[f_804_3]) ).

fof(f_805_1,plain,
    ! [X_a,A_1] :
      ( top_top(fun(X_a,bool)) = ti(fun(X_a,bool),A_1)
      | ? [X_1] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_715_UNIV__eq__I]) ).

fof(f_805_2,plain,
    ! [U_3099,U_3098] :
      ( top_top(fun(U_3099,bool)) = ti(fun(U_3099,bool),U_3098)
      | ? [U_3097] : ~ hBOOL(hAPP(fun(U_3099,bool),bool,hAPP(U_3099,fun(fun(U_3099,bool),bool),member(U_3099),U_3097),U_3098)) ),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ! [U_3099,U_3098] :
      ( top_top(fun(U_3099,bool)) = ti(fun(U_3099,bool),U_3098)
      | ~ hBOOL(hAPP(fun(U_3099,bool),bool,hAPP(U_3099,fun(fun(U_3099,bool),bool),member(U_3099),sK157(U_3099,U_3098)),U_3098)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_3097,sK157(U_3099,U_3098))],[f_805_2]) ).

cnf(f_805_4,plain,
    ( top_top(fun(U_3099,bool)) = ti(fun(U_3099,bool),U_3098)
    | ~ hBOOL(hAPP(fun(U_3099,bool),bool,hAPP(U_3099,fun(fun(U_3099,bool),bool),member(U_3099),sK157(U_3099,U_3098)),U_3098)) ),
    inference(clausify,[status(thm)],[f_805_3]) ).

fof(f_806_1,plain,
    ! [X_a,Q_1,Pa] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(X_a,bool,Q_1,X_1))
          & hBOOL(hAPP(X_a,bool,Pa,X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_716_Collect__mono]) ).

fof(f_806_2,plain,
    ! [U_3103,U_3102,U_3101] :
      ( hBOOL(hAPP(fun(U_3103,bool),bool,hAPP(fun(U_3103,bool),fun(fun(U_3103,bool),bool),ord_less_eq(fun(U_3103,bool)),hAPP(fun(U_3103,bool),fun(U_3103,bool),collect(U_3103),U_3101)),hAPP(fun(U_3103,bool),fun(U_3103,bool),collect(U_3103),U_3102)))
      | ? [U_3100] :
          ( ~ hBOOL(hAPP(U_3103,bool,U_3102,U_3100))
          & hBOOL(hAPP(U_3103,bool,U_3101,U_3100)) ) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ! [U_3103,U_3102,U_3101] :
      ( hBOOL(hAPP(fun(U_3103,bool),bool,hAPP(fun(U_3103,bool),fun(fun(U_3103,bool),bool),ord_less_eq(fun(U_3103,bool)),hAPP(fun(U_3103,bool),fun(U_3103,bool),collect(U_3103),U_3101)),hAPP(fun(U_3103,bool),fun(U_3103,bool),collect(U_3103),U_3102)))
      | ( ~ hBOOL(hAPP(U_3103,bool,U_3102,sK158(U_3103,U_3102,U_3101)))
        & hBOOL(hAPP(U_3103,bool,U_3101,sK158(U_3103,U_3102,U_3101))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_3100,sK158(U_3103,U_3102,U_3101))],[f_806_2]) ).

cnf(f_806_4,plain,
    ( hBOOL(hAPP(U_3103,bool,U_3101,sK158(U_3103,U_3102,U_3101)))
    | hBOOL(hAPP(fun(U_3103,bool),bool,hAPP(fun(U_3103,bool),fun(fun(U_3103,bool),bool),ord_less_eq(fun(U_3103,bool)),hAPP(fun(U_3103,bool),fun(U_3103,bool),collect(U_3103),U_3101)),hAPP(fun(U_3103,bool),fun(U_3103,bool),collect(U_3103),U_3102))) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

cnf(f_806_5,plain,
    ( ~ hBOOL(hAPP(U_3103,bool,U_3102,sK158(U_3103,U_3102,U_3101)))
    | hBOOL(hAPP(fun(U_3103,bool),bool,hAPP(fun(U_3103,bool),fun(fun(U_3103,bool),bool),ord_less_eq(fun(U_3103,bool)),hAPP(fun(U_3103,bool),fun(U_3103,bool),collect(U_3103),U_3101)),hAPP(fun(U_3103,bool),fun(U_3103,bool),collect(U_3103),U_3102))) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

fof(f_807_1,plain,
    ! [X_a,Q_1,Pa] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(X_a,bool,Q_1,X_1))
          & hBOOL(hAPP(X_a,bool,Pa,X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_717_predicate1I]) ).

fof(f_807_2,plain,
    ! [U_3107,U_3106,U_3105] :
      ( hBOOL(hAPP(fun(U_3107,bool),bool,hAPP(fun(U_3107,bool),fun(fun(U_3107,bool),bool),ord_less_eq(fun(U_3107,bool)),U_3105),U_3106))
      | ? [U_3104] :
          ( ~ hBOOL(hAPP(U_3107,bool,U_3106,U_3104))
          & hBOOL(hAPP(U_3107,bool,U_3105,U_3104)) ) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ! [U_3107,U_3106,U_3105] :
      ( hBOOL(hAPP(fun(U_3107,bool),bool,hAPP(fun(U_3107,bool),fun(fun(U_3107,bool),bool),ord_less_eq(fun(U_3107,bool)),U_3105),U_3106))
      | ( ~ hBOOL(hAPP(U_3107,bool,U_3106,sK159(U_3107,U_3106,U_3105)))
        & hBOOL(hAPP(U_3107,bool,U_3105,sK159(U_3107,U_3106,U_3105))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_3104,sK159(U_3107,U_3106,U_3105))],[f_807_2]) ).

cnf(f_807_4,plain,
    ( hBOOL(hAPP(U_3107,bool,U_3105,sK159(U_3107,U_3106,U_3105)))
    | hBOOL(hAPP(fun(U_3107,bool),bool,hAPP(fun(U_3107,bool),fun(fun(U_3107,bool),bool),ord_less_eq(fun(U_3107,bool)),U_3105),U_3106)) ),
    inference(clausify,[status(thm)],[f_807_3]) ).

cnf(f_807_5,plain,
    ( ~ hBOOL(hAPP(U_3107,bool,U_3106,sK159(U_3107,U_3106,U_3105)))
    | hBOOL(hAPP(fun(U_3107,bool),bool,hAPP(fun(U_3107,bool),fun(fun(U_3107,bool),bool),ord_less_eq(fun(U_3107,bool)),U_3105),U_3106)) ),
    inference(clausify,[status(thm)],[f_807_3]) ).

fof(f_808_1,plain,
    ! [X_b,X_a,X_c] :
      ( ! [G,Z_1,Ha,A_1] :
          ( hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),Ha),A_1)) = hAPP(fun(X_a,bool),X_c,hAPP(X_c,fun(fun(X_a,bool),X_c),hAPP(fun(X_a,X_c),fun(X_c,fun(fun(X_a,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_a,X_c),fun(X_c,fun(fun(X_a,bool),X_c))),finite_fold_image(X_c,X_a),times_times(X_c)),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),G),Ha)),Z_1),A_1)
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),Ha),A_1))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ ab_semigroup_mult(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_718_fold__image__reindex]) ).

fof(f_808_2,plain,
    ! [U_3114,U_3113,U_3112] :
      ( ! [U_3111,U_3110,U_3109,U_3108] :
          ( hAPP(fun(U_3114,bool),U_3112,hAPP(U_3112,fun(fun(U_3114,bool),U_3112),hAPP(fun(U_3114,U_3112),fun(U_3112,fun(fun(U_3114,bool),U_3112)),hAPP(fun(U_3112,fun(U_3112,U_3112)),fun(fun(U_3114,U_3112),fun(U_3112,fun(fun(U_3114,bool),U_3112))),finite_fold_image(U_3112,U_3114),times_times(U_3112)),U_3111),U_3110),hAPP(fun(U_3113,bool),fun(U_3114,bool),hAPP(fun(U_3113,U_3114),fun(fun(U_3113,bool),fun(U_3114,bool)),image(U_3113,U_3114),U_3109),U_3108)) = hAPP(fun(U_3113,bool),U_3112,hAPP(U_3112,fun(fun(U_3113,bool),U_3112),hAPP(fun(U_3113,U_3112),fun(U_3112,fun(fun(U_3113,bool),U_3112)),hAPP(fun(U_3112,fun(U_3112,U_3112)),fun(fun(U_3113,U_3112),fun(U_3112,fun(fun(U_3113,bool),U_3112))),finite_fold_image(U_3112,U_3113),times_times(U_3112)),hAPP(fun(U_3113,U_3114),fun(U_3113,U_3112),hAPP(fun(U_3114,U_3112),fun(fun(U_3113,U_3114),fun(U_3113,U_3112)),comp(U_3114,U_3112,U_3113),U_3111),U_3109)),U_3110),U_3108)
          | ~ hBOOL(hAPP(fun(U_3113,bool),bool,hAPP(fun(U_3113,U_3114),fun(fun(U_3113,bool),bool),inj_on(U_3113,U_3114),U_3109),U_3108))
          | ~ hBOOL(hAPP(fun(U_3113,bool),bool,finite_finite_1(U_3113),U_3108)) )
      | ~ ab_semigroup_mult(U_3112) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

cnf(f_808_3,plain,
    ( hAPP(fun(U_3114,bool),U_3112,hAPP(U_3112,fun(fun(U_3114,bool),U_3112),hAPP(fun(U_3114,U_3112),fun(U_3112,fun(fun(U_3114,bool),U_3112)),hAPP(fun(U_3112,fun(U_3112,U_3112)),fun(fun(U_3114,U_3112),fun(U_3112,fun(fun(U_3114,bool),U_3112))),finite_fold_image(U_3112,U_3114),times_times(U_3112)),U_3111),U_3110),hAPP(fun(U_3113,bool),fun(U_3114,bool),hAPP(fun(U_3113,U_3114),fun(fun(U_3113,bool),fun(U_3114,bool)),image(U_3113,U_3114),U_3109),U_3108)) = hAPP(fun(U_3113,bool),U_3112,hAPP(U_3112,fun(fun(U_3113,bool),U_3112),hAPP(fun(U_3113,U_3112),fun(U_3112,fun(fun(U_3113,bool),U_3112)),hAPP(fun(U_3112,fun(U_3112,U_3112)),fun(fun(U_3113,U_3112),fun(U_3112,fun(fun(U_3113,bool),U_3112))),finite_fold_image(U_3112,U_3113),times_times(U_3112)),hAPP(fun(U_3113,U_3114),fun(U_3113,U_3112),hAPP(fun(U_3114,U_3112),fun(fun(U_3113,U_3114),fun(U_3113,U_3112)),comp(U_3114,U_3112,U_3113),U_3111),U_3109)),U_3110),U_3108)
    | ~ hBOOL(hAPP(fun(U_3113,bool),bool,hAPP(fun(U_3113,U_3114),fun(fun(U_3113,bool),bool),inj_on(U_3113,U_3114),U_3109),U_3108))
    | ~ hBOOL(hAPP(fun(U_3113,bool),bool,finite_finite_1(U_3113),U_3108))
    | ~ ab_semigroup_mult(U_3112) ),
    inference(clausify,[status(thm)],[f_808_2]) ).

fof(f_809_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_719_nat_Osize_I2_J]) ).

fof(f_809_2,plain,
    ! [U_3115] : hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,U_3115)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,U_3115)),hAPP(nat,nat,suc,zero_zero(nat))),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

cnf(f_809_3,plain,
    hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,U_3115)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,U_3115)),hAPP(nat,nat,suc,zero_zero(nat))),
    inference(clausify,[status(thm)],[f_809_2]) ).

fof(f_810_1,plain,
    ! [X_c,X_b,X_a,G,F] :
      ( hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),comp(X_a,X_c,X_b),G),F)),top_top(fun(X_b,bool))) = top_top(fun(X_c,bool))
      | hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),G),top_top(fun(X_a,bool))) != top_top(fun(X_c,bool))
      | hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),top_top(fun(X_b,bool))) != top_top(fun(X_a,bool)) ),
    inference(fof_nnf,[status(thm)],[fact_720_comp__surj]) ).

fof(f_810_2,plain,
    ! [U_3120,U_3119,U_3118,U_3117,U_3116] :
      ( hAPP(fun(U_3119,bool),fun(U_3120,bool),hAPP(fun(U_3119,U_3120),fun(fun(U_3119,bool),fun(U_3120,bool)),image(U_3119,U_3120),hAPP(fun(U_3119,U_3118),fun(U_3119,U_3120),hAPP(fun(U_3118,U_3120),fun(fun(U_3119,U_3118),fun(U_3119,U_3120)),comp(U_3118,U_3120,U_3119),U_3117),U_3116)),top_top(fun(U_3119,bool))) = top_top(fun(U_3120,bool))
      | hAPP(fun(U_3118,bool),fun(U_3120,bool),hAPP(fun(U_3118,U_3120),fun(fun(U_3118,bool),fun(U_3120,bool)),image(U_3118,U_3120),U_3117),top_top(fun(U_3118,bool))) != top_top(fun(U_3120,bool))
      | hAPP(fun(U_3119,bool),fun(U_3118,bool),hAPP(fun(U_3119,U_3118),fun(fun(U_3119,bool),fun(U_3118,bool)),image(U_3119,U_3118),U_3116),top_top(fun(U_3119,bool))) != top_top(fun(U_3118,bool)) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

cnf(f_810_3,plain,
    ( hAPP(fun(U_3119,bool),fun(U_3120,bool),hAPP(fun(U_3119,U_3120),fun(fun(U_3119,bool),fun(U_3120,bool)),image(U_3119,U_3120),hAPP(fun(U_3119,U_3118),fun(U_3119,U_3120),hAPP(fun(U_3118,U_3120),fun(fun(U_3119,U_3118),fun(U_3119,U_3120)),comp(U_3118,U_3120,U_3119),U_3117),U_3116)),top_top(fun(U_3119,bool))) = top_top(fun(U_3120,bool))
    | hAPP(fun(U_3118,bool),fun(U_3120,bool),hAPP(fun(U_3118,U_3120),fun(fun(U_3118,bool),fun(U_3120,bool)),image(U_3118,U_3120),U_3117),top_top(fun(U_3118,bool))) != top_top(fun(U_3120,bool))
    | hAPP(fun(U_3119,bool),fun(U_3118,bool),hAPP(fun(U_3119,U_3118),fun(fun(U_3119,bool),fun(U_3118,bool)),image(U_3119,U_3118),U_3116),top_top(fun(U_3119,bool))) != top_top(fun(U_3118,bool)) ),
    inference(clausify,[status(thm)],[f_810_2]) ).

fof(f_811_1,plain,
    ! [X_c,X_a,X_b,G,F] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),bool),inj_on(X_c,X_b),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),comp(X_a,X_b,X_c),F),G)),top_top(fun(X_c,bool))))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),bool),inj_on(X_c,X_a),G),top_top(fun(X_c,bool))))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_721_inj__comp]) ).

fof(f_811_2,plain,
    ! [U_3125,U_3124,U_3123,U_3122,U_3121] :
      ( hBOOL(hAPP(fun(U_3125,bool),bool,hAPP(fun(U_3125,U_3123),fun(fun(U_3125,bool),bool),inj_on(U_3125,U_3123),hAPP(fun(U_3125,U_3124),fun(U_3125,U_3123),hAPP(fun(U_3124,U_3123),fun(fun(U_3125,U_3124),fun(U_3125,U_3123)),comp(U_3124,U_3123,U_3125),U_3121),U_3122)),top_top(fun(U_3125,bool))))
      | ~ hBOOL(hAPP(fun(U_3125,bool),bool,hAPP(fun(U_3125,U_3124),fun(fun(U_3125,bool),bool),inj_on(U_3125,U_3124),U_3122),top_top(fun(U_3125,bool))))
      | ~ hBOOL(hAPP(fun(U_3124,bool),bool,hAPP(fun(U_3124,U_3123),fun(fun(U_3124,bool),bool),inj_on(U_3124,U_3123),U_3121),top_top(fun(U_3124,bool)))) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

cnf(f_811_3,plain,
    ( hBOOL(hAPP(fun(U_3125,bool),bool,hAPP(fun(U_3125,U_3123),fun(fun(U_3125,bool),bool),inj_on(U_3125,U_3123),hAPP(fun(U_3125,U_3124),fun(U_3125,U_3123),hAPP(fun(U_3124,U_3123),fun(fun(U_3125,U_3124),fun(U_3125,U_3123)),comp(U_3124,U_3123,U_3125),U_3121),U_3122)),top_top(fun(U_3125,bool))))
    | ~ hBOOL(hAPP(fun(U_3125,bool),bool,hAPP(fun(U_3125,U_3124),fun(fun(U_3125,bool),bool),inj_on(U_3125,U_3124),U_3122),top_top(fun(U_3125,bool))))
    | ~ hBOOL(hAPP(fun(U_3124,bool),bool,hAPP(fun(U_3124,U_3123),fun(fun(U_3124,bool),bool),inj_on(U_3124,U_3123),U_3121),top_top(fun(U_3124,bool)))) ),
    inference(clausify,[status(thm)],[f_811_2]) ).

fof(f_812_1,plain,
    ! [X_a,X_b,X_c,G,F,A_1] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),bool),inj_on(X_c,X_b),G),hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),G),F)),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_722_inj__on__imageI]) ).

fof(f_812_2,plain,
    ! [U_3131,U_3130,U_3129,U_3128,U_3127,U_3126] :
      ( hBOOL(hAPP(fun(U_3129,bool),bool,hAPP(fun(U_3129,U_3130),fun(fun(U_3129,bool),bool),inj_on(U_3129,U_3130),U_3128),hAPP(fun(U_3131,bool),fun(U_3129,bool),hAPP(fun(U_3131,U_3129),fun(fun(U_3131,bool),fun(U_3129,bool)),image(U_3131,U_3129),U_3127),U_3126)))
      | ~ hBOOL(hAPP(fun(U_3131,bool),bool,hAPP(fun(U_3131,U_3130),fun(fun(U_3131,bool),bool),inj_on(U_3131,U_3130),hAPP(fun(U_3131,U_3129),fun(U_3131,U_3130),hAPP(fun(U_3129,U_3130),fun(fun(U_3131,U_3129),fun(U_3131,U_3130)),comp(U_3129,U_3130,U_3131),U_3128),U_3127)),U_3126)) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

cnf(f_812_3,plain,
    ( hBOOL(hAPP(fun(U_3129,bool),bool,hAPP(fun(U_3129,U_3130),fun(fun(U_3129,bool),bool),inj_on(U_3129,U_3130),U_3128),hAPP(fun(U_3131,bool),fun(U_3129,bool),hAPP(fun(U_3131,U_3129),fun(fun(U_3131,bool),fun(U_3129,bool)),image(U_3131,U_3129),U_3127),U_3126)))
    | ~ hBOOL(hAPP(fun(U_3131,bool),bool,hAPP(fun(U_3131,U_3130),fun(fun(U_3131,bool),bool),inj_on(U_3131,U_3130),hAPP(fun(U_3131,U_3129),fun(U_3131,U_3130),hAPP(fun(U_3129,U_3130),fun(fun(U_3131,U_3129),fun(U_3131,U_3130)),comp(U_3129,U_3130,U_3131),U_3128),U_3127)),U_3126)) ),
    inference(clausify,[status(thm)],[f_812_2]) ).

fof(f_813_1,plain,
    ! [X_c,X_a,X_b,G,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),bool),inj_on(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),G),F)),A_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),bool),inj_on(X_b,X_c),G),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_723_comp__inj__on]) ).

fof(f_813_2,plain,
    ! [U_3137,U_3136,U_3135,U_3134,U_3133,U_3132] :
      ( hBOOL(hAPP(fun(U_3136,bool),bool,hAPP(fun(U_3136,U_3137),fun(fun(U_3136,bool),bool),inj_on(U_3136,U_3137),hAPP(fun(U_3136,U_3135),fun(U_3136,U_3137),hAPP(fun(U_3135,U_3137),fun(fun(U_3136,U_3135),fun(U_3136,U_3137)),comp(U_3135,U_3137,U_3136),U_3134),U_3133)),U_3132))
      | ~ hBOOL(hAPP(fun(U_3135,bool),bool,hAPP(fun(U_3135,U_3137),fun(fun(U_3135,bool),bool),inj_on(U_3135,U_3137),U_3134),hAPP(fun(U_3136,bool),fun(U_3135,bool),hAPP(fun(U_3136,U_3135),fun(fun(U_3136,bool),fun(U_3135,bool)),image(U_3136,U_3135),U_3133),U_3132)))
      | ~ hBOOL(hAPP(fun(U_3136,bool),bool,hAPP(fun(U_3136,U_3135),fun(fun(U_3136,bool),bool),inj_on(U_3136,U_3135),U_3133),U_3132)) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

cnf(f_813_3,plain,
    ( hBOOL(hAPP(fun(U_3136,bool),bool,hAPP(fun(U_3136,U_3137),fun(fun(U_3136,bool),bool),inj_on(U_3136,U_3137),hAPP(fun(U_3136,U_3135),fun(U_3136,U_3137),hAPP(fun(U_3135,U_3137),fun(fun(U_3136,U_3135),fun(U_3136,U_3137)),comp(U_3135,U_3137,U_3136),U_3134),U_3133)),U_3132))
    | ~ hBOOL(hAPP(fun(U_3135,bool),bool,hAPP(fun(U_3135,U_3137),fun(fun(U_3135,bool),bool),inj_on(U_3135,U_3137),U_3134),hAPP(fun(U_3136,bool),fun(U_3135,bool),hAPP(fun(U_3136,U_3135),fun(fun(U_3136,bool),fun(U_3135,bool)),image(U_3136,U_3135),U_3133),U_3132)))
    | ~ hBOOL(hAPP(fun(U_3136,bool),bool,hAPP(fun(U_3136,U_3135),fun(fun(U_3136,bool),bool),inj_on(U_3136,U_3135),U_3133),U_3132)) ),
    inference(clausify,[status(thm)],[f_813_2]) ).

fof(f_814_1,plain,
    ! [X_c,X_a,X_b,F_1,F,A_1] :
      ( ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),bool),inj_on(X_b,X_c),F_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),bool),inj_on(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),F_1),F)),A_1)) )
        & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),bool),inj_on(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),F_1),F)),A_1))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),bool),inj_on(X_b,X_c),F_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_724_comp__inj__on__iff]) ).

fof(f_814_2,plain,
    ! [U_3143,U_3142,U_3141,U_3140,U_3139,U_3138] :
      ( ( ( hBOOL(hAPP(fun(U_3141,bool),bool,hAPP(fun(U_3141,U_3143),fun(fun(U_3141,bool),bool),inj_on(U_3141,U_3143),U_3140),hAPP(fun(U_3142,bool),fun(U_3141,bool),hAPP(fun(U_3142,U_3141),fun(fun(U_3142,bool),fun(U_3141,bool)),image(U_3142,U_3141),U_3139),U_3138)))
          | ~ hBOOL(hAPP(fun(U_3142,bool),bool,hAPP(fun(U_3142,U_3143),fun(fun(U_3142,bool),bool),inj_on(U_3142,U_3143),hAPP(fun(U_3142,U_3141),fun(U_3142,U_3143),hAPP(fun(U_3141,U_3143),fun(fun(U_3142,U_3141),fun(U_3142,U_3143)),comp(U_3141,U_3143,U_3142),U_3140),U_3139)),U_3138)) )
        & ( hBOOL(hAPP(fun(U_3142,bool),bool,hAPP(fun(U_3142,U_3143),fun(fun(U_3142,bool),bool),inj_on(U_3142,U_3143),hAPP(fun(U_3142,U_3141),fun(U_3142,U_3143),hAPP(fun(U_3141,U_3143),fun(fun(U_3142,U_3141),fun(U_3142,U_3143)),comp(U_3141,U_3143,U_3142),U_3140),U_3139)),U_3138))
          | ~ hBOOL(hAPP(fun(U_3141,bool),bool,hAPP(fun(U_3141,U_3143),fun(fun(U_3141,bool),bool),inj_on(U_3141,U_3143),U_3140),hAPP(fun(U_3142,bool),fun(U_3141,bool),hAPP(fun(U_3142,U_3141),fun(fun(U_3142,bool),fun(U_3141,bool)),image(U_3142,U_3141),U_3139),U_3138))) ) )
      | ~ hBOOL(hAPP(fun(U_3142,bool),bool,hAPP(fun(U_3142,U_3141),fun(fun(U_3142,bool),bool),inj_on(U_3142,U_3141),U_3139),U_3138)) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

cnf(f_814_3,plain,
    ( hBOOL(hAPP(fun(U_3142,bool),bool,hAPP(fun(U_3142,U_3143),fun(fun(U_3142,bool),bool),inj_on(U_3142,U_3143),hAPP(fun(U_3142,U_3141),fun(U_3142,U_3143),hAPP(fun(U_3141,U_3143),fun(fun(U_3142,U_3141),fun(U_3142,U_3143)),comp(U_3141,U_3143,U_3142),U_3140),U_3139)),U_3138))
    | ~ hBOOL(hAPP(fun(U_3141,bool),bool,hAPP(fun(U_3141,U_3143),fun(fun(U_3141,bool),bool),inj_on(U_3141,U_3143),U_3140),hAPP(fun(U_3142,bool),fun(U_3141,bool),hAPP(fun(U_3142,U_3141),fun(fun(U_3142,bool),fun(U_3141,bool)),image(U_3142,U_3141),U_3139),U_3138)))
    | ~ hBOOL(hAPP(fun(U_3142,bool),bool,hAPP(fun(U_3142,U_3141),fun(fun(U_3142,bool),bool),inj_on(U_3142,U_3141),U_3139),U_3138)) ),
    inference(clausify,[status(thm)],[f_814_2]) ).

cnf(f_814_4,plain,
    ( hBOOL(hAPP(fun(U_3141,bool),bool,hAPP(fun(U_3141,U_3143),fun(fun(U_3141,bool),bool),inj_on(U_3141,U_3143),U_3140),hAPP(fun(U_3142,bool),fun(U_3141,bool),hAPP(fun(U_3142,U_3141),fun(fun(U_3142,bool),fun(U_3141,bool)),image(U_3142,U_3141),U_3139),U_3138)))
    | ~ hBOOL(hAPP(fun(U_3142,bool),bool,hAPP(fun(U_3142,U_3143),fun(fun(U_3142,bool),bool),inj_on(U_3142,U_3143),hAPP(fun(U_3142,U_3141),fun(U_3142,U_3143),hAPP(fun(U_3141,U_3143),fun(fun(U_3142,U_3141),fun(U_3142,U_3143)),comp(U_3141,U_3143,U_3142),U_3140),U_3139)),U_3138))
    | ~ hBOOL(hAPP(fun(U_3142,bool),bool,hAPP(fun(U_3142,U_3141),fun(fun(U_3142,bool),bool),inj_on(U_3142,U_3141),U_3139),U_3138)) ),
    inference(clausify,[status(thm)],[f_814_2]) ).

fof(f_815_1,plain,
    ! [X_b,X_a,X_c,F,G,R_1] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,X_c),fun(X_b,X_a),hAPP(fun(X_c,X_a),fun(fun(X_b,X_c),fun(X_b,X_a)),comp(X_c,X_a,X_b),F),G)),R_1) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),F),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),R_1)),
    inference(fof_nnf,[status(thm)],[fact_725_image__compose]) ).

fof(f_815_2,plain,
    ! [U_3149,U_3148,U_3147,U_3146,U_3145,U_3144] : hAPP(fun(U_3149,bool),fun(U_3148,bool),hAPP(fun(U_3149,U_3148),fun(fun(U_3149,bool),fun(U_3148,bool)),image(U_3149,U_3148),hAPP(fun(U_3149,U_3147),fun(U_3149,U_3148),hAPP(fun(U_3147,U_3148),fun(fun(U_3149,U_3147),fun(U_3149,U_3148)),comp(U_3147,U_3148,U_3149),U_3146),U_3145)),U_3144) = hAPP(fun(U_3147,bool),fun(U_3148,bool),hAPP(fun(U_3147,U_3148),fun(fun(U_3147,bool),fun(U_3148,bool)),image(U_3147,U_3148),U_3146),hAPP(fun(U_3149,bool),fun(U_3147,bool),hAPP(fun(U_3149,U_3147),fun(fun(U_3149,bool),fun(U_3147,bool)),image(U_3149,U_3147),U_3145),U_3144)),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

cnf(f_815_3,plain,
    hAPP(fun(U_3149,bool),fun(U_3148,bool),hAPP(fun(U_3149,U_3148),fun(fun(U_3149,bool),fun(U_3148,bool)),image(U_3149,U_3148),hAPP(fun(U_3149,U_3147),fun(U_3149,U_3148),hAPP(fun(U_3147,U_3148),fun(fun(U_3149,U_3147),fun(U_3149,U_3148)),comp(U_3147,U_3148,U_3149),U_3146),U_3145)),U_3144) = hAPP(fun(U_3147,bool),fun(U_3148,bool),hAPP(fun(U_3147,U_3148),fun(fun(U_3147,bool),fun(U_3148,bool)),image(U_3147,U_3148),U_3146),hAPP(fun(U_3149,bool),fun(U_3147,bool),hAPP(fun(U_3149,U_3147),fun(fun(U_3149,bool),fun(U_3147,bool)),image(U_3149,U_3147),U_3145),U_3144)),
    inference(clausify,[status(thm)],[f_815_2]) ).

fof(f_816_1,plain,
    ! [X_a,X_b,X_c,F_1,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),bool),inj_on(X_a,X_c),F),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),F_1),F)),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_726_inj__on__imageI2]) ).

fof(f_816_2,plain,
    ! [U_3155,U_3154,U_3153,U_3152,U_3151,U_3150] :
      ( hBOOL(hAPP(fun(U_3155,bool),bool,hAPP(fun(U_3155,U_3153),fun(fun(U_3155,bool),bool),inj_on(U_3155,U_3153),U_3151),U_3150))
      | ~ hBOOL(hAPP(fun(U_3155,bool),bool,hAPP(fun(U_3155,U_3154),fun(fun(U_3155,bool),bool),inj_on(U_3155,U_3154),hAPP(fun(U_3155,U_3153),fun(U_3155,U_3154),hAPP(fun(U_3153,U_3154),fun(fun(U_3155,U_3153),fun(U_3155,U_3154)),comp(U_3153,U_3154,U_3155),U_3152),U_3151)),U_3150)) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

cnf(f_816_3,plain,
    ( hBOOL(hAPP(fun(U_3155,bool),bool,hAPP(fun(U_3155,U_3153),fun(fun(U_3155,bool),bool),inj_on(U_3155,U_3153),U_3151),U_3150))
    | ~ hBOOL(hAPP(fun(U_3155,bool),bool,hAPP(fun(U_3155,U_3154),fun(fun(U_3155,bool),bool),inj_on(U_3155,U_3154),hAPP(fun(U_3155,U_3153),fun(U_3155,U_3154),hAPP(fun(U_3153,U_3154),fun(fun(U_3155,U_3153),fun(U_3155,U_3154)),comp(U_3153,U_3154,U_3155),U_3152),U_3151)),U_3150)) ),
    inference(clausify,[status(thm)],[f_816_2]) ).

fof(f_817_1,plain,
    hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_727_nat_Osize_I1_J]) ).

cnf(f_817_2,plain,
    hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_817_1]) ).

fof(f_818_1,plain,
    ! [X_a,X_b,X_c,F,G,X_1] : hAPP(X_a,X_b,hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),F),G),X_1) = hAPP(X_c,X_b,F,hAPP(X_a,X_c,G,X_1)),
    inference(fof_nnf,[status(thm)],[fact_728_o__def]) ).

fof(f_818_2,plain,
    ! [U_3161,U_3160,U_3159,U_3158,U_3157,U_3156] : hAPP(U_3161,U_3160,hAPP(fun(U_3161,U_3159),fun(U_3161,U_3160),hAPP(fun(U_3159,U_3160),fun(fun(U_3161,U_3159),fun(U_3161,U_3160)),comp(U_3159,U_3160,U_3161),U_3158),U_3157),U_3156) = hAPP(U_3159,U_3160,U_3158,hAPP(U_3161,U_3159,U_3157,U_3156)),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

cnf(f_818_3,plain,
    hAPP(U_3161,U_3160,hAPP(fun(U_3161,U_3159),fun(U_3161,U_3160),hAPP(fun(U_3159,U_3160),fun(fun(U_3161,U_3159),fun(U_3161,U_3160)),comp(U_3159,U_3160,U_3161),U_3158),U_3157),U_3156) = hAPP(U_3159,U_3160,U_3158,hAPP(U_3161,U_3159,U_3157,U_3156)),
    inference(clausify,[status(thm)],[f_818_2]) ).

fof(f_819_1,plain,
    ! [X_a,X_c,X_b,X_d,F,G,Ha] : hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),F),hAPP(fun(X_a,X_d),fun(X_a,X_c),hAPP(fun(X_d,X_c),fun(fun(X_a,X_d),fun(X_a,X_c)),comp(X_d,X_c,X_a),G),Ha)) = hAPP(fun(X_a,X_d),fun(X_a,X_b),hAPP(fun(X_d,X_b),fun(fun(X_a,X_d),fun(X_a,X_b)),comp(X_d,X_b,X_a),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),comp(X_c,X_b,X_d),F),G)),Ha),
    inference(fof_nnf,[status(thm)],[fact_729_o__assoc]) ).

fof(f_819_2,plain,
    ! [U_3168,U_3167,U_3166,U_3165,U_3164,U_3163,U_3162] : hAPP(fun(U_3168,U_3167),fun(U_3168,U_3166),hAPP(fun(U_3167,U_3166),fun(fun(U_3168,U_3167),fun(U_3168,U_3166)),comp(U_3167,U_3166,U_3168),U_3164),hAPP(fun(U_3168,U_3165),fun(U_3168,U_3167),hAPP(fun(U_3165,U_3167),fun(fun(U_3168,U_3165),fun(U_3168,U_3167)),comp(U_3165,U_3167,U_3168),U_3163),U_3162)) = hAPP(fun(U_3168,U_3165),fun(U_3168,U_3166),hAPP(fun(U_3165,U_3166),fun(fun(U_3168,U_3165),fun(U_3168,U_3166)),comp(U_3165,U_3166,U_3168),hAPP(fun(U_3165,U_3167),fun(U_3165,U_3166),hAPP(fun(U_3167,U_3166),fun(fun(U_3165,U_3167),fun(U_3165,U_3166)),comp(U_3167,U_3166,U_3165),U_3164),U_3163)),U_3162),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

cnf(f_819_3,plain,
    hAPP(fun(U_3168,U_3167),fun(U_3168,U_3166),hAPP(fun(U_3167,U_3166),fun(fun(U_3168,U_3167),fun(U_3168,U_3166)),comp(U_3167,U_3166,U_3168),U_3164),hAPP(fun(U_3168,U_3165),fun(U_3168,U_3167),hAPP(fun(U_3165,U_3167),fun(fun(U_3168,U_3165),fun(U_3168,U_3167)),comp(U_3165,U_3167,U_3168),U_3163),U_3162)) = hAPP(fun(U_3168,U_3165),fun(U_3168,U_3166),hAPP(fun(U_3165,U_3166),fun(fun(U_3168,U_3165),fun(U_3168,U_3166)),comp(U_3165,U_3166,U_3168),hAPP(fun(U_3165,U_3167),fun(U_3165,U_3166),hAPP(fun(U_3167,U_3166),fun(fun(U_3165,U_3167),fun(U_3165,U_3166)),comp(U_3167,U_3166,U_3165),U_3164),U_3163)),U_3162),
    inference(clausify,[status(thm)],[f_819_2]) ).

fof(f_820_1,plain,
    ! [X_c,X_a,X_b,F,G,X_2] : hAPP(X_c,X_a,hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),comp(X_b,X_a,X_c),F),G),X_2) = hAPP(X_b,X_a,F,hAPP(X_c,X_b,G,X_2)),
    inference(fof_nnf,[status(thm)],[fact_730_o__apply]) ).

fof(f_820_2,plain,
    ! [U_3174,U_3173,U_3172,U_3171,U_3170,U_3169] : hAPP(U_3174,U_3173,hAPP(fun(U_3174,U_3172),fun(U_3174,U_3173),hAPP(fun(U_3172,U_3173),fun(fun(U_3174,U_3172),fun(U_3174,U_3173)),comp(U_3172,U_3173,U_3174),U_3171),U_3170),U_3169) = hAPP(U_3172,U_3173,U_3171,hAPP(U_3174,U_3172,U_3170,U_3169)),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

cnf(f_820_3,plain,
    hAPP(U_3174,U_3173,hAPP(fun(U_3174,U_3172),fun(U_3174,U_3173),hAPP(fun(U_3172,U_3173),fun(fun(U_3174,U_3172),fun(U_3174,U_3173)),comp(U_3172,U_3173,U_3174),U_3171),U_3170),U_3169) = hAPP(U_3172,U_3173,U_3171,hAPP(U_3174,U_3172,U_3170,U_3169)),
    inference(clausify,[status(thm)],[f_820_2]) ).

fof(f_821_1,plain,
    ! [X_a,X_c,X_b,X_d,V,Aa,Ba,Ca,Da] :
      ( hAPP(X_c,X_b,Aa,hAPP(X_a,X_c,Ba,V)) = hAPP(X_d,X_b,Ca,hAPP(X_a,X_d,Da,V))
      | hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),Aa),Ba) != hAPP(fun(X_a,X_d),fun(X_a,X_b),hAPP(fun(X_d,X_b),fun(fun(X_a,X_d),fun(X_a,X_b)),comp(X_d,X_b,X_a),Ca),Da) ),
    inference(fof_nnf,[status(thm)],[fact_731_o__eq__dest]) ).

fof(f_821_2,plain,
    ! [U_3183,U_3182,U_3181,U_3180,U_3179,U_3178,U_3177,U_3176,U_3175] :
      ( hAPP(U_3182,U_3181,U_3178,hAPP(U_3183,U_3182,U_3177,U_3179)) = hAPP(U_3180,U_3181,U_3176,hAPP(U_3183,U_3180,U_3175,U_3179))
      | hAPP(fun(U_3183,U_3182),fun(U_3183,U_3181),hAPP(fun(U_3182,U_3181),fun(fun(U_3183,U_3182),fun(U_3183,U_3181)),comp(U_3182,U_3181,U_3183),U_3178),U_3177) != hAPP(fun(U_3183,U_3180),fun(U_3183,U_3181),hAPP(fun(U_3180,U_3181),fun(fun(U_3183,U_3180),fun(U_3183,U_3181)),comp(U_3180,U_3181,U_3183),U_3176),U_3175) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

cnf(f_821_3,plain,
    ( hAPP(U_3182,U_3181,U_3178,hAPP(U_3183,U_3182,U_3177,U_3179)) = hAPP(U_3180,U_3181,U_3176,hAPP(U_3183,U_3180,U_3175,U_3179))
    | hAPP(fun(U_3183,U_3182),fun(U_3183,U_3181),hAPP(fun(U_3182,U_3181),fun(fun(U_3183,U_3182),fun(U_3183,U_3181)),comp(U_3182,U_3181,U_3183),U_3178),U_3177) != hAPP(fun(U_3183,U_3180),fun(U_3183,U_3181),hAPP(fun(U_3180,U_3181),fun(fun(U_3183,U_3180),fun(U_3183,U_3181)),comp(U_3180,U_3181,U_3183),U_3176),U_3175) ),
    inference(clausify,[status(thm)],[f_821_2]) ).

fof(f_822_1,plain,
    ! [X_a,X_c,X_b,X_d,Aa,Ba,Ca,Da] :
      ( ! [V_1] : hAPP(X_c,X_b,Aa,hAPP(X_a,X_c,Ba,V_1)) = hAPP(X_d,X_b,Ca,hAPP(X_a,X_d,Da,V_1))
      | hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),Aa),Ba) != hAPP(fun(X_a,X_d),fun(X_a,X_b),hAPP(fun(X_d,X_b),fun(fun(X_a,X_d),fun(X_a,X_b)),comp(X_d,X_b,X_a),Ca),Da) ),
    inference(fof_nnf,[status(thm)],[fact_732_o__eq__elim]) ).

fof(f_822_2,plain,
    ! [U_3192,U_3191,U_3190,U_3189,U_3188,U_3187,U_3186,U_3185] :
      ( ! [U_3184] : hAPP(U_3191,U_3190,U_3188,hAPP(U_3192,U_3191,U_3187,U_3184)) = hAPP(U_3189,U_3190,U_3186,hAPP(U_3192,U_3189,U_3185,U_3184))
      | hAPP(fun(U_3192,U_3191),fun(U_3192,U_3190),hAPP(fun(U_3191,U_3190),fun(fun(U_3192,U_3191),fun(U_3192,U_3190)),comp(U_3191,U_3190,U_3192),U_3188),U_3187) != hAPP(fun(U_3192,U_3189),fun(U_3192,U_3190),hAPP(fun(U_3189,U_3190),fun(fun(U_3192,U_3189),fun(U_3192,U_3190)),comp(U_3189,U_3190,U_3192),U_3186),U_3185) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

cnf(f_822_3,plain,
    ( hAPP(U_3191,U_3190,U_3188,hAPP(U_3192,U_3191,U_3187,U_3184)) = hAPP(U_3189,U_3190,U_3186,hAPP(U_3192,U_3189,U_3185,U_3184))
    | hAPP(fun(U_3192,U_3191),fun(U_3192,U_3190),hAPP(fun(U_3191,U_3190),fun(fun(U_3192,U_3191),fun(U_3192,U_3190)),comp(U_3191,U_3190,U_3192),U_3188),U_3187) != hAPP(fun(U_3192,U_3189),fun(U_3192,U_3190),hAPP(fun(U_3189,U_3190),fun(fun(U_3192,U_3189),fun(U_3192,U_3190)),comp(U_3189,U_3190,U_3192),U_3186),U_3185) ),
    inference(clausify,[status(thm)],[f_822_2]) ).

fof(f_823_1,plain,
    ! [X_a,X_b,X_c,Ca,F,X_1] : hAPP(X_a,X_b,hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),hAPP(X_b,fun(X_c,X_b),combk(X_b,X_c),Ca)),F),X_1) = ti(X_b,Ca),
    inference(fof_nnf,[status(thm)],[fact_733_K__record__comp]) ).

fof(f_823_2,plain,
    ! [U_3198,U_3197,U_3196,U_3195,U_3194,U_3193] : hAPP(U_3198,U_3197,hAPP(fun(U_3198,U_3196),fun(U_3198,U_3197),hAPP(fun(U_3196,U_3197),fun(fun(U_3198,U_3196),fun(U_3198,U_3197)),comp(U_3196,U_3197,U_3198),hAPP(U_3197,fun(U_3196,U_3197),combk(U_3197,U_3196),U_3195)),U_3194),U_3193) = ti(U_3197,U_3195),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

cnf(f_823_3,plain,
    hAPP(U_3198,U_3197,hAPP(fun(U_3198,U_3196),fun(U_3198,U_3197),hAPP(fun(U_3196,U_3197),fun(fun(U_3198,U_3196),fun(U_3198,U_3197)),comp(U_3196,U_3197,U_3198),hAPP(U_3197,fun(U_3196,U_3197),combk(U_3197,U_3196),U_3195)),U_3194),U_3193) = ti(U_3197,U_3195),
    inference(clausify,[status(thm)],[f_823_2]) ).

fof(f_824_1,plain,
    ! [X_a,X_c,X_b,V,Aa,Ba,Ca] :
      ( hAPP(X_c,X_b,Aa,hAPP(X_a,X_c,Ba,V)) = hAPP(X_a,X_b,Ca,V)
      | hAPP(fun(X_a,X_c),fun(X_a,X_b),hAPP(fun(X_c,X_b),fun(fun(X_a,X_c),fun(X_a,X_b)),comp(X_c,X_b,X_a),Aa),Ba) != ti(fun(X_a,X_b),Ca) ),
    inference(fof_nnf,[status(thm)],[fact_734_o__eq__dest__lhs]) ).

fof(f_824_2,plain,
    ! [U_3205,U_3204,U_3203,U_3202,U_3201,U_3200,U_3199] :
      ( hAPP(U_3204,U_3203,U_3201,hAPP(U_3205,U_3204,U_3200,U_3202)) = hAPP(U_3205,U_3203,U_3199,U_3202)
      | hAPP(fun(U_3205,U_3204),fun(U_3205,U_3203),hAPP(fun(U_3204,U_3203),fun(fun(U_3205,U_3204),fun(U_3205,U_3203)),comp(U_3204,U_3203,U_3205),U_3201),U_3200) != ti(fun(U_3205,U_3203),U_3199) ),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

cnf(f_824_3,plain,
    ( hAPP(U_3204,U_3203,U_3201,hAPP(U_3205,U_3204,U_3200,U_3202)) = hAPP(U_3205,U_3203,U_3199,U_3202)
    | hAPP(fun(U_3205,U_3204),fun(U_3205,U_3203),hAPP(fun(U_3204,U_3203),fun(fun(U_3205,U_3204),fun(U_3205,U_3203)),comp(U_3204,U_3203,U_3205),U_3201),U_3200) != ti(fun(U_3205,U_3203),U_3199) ),
    inference(clausify,[status(thm)],[f_824_2]) ).

fof(f_825_1,plain,
    ! [X_b,X_a,X_c,X_d,X_e,F,G,X_2,F_1,G_2,X_3] :
      ( hAPP(X_c,X_a,hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),comp(X_b,X_a,X_c),F),G),X_2) = hAPP(X_e,X_a,hAPP(fun(X_e,X_d),fun(X_e,X_a),hAPP(fun(X_d,X_a),fun(fun(X_e,X_d),fun(X_e,X_a)),comp(X_d,X_a,X_e),F_1),G_2),X_3)
      | hAPP(X_b,X_a,F,hAPP(X_c,X_b,G,X_2)) != hAPP(X_d,X_a,F_1,hAPP(X_e,X_d,G_2,X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_735_comp__cong]) ).

fof(f_825_2,plain,
    ! [U_3216,U_3215,U_3214,U_3213,U_3212,U_3211,U_3210,U_3209,U_3208,U_3207,U_3206] :
      ( hAPP(U_3214,U_3215,hAPP(fun(U_3214,U_3216),fun(U_3214,U_3215),hAPP(fun(U_3216,U_3215),fun(fun(U_3214,U_3216),fun(U_3214,U_3215)),comp(U_3216,U_3215,U_3214),U_3211),U_3210),U_3209) = hAPP(U_3212,U_3215,hAPP(fun(U_3212,U_3213),fun(U_3212,U_3215),hAPP(fun(U_3213,U_3215),fun(fun(U_3212,U_3213),fun(U_3212,U_3215)),comp(U_3213,U_3215,U_3212),U_3208),U_3207),U_3206)
      | hAPP(U_3216,U_3215,U_3211,hAPP(U_3214,U_3216,U_3210,U_3209)) != hAPP(U_3213,U_3215,U_3208,hAPP(U_3212,U_3213,U_3207,U_3206)) ),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

cnf(f_825_3,plain,
    ( hAPP(U_3214,U_3215,hAPP(fun(U_3214,U_3216),fun(U_3214,U_3215),hAPP(fun(U_3216,U_3215),fun(fun(U_3214,U_3216),fun(U_3214,U_3215)),comp(U_3216,U_3215,U_3214),U_3211),U_3210),U_3209) = hAPP(U_3212,U_3215,hAPP(fun(U_3212,U_3213),fun(U_3212,U_3215),hAPP(fun(U_3213,U_3215),fun(fun(U_3212,U_3213),fun(U_3212,U_3215)),comp(U_3213,U_3215,U_3212),U_3208),U_3207),U_3206)
    | hAPP(U_3216,U_3215,U_3211,hAPP(U_3214,U_3216,U_3210,U_3209)) != hAPP(U_3213,U_3215,U_3208,hAPP(U_3212,U_3213,U_3207,U_3206)) ),
    inference(clausify,[status(thm)],[f_825_2]) ).

fof(f_826_1,plain,
    ! [X_c,X_a,X_b,G,F] :
      ( hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),comp(X_a,X_c,X_b),G),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F))),F) = ti(fun(X_a,X_c),G)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_736_o__inv__o__cancel]) ).

fof(f_826_2,plain,
    ! [U_3221,U_3220,U_3219,U_3218,U_3217] :
      ( hAPP(fun(U_3220,U_3219),fun(U_3220,U_3221),hAPP(fun(U_3219,U_3221),fun(fun(U_3220,U_3219),fun(U_3220,U_3221)),comp(U_3219,U_3221,U_3220),hAPP(fun(U_3219,U_3220),fun(U_3219,U_3221),hAPP(fun(U_3220,U_3221),fun(fun(U_3219,U_3220),fun(U_3219,U_3221)),comp(U_3220,U_3221,U_3219),U_3218),hAPP(fun(U_3220,U_3219),fun(U_3219,U_3220),hAPP(fun(U_3220,bool),fun(fun(U_3220,U_3219),fun(U_3219,U_3220)),hilbert_inv_into(U_3220,U_3219),top_top(fun(U_3220,bool))),U_3217))),U_3217) = ti(fun(U_3220,U_3221),U_3218)
      | ~ hBOOL(hAPP(fun(U_3220,bool),bool,hAPP(fun(U_3220,U_3219),fun(fun(U_3220,bool),bool),inj_on(U_3220,U_3219),U_3217),top_top(fun(U_3220,bool)))) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

cnf(f_826_3,plain,
    ( hAPP(fun(U_3220,U_3219),fun(U_3220,U_3221),hAPP(fun(U_3219,U_3221),fun(fun(U_3220,U_3219),fun(U_3220,U_3221)),comp(U_3219,U_3221,U_3220),hAPP(fun(U_3219,U_3220),fun(U_3219,U_3221),hAPP(fun(U_3220,U_3221),fun(fun(U_3219,U_3220),fun(U_3219,U_3221)),comp(U_3220,U_3221,U_3219),U_3218),hAPP(fun(U_3220,U_3219),fun(U_3219,U_3220),hAPP(fun(U_3220,bool),fun(fun(U_3220,U_3219),fun(U_3219,U_3220)),hilbert_inv_into(U_3220,U_3219),top_top(fun(U_3220,bool))),U_3217))),U_3217) = ti(fun(U_3220,U_3221),U_3218)
    | ~ hBOOL(hAPP(fun(U_3220,bool),bool,hAPP(fun(U_3220,U_3219),fun(fun(U_3220,bool),bool),inj_on(U_3220,U_3219),U_3217),top_top(fun(U_3220,bool)))) ),
    inference(clausify,[status(thm)],[f_826_2]) ).

fof(f_827_1,plain,
    ! [X_a,X_b,X_c,X_2,F,G,A_1] :
      ( hAPP(X_b,X_c,hAPP(fun(X_c,X_b),fun(X_b,X_c),hAPP(fun(X_c,bool),fun(fun(X_c,X_b),fun(X_b,X_c)),hilbert_inv_into(X_c,X_b),A_1),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),comp(X_a,X_b,X_c),F),G)),X_2) = hAPP(X_b,X_c,hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),comp(X_a,X_c,X_b),hAPP(fun(X_c,X_a),fun(X_a,X_c),hAPP(fun(X_c,bool),fun(fun(X_c,X_a),fun(X_a,X_c)),hilbert_inv_into(X_c,X_a),A_1),G)),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1)),F)),X_2)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1))))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),bool),inj_on(X_c,X_a),G),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_737_inv__into__comp]) ).

fof(f_827_2,plain,
    ! [U_3228,U_3227,U_3226,U_3225,U_3224,U_3223,U_3222] :
      ( hAPP(U_3227,U_3226,hAPP(fun(U_3226,U_3227),fun(U_3227,U_3226),hAPP(fun(U_3226,bool),fun(fun(U_3226,U_3227),fun(U_3227,U_3226)),hilbert_inv_into(U_3226,U_3227),U_3222),hAPP(fun(U_3226,U_3228),fun(U_3226,U_3227),hAPP(fun(U_3228,U_3227),fun(fun(U_3226,U_3228),fun(U_3226,U_3227)),comp(U_3228,U_3227,U_3226),U_3224),U_3223)),U_3225) = hAPP(U_3227,U_3226,hAPP(fun(U_3227,U_3228),fun(U_3227,U_3226),hAPP(fun(U_3228,U_3226),fun(fun(U_3227,U_3228),fun(U_3227,U_3226)),comp(U_3228,U_3226,U_3227),hAPP(fun(U_3226,U_3228),fun(U_3228,U_3226),hAPP(fun(U_3226,bool),fun(fun(U_3226,U_3228),fun(U_3228,U_3226)),hilbert_inv_into(U_3226,U_3228),U_3222),U_3223)),hAPP(fun(U_3228,U_3227),fun(U_3227,U_3228),hAPP(fun(U_3228,bool),fun(fun(U_3228,U_3227),fun(U_3227,U_3228)),hilbert_inv_into(U_3228,U_3227),hAPP(fun(U_3226,bool),fun(U_3228,bool),hAPP(fun(U_3226,U_3228),fun(fun(U_3226,bool),fun(U_3228,bool)),image(U_3226,U_3228),U_3223),U_3222)),U_3224)),U_3225)
      | ~ hBOOL(hAPP(fun(U_3227,bool),bool,hAPP(U_3227,fun(fun(U_3227,bool),bool),member(U_3227),U_3225),hAPP(fun(U_3228,bool),fun(U_3227,bool),hAPP(fun(U_3228,U_3227),fun(fun(U_3228,bool),fun(U_3227,bool)),image(U_3228,U_3227),U_3224),hAPP(fun(U_3226,bool),fun(U_3228,bool),hAPP(fun(U_3226,U_3228),fun(fun(U_3226,bool),fun(U_3228,bool)),image(U_3226,U_3228),U_3223),U_3222))))
      | ~ hBOOL(hAPP(fun(U_3226,bool),bool,hAPP(fun(U_3226,U_3228),fun(fun(U_3226,bool),bool),inj_on(U_3226,U_3228),U_3223),U_3222))
      | ~ hBOOL(hAPP(fun(U_3228,bool),bool,hAPP(fun(U_3228,U_3227),fun(fun(U_3228,bool),bool),inj_on(U_3228,U_3227),U_3224),hAPP(fun(U_3226,bool),fun(U_3228,bool),hAPP(fun(U_3226,U_3228),fun(fun(U_3226,bool),fun(U_3228,bool)),image(U_3226,U_3228),U_3223),U_3222))) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

cnf(f_827_3,plain,
    ( hAPP(U_3227,U_3226,hAPP(fun(U_3226,U_3227),fun(U_3227,U_3226),hAPP(fun(U_3226,bool),fun(fun(U_3226,U_3227),fun(U_3227,U_3226)),hilbert_inv_into(U_3226,U_3227),U_3222),hAPP(fun(U_3226,U_3228),fun(U_3226,U_3227),hAPP(fun(U_3228,U_3227),fun(fun(U_3226,U_3228),fun(U_3226,U_3227)),comp(U_3228,U_3227,U_3226),U_3224),U_3223)),U_3225) = hAPP(U_3227,U_3226,hAPP(fun(U_3227,U_3228),fun(U_3227,U_3226),hAPP(fun(U_3228,U_3226),fun(fun(U_3227,U_3228),fun(U_3227,U_3226)),comp(U_3228,U_3226,U_3227),hAPP(fun(U_3226,U_3228),fun(U_3228,U_3226),hAPP(fun(U_3226,bool),fun(fun(U_3226,U_3228),fun(U_3228,U_3226)),hilbert_inv_into(U_3226,U_3228),U_3222),U_3223)),hAPP(fun(U_3228,U_3227),fun(U_3227,U_3228),hAPP(fun(U_3228,bool),fun(fun(U_3228,U_3227),fun(U_3227,U_3228)),hilbert_inv_into(U_3228,U_3227),hAPP(fun(U_3226,bool),fun(U_3228,bool),hAPP(fun(U_3226,U_3228),fun(fun(U_3226,bool),fun(U_3228,bool)),image(U_3226,U_3228),U_3223),U_3222)),U_3224)),U_3225)
    | ~ hBOOL(hAPP(fun(U_3227,bool),bool,hAPP(U_3227,fun(fun(U_3227,bool),bool),member(U_3227),U_3225),hAPP(fun(U_3228,bool),fun(U_3227,bool),hAPP(fun(U_3228,U_3227),fun(fun(U_3228,bool),fun(U_3227,bool)),image(U_3228,U_3227),U_3224),hAPP(fun(U_3226,bool),fun(U_3228,bool),hAPP(fun(U_3226,U_3228),fun(fun(U_3226,bool),fun(U_3228,bool)),image(U_3226,U_3228),U_3223),U_3222))))
    | ~ hBOOL(hAPP(fun(U_3226,bool),bool,hAPP(fun(U_3226,U_3228),fun(fun(U_3226,bool),bool),inj_on(U_3226,U_3228),U_3223),U_3222))
    | ~ hBOOL(hAPP(fun(U_3228,bool),bool,hAPP(fun(U_3228,U_3227),fun(fun(U_3228,bool),bool),inj_on(U_3228,U_3227),U_3224),hAPP(fun(U_3226,bool),fun(U_3228,bool),hAPP(fun(U_3226,U_3228),fun(fun(U_3226,bool),fun(U_3228,bool)),image(U_3226,U_3228),U_3223),U_3222))) ),
    inference(clausify,[status(thm)],[f_827_2]) ).

fof(f_828_1,plain,
    ! [X_a,X_b,X_c,X_2,F,G,A_1] :
      ( hAPP(X_b,X_c,hAPP(fun(X_c,X_b),fun(X_b,X_c),hAPP(fun(X_c,bool),fun(fun(X_c,X_b),fun(X_b,X_c)),the_inv_into(X_c,X_b),A_1),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),comp(X_a,X_b,X_c),F),G)),X_2) = hAPP(X_b,X_c,hAPP(fun(X_b,X_a),fun(X_b,X_c),hAPP(fun(X_a,X_c),fun(fun(X_b,X_a),fun(X_b,X_c)),comp(X_a,X_c,X_b),hAPP(fun(X_c,X_a),fun(X_a,X_c),hAPP(fun(X_c,bool),fun(fun(X_c,X_a),fun(X_a,X_c)),the_inv_into(X_c,X_a),A_1),G)),hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),the_inv_into(X_a,X_b),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1)),F)),X_2)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1))))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),bool),inj_on(X_c,X_a),G),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),G),A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_738_the__inv__into__comp]) ).

fof(f_828_2,plain,
    ! [U_3235,U_3234,U_3233,U_3232,U_3231,U_3230,U_3229] :
      ( hAPP(U_3234,U_3233,hAPP(fun(U_3233,U_3234),fun(U_3234,U_3233),hAPP(fun(U_3233,bool),fun(fun(U_3233,U_3234),fun(U_3234,U_3233)),the_inv_into(U_3233,U_3234),U_3229),hAPP(fun(U_3233,U_3235),fun(U_3233,U_3234),hAPP(fun(U_3235,U_3234),fun(fun(U_3233,U_3235),fun(U_3233,U_3234)),comp(U_3235,U_3234,U_3233),U_3231),U_3230)),U_3232) = hAPP(U_3234,U_3233,hAPP(fun(U_3234,U_3235),fun(U_3234,U_3233),hAPP(fun(U_3235,U_3233),fun(fun(U_3234,U_3235),fun(U_3234,U_3233)),comp(U_3235,U_3233,U_3234),hAPP(fun(U_3233,U_3235),fun(U_3235,U_3233),hAPP(fun(U_3233,bool),fun(fun(U_3233,U_3235),fun(U_3235,U_3233)),the_inv_into(U_3233,U_3235),U_3229),U_3230)),hAPP(fun(U_3235,U_3234),fun(U_3234,U_3235),hAPP(fun(U_3235,bool),fun(fun(U_3235,U_3234),fun(U_3234,U_3235)),the_inv_into(U_3235,U_3234),hAPP(fun(U_3233,bool),fun(U_3235,bool),hAPP(fun(U_3233,U_3235),fun(fun(U_3233,bool),fun(U_3235,bool)),image(U_3233,U_3235),U_3230),U_3229)),U_3231)),U_3232)
      | ~ hBOOL(hAPP(fun(U_3234,bool),bool,hAPP(U_3234,fun(fun(U_3234,bool),bool),member(U_3234),U_3232),hAPP(fun(U_3235,bool),fun(U_3234,bool),hAPP(fun(U_3235,U_3234),fun(fun(U_3235,bool),fun(U_3234,bool)),image(U_3235,U_3234),U_3231),hAPP(fun(U_3233,bool),fun(U_3235,bool),hAPP(fun(U_3233,U_3235),fun(fun(U_3233,bool),fun(U_3235,bool)),image(U_3233,U_3235),U_3230),U_3229))))
      | ~ hBOOL(hAPP(fun(U_3233,bool),bool,hAPP(fun(U_3233,U_3235),fun(fun(U_3233,bool),bool),inj_on(U_3233,U_3235),U_3230),U_3229))
      | ~ hBOOL(hAPP(fun(U_3235,bool),bool,hAPP(fun(U_3235,U_3234),fun(fun(U_3235,bool),bool),inj_on(U_3235,U_3234),U_3231),hAPP(fun(U_3233,bool),fun(U_3235,bool),hAPP(fun(U_3233,U_3235),fun(fun(U_3233,bool),fun(U_3235,bool)),image(U_3233,U_3235),U_3230),U_3229))) ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

cnf(f_828_3,plain,
    ( hAPP(U_3234,U_3233,hAPP(fun(U_3233,U_3234),fun(U_3234,U_3233),hAPP(fun(U_3233,bool),fun(fun(U_3233,U_3234),fun(U_3234,U_3233)),the_inv_into(U_3233,U_3234),U_3229),hAPP(fun(U_3233,U_3235),fun(U_3233,U_3234),hAPP(fun(U_3235,U_3234),fun(fun(U_3233,U_3235),fun(U_3233,U_3234)),comp(U_3235,U_3234,U_3233),U_3231),U_3230)),U_3232) = hAPP(U_3234,U_3233,hAPP(fun(U_3234,U_3235),fun(U_3234,U_3233),hAPP(fun(U_3235,U_3233),fun(fun(U_3234,U_3235),fun(U_3234,U_3233)),comp(U_3235,U_3233,U_3234),hAPP(fun(U_3233,U_3235),fun(U_3235,U_3233),hAPP(fun(U_3233,bool),fun(fun(U_3233,U_3235),fun(U_3235,U_3233)),the_inv_into(U_3233,U_3235),U_3229),U_3230)),hAPP(fun(U_3235,U_3234),fun(U_3234,U_3235),hAPP(fun(U_3235,bool),fun(fun(U_3235,U_3234),fun(U_3234,U_3235)),the_inv_into(U_3235,U_3234),hAPP(fun(U_3233,bool),fun(U_3235,bool),hAPP(fun(U_3233,U_3235),fun(fun(U_3233,bool),fun(U_3235,bool)),image(U_3233,U_3235),U_3230),U_3229)),U_3231)),U_3232)
    | ~ hBOOL(hAPP(fun(U_3234,bool),bool,hAPP(U_3234,fun(fun(U_3234,bool),bool),member(U_3234),U_3232),hAPP(fun(U_3235,bool),fun(U_3234,bool),hAPP(fun(U_3235,U_3234),fun(fun(U_3235,bool),fun(U_3234,bool)),image(U_3235,U_3234),U_3231),hAPP(fun(U_3233,bool),fun(U_3235,bool),hAPP(fun(U_3233,U_3235),fun(fun(U_3233,bool),fun(U_3235,bool)),image(U_3233,U_3235),U_3230),U_3229))))
    | ~ hBOOL(hAPP(fun(U_3233,bool),bool,hAPP(fun(U_3233,U_3235),fun(fun(U_3233,bool),bool),inj_on(U_3233,U_3235),U_3230),U_3229))
    | ~ hBOOL(hAPP(fun(U_3235,bool),bool,hAPP(fun(U_3235,U_3234),fun(fun(U_3235,bool),bool),inj_on(U_3235,U_3234),U_3231),hAPP(fun(U_3233,bool),fun(U_3235,bool),hAPP(fun(U_3233,U_3235),fun(fun(U_3233,bool),fun(U_3235,bool)),image(U_3233,U_3235),U_3230),U_3229))) ),
    inference(clausify,[status(thm)],[f_828_2]) ).

fof(f_829_1,plain,
    ! [X_b,X_a,G,Ha,A_1,F,Z_1,Fa] :
      ( hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),Ha),A_1)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,hAPP(fun(X_b,X_b),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_b),fun(X_b,X_a)),comp(X_b,X_a,X_b),G),Ha)),A_1)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_b),fun(fun(X_b,bool),bool),inj_on(X_b,X_b),Ha),A_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_739_folding__image_Oreindex]) ).

fof(f_829_2,plain,
    ! [U_3243,U_3242,U_3241,U_3240,U_3239,U_3238,U_3237,U_3236] :
      ( hAPP(fun(U_3243,bool),U_3242,hAPP(fun(U_3243,U_3242),fun(fun(U_3243,bool),U_3242),U_3236,U_3241),hAPP(fun(U_3243,bool),fun(U_3243,bool),hAPP(fun(U_3243,U_3243),fun(fun(U_3243,bool),fun(U_3243,bool)),image(U_3243,U_3243),U_3240),U_3239)) = hAPP(fun(U_3243,bool),U_3242,hAPP(fun(U_3243,U_3242),fun(fun(U_3243,bool),U_3242),U_3236,hAPP(fun(U_3243,U_3243),fun(U_3243,U_3242),hAPP(fun(U_3243,U_3242),fun(fun(U_3243,U_3243),fun(U_3243,U_3242)),comp(U_3243,U_3242,U_3243),U_3241),U_3240)),U_3239)
      | ~ hBOOL(hAPP(fun(U_3243,bool),bool,hAPP(fun(U_3243,U_3243),fun(fun(U_3243,bool),bool),inj_on(U_3243,U_3243),U_3240),U_3239))
      | ~ hBOOL(hAPP(fun(U_3243,bool),bool,finite_finite_1(U_3243),U_3239))
      | ~ hBOOL(hAPP(fun(fun(U_3243,U_3242),fun(fun(U_3243,bool),U_3242)),bool,hAPP(U_3242,fun(fun(fun(U_3243,U_3242),fun(fun(U_3243,bool),U_3242)),bool),hAPP(fun(U_3242,fun(U_3242,U_3242)),fun(U_3242,fun(fun(fun(U_3243,U_3242),fun(fun(U_3243,bool),U_3242)),bool)),finite_folding_image(U_3242,U_3243),U_3238),U_3237),U_3236)) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

cnf(f_829_3,plain,
    ( hAPP(fun(U_3243,bool),U_3242,hAPP(fun(U_3243,U_3242),fun(fun(U_3243,bool),U_3242),U_3236,U_3241),hAPP(fun(U_3243,bool),fun(U_3243,bool),hAPP(fun(U_3243,U_3243),fun(fun(U_3243,bool),fun(U_3243,bool)),image(U_3243,U_3243),U_3240),U_3239)) = hAPP(fun(U_3243,bool),U_3242,hAPP(fun(U_3243,U_3242),fun(fun(U_3243,bool),U_3242),U_3236,hAPP(fun(U_3243,U_3243),fun(U_3243,U_3242),hAPP(fun(U_3243,U_3242),fun(fun(U_3243,U_3243),fun(U_3243,U_3242)),comp(U_3243,U_3242,U_3243),U_3241),U_3240)),U_3239)
    | ~ hBOOL(hAPP(fun(U_3243,bool),bool,hAPP(fun(U_3243,U_3243),fun(fun(U_3243,bool),bool),inj_on(U_3243,U_3243),U_3240),U_3239))
    | ~ hBOOL(hAPP(fun(U_3243,bool),bool,finite_finite_1(U_3243),U_3239))
    | ~ hBOOL(hAPP(fun(fun(U_3243,U_3242),fun(fun(U_3243,bool),U_3242)),bool,hAPP(U_3242,fun(fun(fun(U_3243,U_3242),fun(fun(U_3243,bool),U_3242)),bool),hAPP(fun(U_3242,fun(U_3242,U_3242)),fun(U_3242,fun(fun(fun(U_3243,U_3242),fun(fun(U_3243,bool),U_3242)),bool)),finite_folding_image(U_3242,U_3243),U_3238),U_3237),U_3236)) ),
    inference(clausify,[status(thm)],[f_829_2]) ).

fof(f_830_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_740_nat_Osize_I4_J]) ).

fof(f_830_2,plain,
    ! [U_3244] : hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,U_3244)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),U_3244)),hAPP(nat,nat,suc,zero_zero(nat))),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

cnf(f_830_3,plain,
    hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,U_3244)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),U_3244)),hAPP(nat,nat,suc,zero_zero(nat))),
    inference(clausify,[status(thm)],[f_830_2]) ).

fof(f_831_1,plain,
    ! [N] : hAPP(nat,nat,size_size(nat),N) = N,
    inference(fof_nnf,[status(thm)],[fact_741_nat__size]) ).

fof(f_831_2,plain,
    ! [U_3245] : hAPP(nat,nat,size_size(nat),U_3245) = U_3245,
    inference(variable_rename,[status(thm)],[f_831_1]) ).

cnf(f_831_3,plain,
    hAPP(nat,nat,size_size(nat),U_3245) = U_3245,
    inference(clausify,[status(thm)],[f_831_2]) ).

fof(f_832_1,plain,
    ! [X_b,X_a,G,Ha,A_1,F,Z_1,Fa] :
      ( hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),F),G)),Ha)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),A_1)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,Ha),A_1))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_742_folding__image_Odistrib]) ).

fof(f_832_2,plain,
    ! [U_3253,U_3252,U_3251,U_3250,U_3249,U_3248,U_3247,U_3246] :
      ( hAPP(fun(U_3253,bool),U_3252,hAPP(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252),U_3246,hAPP(fun(U_3253,U_3252),fun(U_3253,U_3252),hAPP(fun(U_3253,fun(U_3252,U_3252)),fun(fun(U_3253,U_3252),fun(U_3253,U_3252)),combs(U_3253,U_3252,U_3252),hAPP(fun(U_3253,U_3252),fun(U_3253,fun(U_3252,U_3252)),hAPP(fun(U_3252,fun(U_3252,U_3252)),fun(fun(U_3253,U_3252),fun(U_3253,fun(U_3252,U_3252))),combb(U_3252,fun(U_3252,U_3252),U_3253),U_3248),U_3251)),U_3250)),U_3249) = hAPP(U_3252,U_3252,hAPP(U_3252,fun(U_3252,U_3252),U_3248,hAPP(fun(U_3253,bool),U_3252,hAPP(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252),U_3246,U_3251),U_3249)),hAPP(fun(U_3253,bool),U_3252,hAPP(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252),U_3246,U_3250),U_3249))
      | ~ hBOOL(hAPP(fun(U_3253,bool),bool,finite_finite_1(U_3253),U_3249))
      | ~ hBOOL(hAPP(fun(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252)),bool,hAPP(U_3252,fun(fun(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252)),bool),hAPP(fun(U_3252,fun(U_3252,U_3252)),fun(U_3252,fun(fun(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252)),bool)),finite_folding_image(U_3252,U_3253),U_3248),U_3247),U_3246)) ),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

cnf(f_832_3,plain,
    ( hAPP(fun(U_3253,bool),U_3252,hAPP(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252),U_3246,hAPP(fun(U_3253,U_3252),fun(U_3253,U_3252),hAPP(fun(U_3253,fun(U_3252,U_3252)),fun(fun(U_3253,U_3252),fun(U_3253,U_3252)),combs(U_3253,U_3252,U_3252),hAPP(fun(U_3253,U_3252),fun(U_3253,fun(U_3252,U_3252)),hAPP(fun(U_3252,fun(U_3252,U_3252)),fun(fun(U_3253,U_3252),fun(U_3253,fun(U_3252,U_3252))),combb(U_3252,fun(U_3252,U_3252),U_3253),U_3248),U_3251)),U_3250)),U_3249) = hAPP(U_3252,U_3252,hAPP(U_3252,fun(U_3252,U_3252),U_3248,hAPP(fun(U_3253,bool),U_3252,hAPP(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252),U_3246,U_3251),U_3249)),hAPP(fun(U_3253,bool),U_3252,hAPP(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252),U_3246,U_3250),U_3249))
    | ~ hBOOL(hAPP(fun(U_3253,bool),bool,finite_finite_1(U_3253),U_3249))
    | ~ hBOOL(hAPP(fun(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252)),bool,hAPP(U_3252,fun(fun(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252)),bool),hAPP(fun(U_3252,fun(U_3252,U_3252)),fun(U_3252,fun(fun(fun(U_3253,U_3252),fun(fun(U_3253,bool),U_3252)),bool)),finite_folding_image(U_3252,U_3253),U_3248),U_3247),U_3246)) ),
    inference(clausify,[status(thm)],[f_832_2]) ).

fof(f_833_1,plain,
    hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_743_nat_Osize_I3_J]) ).

cnf(f_833_2,plain,
    hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_833_1]) ).

fof(f_834_1,plain,
    ! [X_b,X_a,G,A_1,F,Z_1,Fa] :
      ( hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),A_1) = hAPP(fun(X_b,bool),X_a,hAPP(X_a,fun(fun(X_b,bool),X_a),hAPP(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_a,fun(fun(X_b,bool),X_a))),finite_fold_image(X_a,X_b),F),G),Z_1),A_1)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_744_folding__image_Oeq__fold]) ).

fof(f_834_2,plain,
    ! [U_3260,U_3259,U_3258,U_3257,U_3256,U_3255,U_3254] :
      ( hAPP(fun(U_3260,bool),U_3259,hAPP(fun(U_3260,U_3259),fun(fun(U_3260,bool),U_3259),U_3254,U_3258),U_3257) = hAPP(fun(U_3260,bool),U_3259,hAPP(U_3259,fun(fun(U_3260,bool),U_3259),hAPP(fun(U_3260,U_3259),fun(U_3259,fun(fun(U_3260,bool),U_3259)),hAPP(fun(U_3259,fun(U_3259,U_3259)),fun(fun(U_3260,U_3259),fun(U_3259,fun(fun(U_3260,bool),U_3259))),finite_fold_image(U_3259,U_3260),U_3256),U_3258),U_3255),U_3257)
      | ~ hBOOL(hAPP(fun(U_3260,bool),bool,finite_finite_1(U_3260),U_3257))
      | ~ hBOOL(hAPP(fun(fun(U_3260,U_3259),fun(fun(U_3260,bool),U_3259)),bool,hAPP(U_3259,fun(fun(fun(U_3260,U_3259),fun(fun(U_3260,bool),U_3259)),bool),hAPP(fun(U_3259,fun(U_3259,U_3259)),fun(U_3259,fun(fun(fun(U_3260,U_3259),fun(fun(U_3260,bool),U_3259)),bool)),finite_folding_image(U_3259,U_3260),U_3256),U_3255),U_3254)) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

cnf(f_834_3,plain,
    ( hAPP(fun(U_3260,bool),U_3259,hAPP(fun(U_3260,U_3259),fun(fun(U_3260,bool),U_3259),U_3254,U_3258),U_3257) = hAPP(fun(U_3260,bool),U_3259,hAPP(U_3259,fun(fun(U_3260,bool),U_3259),hAPP(fun(U_3260,U_3259),fun(U_3259,fun(fun(U_3260,bool),U_3259)),hAPP(fun(U_3259,fun(U_3259,U_3259)),fun(fun(U_3260,U_3259),fun(U_3259,fun(fun(U_3260,bool),U_3259))),finite_fold_image(U_3259,U_3260),U_3256),U_3258),U_3255),U_3257)
    | ~ hBOOL(hAPP(fun(U_3260,bool),bool,finite_finite_1(U_3260),U_3257))
    | ~ hBOOL(hAPP(fun(fun(U_3260,U_3259),fun(fun(U_3260,bool),U_3259)),bool,hAPP(U_3259,fun(fun(fun(U_3260,U_3259),fun(fun(U_3260,bool),U_3259)),bool),hAPP(fun(U_3259,fun(U_3259,U_3259)),fun(U_3259,fun(fun(fun(U_3260,U_3259),fun(fun(U_3260,bool),U_3259)),bool)),finite_folding_image(U_3259,U_3260),U_3256),U_3255),U_3254)) ),
    inference(clausify,[status(thm)],[f_834_2]) ).

fof(f_835_1,plain,
    ! [X_b,X_a,G,Ha,A_1,F,Z_1,Fa] :
      ( hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),A_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,Ha),A_1)
      | ? [X_1] :
          ( hAPP(X_b,X_a,G,X_1) != hAPP(X_b,X_a,Ha,X_1)
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_745_folding__image_Ocong]) ).

fof(f_835_2,plain,
    ! [U_3269,U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262] :
      ( hAPP(fun(U_3269,bool),U_3268,hAPP(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268),U_3262,U_3267),U_3265) = hAPP(fun(U_3269,bool),U_3268,hAPP(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268),U_3262,U_3266),U_3265)
      | ? [U_3261] :
          ( hAPP(U_3269,U_3268,U_3267,U_3261) != hAPP(U_3269,U_3268,U_3266,U_3261)
          & hBOOL(hAPP(fun(U_3269,bool),bool,hAPP(U_3269,fun(fun(U_3269,bool),bool),member(U_3269),U_3261),U_3265)) )
      | ~ hBOOL(hAPP(fun(U_3269,bool),bool,finite_finite_1(U_3269),U_3265))
      | ~ hBOOL(hAPP(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool,hAPP(U_3268,fun(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool),hAPP(fun(U_3268,fun(U_3268,U_3268)),fun(U_3268,fun(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool)),finite_folding_image(U_3268,U_3269),U_3264),U_3263),U_3262)) ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

fof(f_835_3,plain,
    ! [U_3269,U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262] :
      ( hAPP(fun(U_3269,bool),U_3268,hAPP(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268),U_3262,U_3267),U_3265) = hAPP(fun(U_3269,bool),U_3268,hAPP(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268),U_3262,U_3266),U_3265)
      | ( hAPP(U_3269,U_3268,U_3267,sK160(U_3269,U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262)) != hAPP(U_3269,U_3268,U_3266,sK160(U_3269,U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262))
        & hBOOL(hAPP(fun(U_3269,bool),bool,hAPP(U_3269,fun(fun(U_3269,bool),bool),member(U_3269),sK160(U_3269,U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262)),U_3265)) )
      | ~ hBOOL(hAPP(fun(U_3269,bool),bool,finite_finite_1(U_3269),U_3265))
      | ~ hBOOL(hAPP(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool,hAPP(U_3268,fun(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool),hAPP(fun(U_3268,fun(U_3268,U_3268)),fun(U_3268,fun(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool)),finite_folding_image(U_3268,U_3269),U_3264),U_3263),U_3262)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_3261,sK160(U_3269,U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262))],[f_835_2]) ).

cnf(f_835_4,plain,
    ( hBOOL(hAPP(fun(U_3269,bool),bool,hAPP(U_3269,fun(fun(U_3269,bool),bool),member(U_3269),sK160(U_3269,U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262)),U_3265))
    | hAPP(fun(U_3269,bool),U_3268,hAPP(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268),U_3262,U_3267),U_3265) = hAPP(fun(U_3269,bool),U_3268,hAPP(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268),U_3262,U_3266),U_3265)
    | ~ hBOOL(hAPP(fun(U_3269,bool),bool,finite_finite_1(U_3269),U_3265))
    | ~ hBOOL(hAPP(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool,hAPP(U_3268,fun(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool),hAPP(fun(U_3268,fun(U_3268,U_3268)),fun(U_3268,fun(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool)),finite_folding_image(U_3268,U_3269),U_3264),U_3263),U_3262)) ),
    inference(clausify,[status(thm)],[f_835_3]) ).

cnf(f_835_5,plain,
    ( hAPP(U_3269,U_3268,U_3267,sK160(U_3269,U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262)) != hAPP(U_3269,U_3268,U_3266,sK160(U_3269,U_3268,U_3267,U_3266,U_3265,U_3264,U_3263,U_3262))
    | hAPP(fun(U_3269,bool),U_3268,hAPP(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268),U_3262,U_3267),U_3265) = hAPP(fun(U_3269,bool),U_3268,hAPP(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268),U_3262,U_3266),U_3265)
    | ~ hBOOL(hAPP(fun(U_3269,bool),bool,finite_finite_1(U_3269),U_3265))
    | ~ hBOOL(hAPP(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool,hAPP(U_3268,fun(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool),hAPP(fun(U_3268,fun(U_3268,U_3268)),fun(U_3268,fun(fun(fun(U_3269,U_3268),fun(fun(U_3269,bool),U_3268)),bool)),finite_folding_image(U_3268,U_3269),U_3264),U_3263),U_3262)) ),
    inference(clausify,[status(thm)],[f_835_3]) ).

fof(f_836_1,plain,
    ! [X_a,A_1,B] :
      ( ( hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_a,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool))),product_Pair(fun(X_a,bool),fun(X_a,bool)),A_1),B)),finite_psubset(X_a)))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) )
      & ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) )
        | ~ hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_a,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool))),product_Pair(fun(X_a,bool),fun(X_a,bool)),A_1),B)),finite_psubset(X_a))) ) ),
    inference(fof_nnf,[status(thm)],[fact_746_in__finite__psubset]) ).

fof(f_836_2,plain,
    ! [U_3272,U_3271,U_3270] :
      ( ( hBOOL(hAPP(fun(product_prod(fun(U_3272,bool),fun(U_3272,bool)),bool),bool,hAPP(product_prod(fun(U_3272,bool),fun(U_3272,bool)),fun(fun(product_prod(fun(U_3272,bool),fun(U_3272,bool)),bool),bool),member(product_prod(fun(U_3272,bool),fun(U_3272,bool))),hAPP(fun(U_3272,bool),product_prod(fun(U_3272,bool),fun(U_3272,bool)),hAPP(fun(U_3272,bool),fun(fun(U_3272,bool),product_prod(fun(U_3272,bool),fun(U_3272,bool))),product_Pair(fun(U_3272,bool),fun(U_3272,bool)),U_3271),U_3270)),finite_psubset(U_3272)))
        | ~ hBOOL(hAPP(fun(U_3272,bool),bool,finite_finite_1(U_3272),U_3270))
        | ~ hBOOL(hAPP(fun(U_3272,bool),bool,hAPP(fun(U_3272,bool),fun(fun(U_3272,bool),bool),ord_less(fun(U_3272,bool)),U_3271),U_3270)) )
      & ( ( hBOOL(hAPP(fun(U_3272,bool),bool,finite_finite_1(U_3272),U_3270))
          & hBOOL(hAPP(fun(U_3272,bool),bool,hAPP(fun(U_3272,bool),fun(fun(U_3272,bool),bool),ord_less(fun(U_3272,bool)),U_3271),U_3270)) )
        | ~ hBOOL(hAPP(fun(product_prod(fun(U_3272,bool),fun(U_3272,bool)),bool),bool,hAPP(product_prod(fun(U_3272,bool),fun(U_3272,bool)),fun(fun(product_prod(fun(U_3272,bool),fun(U_3272,bool)),bool),bool),member(product_prod(fun(U_3272,bool),fun(U_3272,bool))),hAPP(fun(U_3272,bool),product_prod(fun(U_3272,bool),fun(U_3272,bool)),hAPP(fun(U_3272,bool),fun(fun(U_3272,bool),product_prod(fun(U_3272,bool),fun(U_3272,bool))),product_Pair(fun(U_3272,bool),fun(U_3272,bool)),U_3271),U_3270)),finite_psubset(U_3272))) ) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ( ! [U_3278,U_3276,U_3274] :
        ( hBOOL(hAPP(fun(product_prod(fun(U_3278,bool),fun(U_3278,bool)),bool),bool,hAPP(product_prod(fun(U_3278,bool),fun(U_3278,bool)),fun(fun(product_prod(fun(U_3278,bool),fun(U_3278,bool)),bool),bool),member(product_prod(fun(U_3278,bool),fun(U_3278,bool))),hAPP(fun(U_3278,bool),product_prod(fun(U_3278,bool),fun(U_3278,bool)),hAPP(fun(U_3278,bool),fun(fun(U_3278,bool),product_prod(fun(U_3278,bool),fun(U_3278,bool))),product_Pair(fun(U_3278,bool),fun(U_3278,bool)),U_3276),U_3274)),finite_psubset(U_3278)))
        | ~ hBOOL(hAPP(fun(U_3278,bool),bool,finite_finite_1(U_3278),U_3274))
        | ~ hBOOL(hAPP(fun(U_3278,bool),bool,hAPP(fun(U_3278,bool),fun(fun(U_3278,bool),bool),ord_less(fun(U_3278,bool)),U_3276),U_3274)) )
    & ! [U_3277,U_3275,U_3273] :
        ( ( hBOOL(hAPP(fun(U_3277,bool),bool,finite_finite_1(U_3277),U_3273))
          & hBOOL(hAPP(fun(U_3277,bool),bool,hAPP(fun(U_3277,bool),fun(fun(U_3277,bool),bool),ord_less(fun(U_3277,bool)),U_3275),U_3273)) )
        | ~ hBOOL(hAPP(fun(product_prod(fun(U_3277,bool),fun(U_3277,bool)),bool),bool,hAPP(product_prod(fun(U_3277,bool),fun(U_3277,bool)),fun(fun(product_prod(fun(U_3277,bool),fun(U_3277,bool)),bool),bool),member(product_prod(fun(U_3277,bool),fun(U_3277,bool))),hAPP(fun(U_3277,bool),product_prod(fun(U_3277,bool),fun(U_3277,bool)),hAPP(fun(U_3277,bool),fun(fun(U_3277,bool),product_prod(fun(U_3277,bool),fun(U_3277,bool))),product_Pair(fun(U_3277,bool),fun(U_3277,bool)),U_3275),U_3273)),finite_psubset(U_3277))) ) ),
    inference(miniscope,[status(thm)],[f_836_2]) ).

cnf(f_836_4,plain,
    ( hBOOL(hAPP(fun(U_3277,bool),bool,hAPP(fun(U_3277,bool),fun(fun(U_3277,bool),bool),ord_less(fun(U_3277,bool)),U_3275),U_3273))
    | ~ hBOOL(hAPP(fun(product_prod(fun(U_3277,bool),fun(U_3277,bool)),bool),bool,hAPP(product_prod(fun(U_3277,bool),fun(U_3277,bool)),fun(fun(product_prod(fun(U_3277,bool),fun(U_3277,bool)),bool),bool),member(product_prod(fun(U_3277,bool),fun(U_3277,bool))),hAPP(fun(U_3277,bool),product_prod(fun(U_3277,bool),fun(U_3277,bool)),hAPP(fun(U_3277,bool),fun(fun(U_3277,bool),product_prod(fun(U_3277,bool),fun(U_3277,bool))),product_Pair(fun(U_3277,bool),fun(U_3277,bool)),U_3275),U_3273)),finite_psubset(U_3277))) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

cnf(f_836_5,plain,
    ( hBOOL(hAPP(fun(U_3277,bool),bool,finite_finite_1(U_3277),U_3273))
    | ~ hBOOL(hAPP(fun(product_prod(fun(U_3277,bool),fun(U_3277,bool)),bool),bool,hAPP(product_prod(fun(U_3277,bool),fun(U_3277,bool)),fun(fun(product_prod(fun(U_3277,bool),fun(U_3277,bool)),bool),bool),member(product_prod(fun(U_3277,bool),fun(U_3277,bool))),hAPP(fun(U_3277,bool),product_prod(fun(U_3277,bool),fun(U_3277,bool)),hAPP(fun(U_3277,bool),fun(fun(U_3277,bool),product_prod(fun(U_3277,bool),fun(U_3277,bool))),product_Pair(fun(U_3277,bool),fun(U_3277,bool)),U_3275),U_3273)),finite_psubset(U_3277))) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

cnf(f_836_6,plain,
    ( hBOOL(hAPP(fun(product_prod(fun(U_3278,bool),fun(U_3278,bool)),bool),bool,hAPP(product_prod(fun(U_3278,bool),fun(U_3278,bool)),fun(fun(product_prod(fun(U_3278,bool),fun(U_3278,bool)),bool),bool),member(product_prod(fun(U_3278,bool),fun(U_3278,bool))),hAPP(fun(U_3278,bool),product_prod(fun(U_3278,bool),fun(U_3278,bool)),hAPP(fun(U_3278,bool),fun(fun(U_3278,bool),product_prod(fun(U_3278,bool),fun(U_3278,bool))),product_Pair(fun(U_3278,bool),fun(U_3278,bool)),U_3276),U_3274)),finite_psubset(U_3278)))
    | ~ hBOOL(hAPP(fun(U_3278,bool),bool,finite_finite_1(U_3278),U_3274))
    | ~ hBOOL(hAPP(fun(U_3278,bool),bool,hAPP(fun(U_3278,bool),fun(fun(U_3278,bool),bool),ord_less(fun(U_3278,bool)),U_3276),U_3274)) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

fof(f_837_1,plain,
    ! [X_a,X_b,B,A_1,F,Fa] :
      ( hAPP(fun(X_b,X_b),fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(fun(X_b,X_b),fun(X_b,X_b)),comp(X_b,X_b,X_b),hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,A_1)),hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,B)) = hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,A_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_a,bool),fun(X_b,X_b)),bool,hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool),finite_folding_idem(X_a,X_b),F),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_747_folding__idem_Osubset__comp__idem]) ).

fof(f_837_2,plain,
    ! [U_3284,U_3283,U_3282,U_3281,U_3280,U_3279] :
      ( hAPP(fun(U_3283,U_3283),fun(U_3283,U_3283),hAPP(fun(U_3283,U_3283),fun(fun(U_3283,U_3283),fun(U_3283,U_3283)),comp(U_3283,U_3283,U_3283),hAPP(fun(U_3284,bool),fun(U_3283,U_3283),U_3279,U_3281)),hAPP(fun(U_3284,bool),fun(U_3283,U_3283),U_3279,U_3282)) = hAPP(fun(U_3284,bool),fun(U_3283,U_3283),U_3279,U_3281)
      | ~ hBOOL(hAPP(fun(U_3284,bool),bool,hAPP(fun(U_3284,bool),fun(fun(U_3284,bool),bool),ord_less_eq(fun(U_3284,bool)),U_3282),U_3281))
      | ~ hBOOL(hAPP(fun(U_3284,bool),bool,finite_finite_1(U_3284),U_3281))
      | ~ hBOOL(hAPP(fun(fun(U_3284,bool),fun(U_3283,U_3283)),bool,hAPP(fun(U_3284,fun(U_3283,U_3283)),fun(fun(fun(U_3284,bool),fun(U_3283,U_3283)),bool),finite_folding_idem(U_3284,U_3283),U_3280),U_3279)) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

cnf(f_837_3,plain,
    ( hAPP(fun(U_3283,U_3283),fun(U_3283,U_3283),hAPP(fun(U_3283,U_3283),fun(fun(U_3283,U_3283),fun(U_3283,U_3283)),comp(U_3283,U_3283,U_3283),hAPP(fun(U_3284,bool),fun(U_3283,U_3283),U_3279,U_3281)),hAPP(fun(U_3284,bool),fun(U_3283,U_3283),U_3279,U_3282)) = hAPP(fun(U_3284,bool),fun(U_3283,U_3283),U_3279,U_3281)
    | ~ hBOOL(hAPP(fun(U_3284,bool),bool,hAPP(fun(U_3284,bool),fun(fun(U_3284,bool),bool),ord_less_eq(fun(U_3284,bool)),U_3282),U_3281))
    | ~ hBOOL(hAPP(fun(U_3284,bool),bool,finite_finite_1(U_3284),U_3281))
    | ~ hBOOL(hAPP(fun(fun(U_3284,bool),fun(U_3283,U_3283)),bool,hAPP(fun(U_3284,fun(U_3283,U_3283)),fun(fun(fun(U_3284,bool),fun(U_3283,U_3283)),bool),finite_folding_idem(U_3284,U_3283),U_3280),U_3279)) ),
    inference(clausify,[status(thm)],[f_837_2]) ).

fof(f_838_1,plain,
    ! [X_a,X_2,Y_1,F] :
      ( ( hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),hAPP(fun(X_a,nat),fun(product_prod(X_a,X_a),bool),measure(X_a),F)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_2)),hAPP(X_a,nat,F,Y_1))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_2)),hAPP(X_a,nat,F,Y_1)))
        | ~ hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),hAPP(fun(X_a,nat),fun(product_prod(X_a,X_a),bool),measure(X_a),F))) ) ),
    inference(fof_nnf,[status(thm)],[fact_748_in__measure]) ).

fof(f_838_2,plain,
    ! [U_3288,U_3287,U_3286,U_3285] :
      ( ( hBOOL(hAPP(fun(product_prod(U_3288,U_3288),bool),bool,hAPP(product_prod(U_3288,U_3288),fun(fun(product_prod(U_3288,U_3288),bool),bool),member(product_prod(U_3288,U_3288)),hAPP(U_3288,product_prod(U_3288,U_3288),hAPP(U_3288,fun(U_3288,product_prod(U_3288,U_3288)),product_Pair(U_3288,U_3288),U_3287),U_3286)),hAPP(fun(U_3288,nat),fun(product_prod(U_3288,U_3288),bool),measure(U_3288),U_3285)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(U_3288,nat,U_3285,U_3287)),hAPP(U_3288,nat,U_3285,U_3286))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(U_3288,nat,U_3285,U_3287)),hAPP(U_3288,nat,U_3285,U_3286)))
        | ~ hBOOL(hAPP(fun(product_prod(U_3288,U_3288),bool),bool,hAPP(product_prod(U_3288,U_3288),fun(fun(product_prod(U_3288,U_3288),bool),bool),member(product_prod(U_3288,U_3288)),hAPP(U_3288,product_prod(U_3288,U_3288),hAPP(U_3288,fun(U_3288,product_prod(U_3288,U_3288)),product_Pair(U_3288,U_3288),U_3287),U_3286)),hAPP(fun(U_3288,nat),fun(product_prod(U_3288,U_3288),bool),measure(U_3288),U_3285))) ) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

fof(f_838_3,plain,
    ( ! [U_3296,U_3294,U_3292,U_3290] :
        ( hBOOL(hAPP(fun(product_prod(U_3296,U_3296),bool),bool,hAPP(product_prod(U_3296,U_3296),fun(fun(product_prod(U_3296,U_3296),bool),bool),member(product_prod(U_3296,U_3296)),hAPP(U_3296,product_prod(U_3296,U_3296),hAPP(U_3296,fun(U_3296,product_prod(U_3296,U_3296)),product_Pair(U_3296,U_3296),U_3294),U_3292)),hAPP(fun(U_3296,nat),fun(product_prod(U_3296,U_3296),bool),measure(U_3296),U_3290)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(U_3296,nat,U_3290,U_3294)),hAPP(U_3296,nat,U_3290,U_3292))) )
    & ! [U_3295,U_3293,U_3291,U_3289] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(U_3295,nat,U_3289,U_3293)),hAPP(U_3295,nat,U_3289,U_3291)))
        | ~ hBOOL(hAPP(fun(product_prod(U_3295,U_3295),bool),bool,hAPP(product_prod(U_3295,U_3295),fun(fun(product_prod(U_3295,U_3295),bool),bool),member(product_prod(U_3295,U_3295)),hAPP(U_3295,product_prod(U_3295,U_3295),hAPP(U_3295,fun(U_3295,product_prod(U_3295,U_3295)),product_Pair(U_3295,U_3295),U_3293),U_3291)),hAPP(fun(U_3295,nat),fun(product_prod(U_3295,U_3295),bool),measure(U_3295),U_3289))) ) ),
    inference(miniscope,[status(thm)],[f_838_2]) ).

cnf(f_838_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(U_3295,nat,U_3289,U_3293)),hAPP(U_3295,nat,U_3289,U_3291)))
    | ~ hBOOL(hAPP(fun(product_prod(U_3295,U_3295),bool),bool,hAPP(product_prod(U_3295,U_3295),fun(fun(product_prod(U_3295,U_3295),bool),bool),member(product_prod(U_3295,U_3295)),hAPP(U_3295,product_prod(U_3295,U_3295),hAPP(U_3295,fun(U_3295,product_prod(U_3295,U_3295)),product_Pair(U_3295,U_3295),U_3293),U_3291)),hAPP(fun(U_3295,nat),fun(product_prod(U_3295,U_3295),bool),measure(U_3295),U_3289))) ),
    inference(clausify,[status(thm)],[f_838_3]) ).

cnf(f_838_5,plain,
    ( hBOOL(hAPP(fun(product_prod(U_3296,U_3296),bool),bool,hAPP(product_prod(U_3296,U_3296),fun(fun(product_prod(U_3296,U_3296),bool),bool),member(product_prod(U_3296,U_3296)),hAPP(U_3296,product_prod(U_3296,U_3296),hAPP(U_3296,fun(U_3296,product_prod(U_3296,U_3296)),product_Pair(U_3296,U_3296),U_3294),U_3292)),hAPP(fun(U_3296,nat),fun(product_prod(U_3296,U_3296),bool),measure(U_3296),U_3290)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(U_3296,nat,U_3290,U_3294)),hAPP(U_3296,nat,U_3290,U_3292))) ),
    inference(clausify,[status(thm)],[f_838_3]) ).

fof(f_839_1,plain,
    ! [X_c,X_a,X_b,X_2,G,F,Fa] :
      ( hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),comp(X_b,X_b,X_c),hAPP(X_a,fun(X_b,X_b),F,X_2)),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),comp(X_b,X_b,X_c),hAPP(X_a,fun(X_b,X_b),F,X_2)),G)) = hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),comp(X_b,X_b,X_c),hAPP(X_a,fun(X_b,X_b),F,X_2)),G)
      | ~ hBOOL(hAPP(fun(fun(X_a,bool),fun(X_b,X_b)),bool,hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool),finite_folding_idem(X_a,X_b),F),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_749_folding__idem_Oidem__left__comp]) ).

fof(f_839_2,plain,
    ! [U_3303,U_3302,U_3301,U_3300,U_3299,U_3298,U_3297] :
      ( hAPP(fun(U_3303,U_3301),fun(U_3303,U_3301),hAPP(fun(U_3301,U_3301),fun(fun(U_3303,U_3301),fun(U_3303,U_3301)),comp(U_3301,U_3301,U_3303),hAPP(U_3302,fun(U_3301,U_3301),U_3298,U_3300)),hAPP(fun(U_3303,U_3301),fun(U_3303,U_3301),hAPP(fun(U_3301,U_3301),fun(fun(U_3303,U_3301),fun(U_3303,U_3301)),comp(U_3301,U_3301,U_3303),hAPP(U_3302,fun(U_3301,U_3301),U_3298,U_3300)),U_3299)) = hAPP(fun(U_3303,U_3301),fun(U_3303,U_3301),hAPP(fun(U_3301,U_3301),fun(fun(U_3303,U_3301),fun(U_3303,U_3301)),comp(U_3301,U_3301,U_3303),hAPP(U_3302,fun(U_3301,U_3301),U_3298,U_3300)),U_3299)
      | ~ hBOOL(hAPP(fun(fun(U_3302,bool),fun(U_3301,U_3301)),bool,hAPP(fun(U_3302,fun(U_3301,U_3301)),fun(fun(fun(U_3302,bool),fun(U_3301,U_3301)),bool),finite_folding_idem(U_3302,U_3301),U_3298),U_3297)) ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

fof(f_839_3,plain,
    ! [U_3303,U_3302,U_3301,U_3300,U_3299,U_3298] :
      ( ! [U_3297] : ~ hBOOL(hAPP(fun(fun(U_3302,bool),fun(U_3301,U_3301)),bool,hAPP(fun(U_3302,fun(U_3301,U_3301)),fun(fun(fun(U_3302,bool),fun(U_3301,U_3301)),bool),finite_folding_idem(U_3302,U_3301),U_3298),U_3297))
      | hAPP(fun(U_3303,U_3301),fun(U_3303,U_3301),hAPP(fun(U_3301,U_3301),fun(fun(U_3303,U_3301),fun(U_3303,U_3301)),comp(U_3301,U_3301,U_3303),hAPP(U_3302,fun(U_3301,U_3301),U_3298,U_3300)),hAPP(fun(U_3303,U_3301),fun(U_3303,U_3301),hAPP(fun(U_3301,U_3301),fun(fun(U_3303,U_3301),fun(U_3303,U_3301)),comp(U_3301,U_3301,U_3303),hAPP(U_3302,fun(U_3301,U_3301),U_3298,U_3300)),U_3299)) = hAPP(fun(U_3303,U_3301),fun(U_3303,U_3301),hAPP(fun(U_3301,U_3301),fun(fun(U_3303,U_3301),fun(U_3303,U_3301)),comp(U_3301,U_3301,U_3303),hAPP(U_3302,fun(U_3301,U_3301),U_3298,U_3300)),U_3299) ),
    inference(miniscope,[status(thm)],[f_839_2]) ).

cnf(f_839_4,plain,
    ( ~ hBOOL(hAPP(fun(fun(U_3302,bool),fun(U_3301,U_3301)),bool,hAPP(fun(U_3302,fun(U_3301,U_3301)),fun(fun(fun(U_3302,bool),fun(U_3301,U_3301)),bool),finite_folding_idem(U_3302,U_3301),U_3298),U_3297))
    | hAPP(fun(U_3303,U_3301),fun(U_3303,U_3301),hAPP(fun(U_3301,U_3301),fun(fun(U_3303,U_3301),fun(U_3303,U_3301)),comp(U_3301,U_3301,U_3303),hAPP(U_3302,fun(U_3301,U_3301),U_3298,U_3300)),hAPP(fun(U_3303,U_3301),fun(U_3303,U_3301),hAPP(fun(U_3301,U_3301),fun(fun(U_3303,U_3301),fun(U_3303,U_3301)),comp(U_3301,U_3301,U_3303),hAPP(U_3302,fun(U_3301,U_3301),U_3298,U_3300)),U_3299)) = hAPP(fun(U_3303,U_3301),fun(U_3303,U_3301),hAPP(fun(U_3301,U_3301),fun(fun(U_3303,U_3301),fun(U_3303,U_3301)),comp(U_3301,U_3301,U_3303),hAPP(U_3302,fun(U_3301,U_3301),U_3298,U_3300)),U_3299) ),
    inference(clausify,[status(thm)],[f_839_3]) ).

fof(f_840_1,plain,
    ! [X_a,X_b,X_2,F,Fa] :
      ( hAPP(fun(X_b,X_b),fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(fun(X_b,X_b),fun(X_b,X_b)),comp(X_b,X_b,X_b),hAPP(X_a,fun(X_b,X_b),F,X_2)),hAPP(X_a,fun(X_b,X_b),F,X_2)) = hAPP(X_a,fun(X_b,X_b),F,X_2)
      | ~ hBOOL(hAPP(fun(fun(X_a,bool),fun(X_b,X_b)),bool,hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool),finite_folding_idem(X_a,X_b),F),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_750_folding__idem_Oidem__comp]) ).

fof(f_840_2,plain,
    ! [U_3308,U_3307,U_3306,U_3305,U_3304] :
      ( hAPP(fun(U_3307,U_3307),fun(U_3307,U_3307),hAPP(fun(U_3307,U_3307),fun(fun(U_3307,U_3307),fun(U_3307,U_3307)),comp(U_3307,U_3307,U_3307),hAPP(U_3308,fun(U_3307,U_3307),U_3305,U_3306)),hAPP(U_3308,fun(U_3307,U_3307),U_3305,U_3306)) = hAPP(U_3308,fun(U_3307,U_3307),U_3305,U_3306)
      | ~ hBOOL(hAPP(fun(fun(U_3308,bool),fun(U_3307,U_3307)),bool,hAPP(fun(U_3308,fun(U_3307,U_3307)),fun(fun(fun(U_3308,bool),fun(U_3307,U_3307)),bool),finite_folding_idem(U_3308,U_3307),U_3305),U_3304)) ),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

fof(f_840_3,plain,
    ! [U_3308,U_3307,U_3306,U_3305] :
      ( ! [U_3304] : ~ hBOOL(hAPP(fun(fun(U_3308,bool),fun(U_3307,U_3307)),bool,hAPP(fun(U_3308,fun(U_3307,U_3307)),fun(fun(fun(U_3308,bool),fun(U_3307,U_3307)),bool),finite_folding_idem(U_3308,U_3307),U_3305),U_3304))
      | hAPP(fun(U_3307,U_3307),fun(U_3307,U_3307),hAPP(fun(U_3307,U_3307),fun(fun(U_3307,U_3307),fun(U_3307,U_3307)),comp(U_3307,U_3307,U_3307),hAPP(U_3308,fun(U_3307,U_3307),U_3305,U_3306)),hAPP(U_3308,fun(U_3307,U_3307),U_3305,U_3306)) = hAPP(U_3308,fun(U_3307,U_3307),U_3305,U_3306) ),
    inference(miniscope,[status(thm)],[f_840_2]) ).

cnf(f_840_4,plain,
    ( ~ hBOOL(hAPP(fun(fun(U_3308,bool),fun(U_3307,U_3307)),bool,hAPP(fun(U_3308,fun(U_3307,U_3307)),fun(fun(fun(U_3308,bool),fun(U_3307,U_3307)),bool),finite_folding_idem(U_3308,U_3307),U_3305),U_3304))
    | hAPP(fun(U_3307,U_3307),fun(U_3307,U_3307),hAPP(fun(U_3307,U_3307),fun(fun(U_3307,U_3307),fun(U_3307,U_3307)),comp(U_3307,U_3307,U_3307),hAPP(U_3308,fun(U_3307,U_3307),U_3305,U_3306)),hAPP(U_3308,fun(U_3307,U_3307),U_3305,U_3306)) = hAPP(U_3308,fun(U_3307,U_3307),U_3305,U_3306) ),
    inference(clausify,[status(thm)],[f_840_3]) ).

fof(f_841_1,plain,
    ! [X_a,X_b,X_2,A_1,F,Fa] :
      ( hAPP(fun(X_b,X_b),fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(fun(X_b,X_b),fun(X_b,X_b)),comp(X_b,X_b,X_b),hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,A_1)),hAPP(X_a,fun(X_b,X_b),F,X_2)) = hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,A_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_a,bool),fun(X_b,X_b)),bool,hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool),finite_folding_idem(X_a,X_b),F),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_751_folding__idem_Oin__comp__idem]) ).

fof(f_841_2,plain,
    ! [U_3314,U_3313,U_3312,U_3311,U_3310,U_3309] :
      ( hAPP(fun(U_3313,U_3313),fun(U_3313,U_3313),hAPP(fun(U_3313,U_3313),fun(fun(U_3313,U_3313),fun(U_3313,U_3313)),comp(U_3313,U_3313,U_3313),hAPP(fun(U_3314,bool),fun(U_3313,U_3313),U_3309,U_3311)),hAPP(U_3314,fun(U_3313,U_3313),U_3310,U_3312)) = hAPP(fun(U_3314,bool),fun(U_3313,U_3313),U_3309,U_3311)
      | ~ hBOOL(hAPP(fun(U_3314,bool),bool,hAPP(U_3314,fun(fun(U_3314,bool),bool),member(U_3314),U_3312),U_3311))
      | ~ hBOOL(hAPP(fun(U_3314,bool),bool,finite_finite_1(U_3314),U_3311))
      | ~ hBOOL(hAPP(fun(fun(U_3314,bool),fun(U_3313,U_3313)),bool,hAPP(fun(U_3314,fun(U_3313,U_3313)),fun(fun(fun(U_3314,bool),fun(U_3313,U_3313)),bool),finite_folding_idem(U_3314,U_3313),U_3310),U_3309)) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

cnf(f_841_3,plain,
    ( hAPP(fun(U_3313,U_3313),fun(U_3313,U_3313),hAPP(fun(U_3313,U_3313),fun(fun(U_3313,U_3313),fun(U_3313,U_3313)),comp(U_3313,U_3313,U_3313),hAPP(fun(U_3314,bool),fun(U_3313,U_3313),U_3309,U_3311)),hAPP(U_3314,fun(U_3313,U_3313),U_3310,U_3312)) = hAPP(fun(U_3314,bool),fun(U_3313,U_3313),U_3309,U_3311)
    | ~ hBOOL(hAPP(fun(U_3314,bool),bool,hAPP(U_3314,fun(fun(U_3314,bool),bool),member(U_3314),U_3312),U_3311))
    | ~ hBOOL(hAPP(fun(U_3314,bool),bool,finite_finite_1(U_3314),U_3311))
    | ~ hBOOL(hAPP(fun(fun(U_3314,bool),fun(U_3313,U_3313)),bool,hAPP(fun(U_3314,fun(U_3313,U_3313)),fun(fun(fun(U_3314,bool),fun(U_3313,U_3313)),bool),finite_folding_idem(U_3314,U_3313),U_3310),U_3309)) ),
    inference(clausify,[status(thm)],[f_841_2]) ).

fof(f_842_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(nat,fun(nat,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_752_weak__decr__stable]) ).

fof(f_842_2,plain,
    ! [U_3318] :
      ( ? [U_3317] :
        ! [U_3316] : hAPP(nat,nat,U_3318,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3317),U_3316)) = hAPP(nat,nat,U_3318,U_3317)
      | ? [U_3315] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_3318,hAPP(nat,nat,suc,U_3315))),hAPP(nat,nat,U_3318,U_3315))) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ! [U_3318] :
      ( ? [U_3317] :
        ! [U_3316] : hAPP(nat,nat,U_3318,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3317),U_3316)) = hAPP(nat,nat,U_3318,U_3317)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_3318,hAPP(nat,nat,suc,sK161(U_3318)))),hAPP(nat,nat,U_3318,sK161(U_3318)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_3315,sK161(U_3318))],[f_842_2]) ).

fof(f_842_4,plain,
    ! [U_3318] :
      ( ! [U_3316] : hAPP(nat,nat,U_3318,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK162(U_3318)),U_3316)) = hAPP(nat,nat,U_3318,sK162(U_3318))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_3318,hAPP(nat,nat,suc,sK161(U_3318)))),hAPP(nat,nat,U_3318,sK161(U_3318)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_3317,sK162(U_3318))],[f_842_3]) ).

cnf(f_842_5,plain,
    ( hAPP(nat,nat,U_3318,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK162(U_3318)),U_3316)) = hAPP(nat,nat,U_3318,sK162(U_3318))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_3318,hAPP(nat,nat,suc,sK161(U_3318)))),hAPP(nat,nat,U_3318,sK161(U_3318)))) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

fof(f_843_1,plain,
    ! [X_a,R_2,F,X_2,Y_1] :
      ( hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_2)))
      | ~ hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),R_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X_a,nat,F,X_2)),hAPP(X_a,nat,F,Y_1))) ),
    inference(fof_nnf,[status(thm)],[fact_753_mlex__leq]) ).

fof(f_843_2,plain,
    ! [U_3323,U_3322,U_3321,U_3320,U_3319] :
      ( hBOOL(hAPP(fun(product_prod(U_3323,U_3323),bool),bool,hAPP(product_prod(U_3323,U_3323),fun(fun(product_prod(U_3323,U_3323),bool),bool),member(product_prod(U_3323,U_3323)),hAPP(U_3323,product_prod(U_3323,U_3323),hAPP(U_3323,fun(U_3323,product_prod(U_3323,U_3323)),product_Pair(U_3323,U_3323),U_3320),U_3319)),hAPP(fun(product_prod(U_3323,U_3323),bool),fun(product_prod(U_3323,U_3323),bool),hAPP(fun(U_3323,nat),fun(fun(product_prod(U_3323,U_3323),bool),fun(product_prod(U_3323,U_3323),bool)),mlex_prod(U_3323),U_3321),U_3322)))
      | ~ hBOOL(hAPP(fun(product_prod(U_3323,U_3323),bool),bool,hAPP(product_prod(U_3323,U_3323),fun(fun(product_prod(U_3323,U_3323),bool),bool),member(product_prod(U_3323,U_3323)),hAPP(U_3323,product_prod(U_3323,U_3323),hAPP(U_3323,fun(U_3323,product_prod(U_3323,U_3323)),product_Pair(U_3323,U_3323),U_3320),U_3319)),U_3322))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(U_3323,nat,U_3321,U_3320)),hAPP(U_3323,nat,U_3321,U_3319))) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

cnf(f_843_3,plain,
    ( hBOOL(hAPP(fun(product_prod(U_3323,U_3323),bool),bool,hAPP(product_prod(U_3323,U_3323),fun(fun(product_prod(U_3323,U_3323),bool),bool),member(product_prod(U_3323,U_3323)),hAPP(U_3323,product_prod(U_3323,U_3323),hAPP(U_3323,fun(U_3323,product_prod(U_3323,U_3323)),product_Pair(U_3323,U_3323),U_3320),U_3319)),hAPP(fun(product_prod(U_3323,U_3323),bool),fun(product_prod(U_3323,U_3323),bool),hAPP(fun(U_3323,nat),fun(fun(product_prod(U_3323,U_3323),bool),fun(product_prod(U_3323,U_3323),bool)),mlex_prod(U_3323),U_3321),U_3322)))
    | ~ hBOOL(hAPP(fun(product_prod(U_3323,U_3323),bool),bool,hAPP(product_prod(U_3323,U_3323),fun(fun(product_prod(U_3323,U_3323),bool),bool),member(product_prod(U_3323,U_3323)),hAPP(U_3323,product_prod(U_3323,U_3323),hAPP(U_3323,fun(U_3323,product_prod(U_3323,U_3323)),product_Pair(U_3323,U_3323),U_3320),U_3319)),U_3322))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(U_3323,nat,U_3321,U_3320)),hAPP(U_3323,nat,U_3321,U_3319))) ),
    inference(clausify,[status(thm)],[f_843_2]) ).

fof(f_844_1,plain,
    ! [X_a,R_2,F,X_2,Y_1] :
      ( hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_2)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_2)),hAPP(X_a,nat,F,Y_1))) ),
    inference(fof_nnf,[status(thm)],[fact_754_mlex__less]) ).

fof(f_844_2,plain,
    ! [U_3328,U_3327,U_3326,U_3325,U_3324] :
      ( hBOOL(hAPP(fun(product_prod(U_3328,U_3328),bool),bool,hAPP(product_prod(U_3328,U_3328),fun(fun(product_prod(U_3328,U_3328),bool),bool),member(product_prod(U_3328,U_3328)),hAPP(U_3328,product_prod(U_3328,U_3328),hAPP(U_3328,fun(U_3328,product_prod(U_3328,U_3328)),product_Pair(U_3328,U_3328),U_3325),U_3324)),hAPP(fun(product_prod(U_3328,U_3328),bool),fun(product_prod(U_3328,U_3328),bool),hAPP(fun(U_3328,nat),fun(fun(product_prod(U_3328,U_3328),bool),fun(product_prod(U_3328,U_3328),bool)),mlex_prod(U_3328),U_3326),U_3327)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(U_3328,nat,U_3326,U_3325)),hAPP(U_3328,nat,U_3326,U_3324))) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

cnf(f_844_3,plain,
    ( hBOOL(hAPP(fun(product_prod(U_3328,U_3328),bool),bool,hAPP(product_prod(U_3328,U_3328),fun(fun(product_prod(U_3328,U_3328),bool),bool),member(product_prod(U_3328,U_3328)),hAPP(U_3328,product_prod(U_3328,U_3328),hAPP(U_3328,fun(U_3328,product_prod(U_3328,U_3328)),product_Pair(U_3328,U_3328),U_3325),U_3324)),hAPP(fun(product_prod(U_3328,U_3328),bool),fun(product_prod(U_3328,U_3328),bool),hAPP(fun(U_3328,nat),fun(fun(product_prod(U_3328,U_3328),bool),fun(product_prod(U_3328,U_3328),bool)),mlex_prod(U_3328),U_3326),U_3327)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(U_3328,nat,U_3326,U_3325)),hAPP(U_3328,nat,U_3326,U_3324))) ),
    inference(clausify,[status(thm)],[f_844_2]) ).

fof(f_845_1,plain,
    hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_755_bool_Osize_I1_J]) ).

cnf(f_845_2,plain,
    hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_845_1]) ).

fof(f_846_1,plain,
    hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_756_bool_Osize_I2_J]) ).

cnf(f_846_2,plain,
    hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_846_1]) ).

fof(f_847_1,plain,
    ! [X_b,X_a,G,J,Ha,K,T_3,S,F,Z_1,Fa] :
      ( hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,J),S) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),T_3)
      | ? [X_1] :
          ( ( hAPP(X_b,X_a,G,hAPP(X_b,X_b,Ha,X_1)) != hAPP(X_b,X_a,J,X_1)
            | hAPP(X_b,X_b,K,hAPP(X_b,X_b,Ha,X_1)) != ti(X_b,X_1)
            | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,Ha,X_1)),T_3)) )
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),S)) )
      | ? [Y_2] :
          ( ( hAPP(X_b,X_b,Ha,hAPP(X_b,X_b,K,Y_2)) != ti(X_b,Y_2)
            | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,K,Y_2)),S)) )
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),T_3)) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S))
      | ~ hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_757_folding__image_Oeq__general__inverses]) ).

fof(f_847_2,plain,
    ! [U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331] :
      ( hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3338),U_3334) = hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3339),U_3335)
      | ? [U_3330] :
          ( ( hAPP(U_3341,U_3340,U_3339,hAPP(U_3341,U_3341,U_3337,U_3330)) != hAPP(U_3341,U_3340,U_3338,U_3330)
            | hAPP(U_3341,U_3341,U_3336,hAPP(U_3341,U_3341,U_3337,U_3330)) != ti(U_3341,U_3330)
            | ~ hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),hAPP(U_3341,U_3341,U_3337,U_3330)),U_3335)) )
          & hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),U_3330),U_3334)) )
      | ? [U_3329] :
          ( ( hAPP(U_3341,U_3341,U_3337,hAPP(U_3341,U_3341,U_3336,U_3329)) != ti(U_3341,U_3329)
            | ~ hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),hAPP(U_3341,U_3341,U_3336,U_3329)),U_3334)) )
          & hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),U_3329),U_3335)) )
      | ~ hBOOL(hAPP(fun(U_3341,bool),bool,finite_finite_1(U_3341),U_3334))
      | ~ hBOOL(hAPP(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool,hAPP(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool),hAPP(fun(U_3340,fun(U_3340,U_3340)),fun(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool)),finite_folding_image(U_3340,U_3341),U_3333),U_3332),U_3331)) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ! [U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331] :
      ( hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3338),U_3334) = hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3339),U_3335)
      | ? [U_3330] :
          ( ( hAPP(U_3341,U_3340,U_3339,hAPP(U_3341,U_3341,U_3337,U_3330)) != hAPP(U_3341,U_3340,U_3338,U_3330)
            | hAPP(U_3341,U_3341,U_3336,hAPP(U_3341,U_3341,U_3337,U_3330)) != ti(U_3341,U_3330)
            | ~ hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),hAPP(U_3341,U_3341,U_3337,U_3330)),U_3335)) )
          & hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),U_3330),U_3334)) )
      | ( ( hAPP(U_3341,U_3341,U_3337,hAPP(U_3341,U_3341,U_3336,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))) != ti(U_3341,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))
          | ~ hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),hAPP(U_3341,U_3341,U_3336,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))),U_3334)) )
        & hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331)),U_3335)) )
      | ~ hBOOL(hAPP(fun(U_3341,bool),bool,finite_finite_1(U_3341),U_3334))
      | ~ hBOOL(hAPP(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool,hAPP(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool),hAPP(fun(U_3340,fun(U_3340,U_3340)),fun(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool)),finite_folding_image(U_3340,U_3341),U_3333),U_3332),U_3331)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_3329,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))],[f_847_2]) ).

fof(f_847_4,plain,
    ! [U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331] :
      ( hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3338),U_3334) = hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3339),U_3335)
      | ( ( hAPP(U_3341,U_3340,U_3339,hAPP(U_3341,U_3341,U_3337,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))) != hAPP(U_3341,U_3340,U_3338,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))
          | hAPP(U_3341,U_3341,U_3336,hAPP(U_3341,U_3341,U_3337,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))) != ti(U_3341,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))
          | ~ hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),hAPP(U_3341,U_3341,U_3337,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))),U_3335)) )
        & hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331)),U_3334)) )
      | ( ( hAPP(U_3341,U_3341,U_3337,hAPP(U_3341,U_3341,U_3336,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))) != ti(U_3341,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))
          | ~ hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),hAPP(U_3341,U_3341,U_3336,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))),U_3334)) )
        & hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331)),U_3335)) )
      | ~ hBOOL(hAPP(fun(U_3341,bool),bool,finite_finite_1(U_3341),U_3334))
      | ~ hBOOL(hAPP(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool,hAPP(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool),hAPP(fun(U_3340,fun(U_3340,U_3340)),fun(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool)),finite_folding_image(U_3340,U_3341),U_3333),U_3332),U_3331)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_3330,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))],[f_847_3]) ).

cnf(f_847_5,plain,
    ( hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331)),U_3334))
    | hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3338),U_3334) = hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3339),U_3335)
    | hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331)),U_3335))
    | ~ hBOOL(hAPP(fun(U_3341,bool),bool,finite_finite_1(U_3341),U_3334))
    | ~ hBOOL(hAPP(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool,hAPP(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool),hAPP(fun(U_3340,fun(U_3340,U_3340)),fun(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool)),finite_folding_image(U_3340,U_3341),U_3333),U_3332),U_3331)) ),
    inference(clausify,[status(thm)],[f_847_4]) ).

cnf(f_847_6,plain,
    ( hAPP(U_3341,U_3340,U_3339,hAPP(U_3341,U_3341,U_3337,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))) != hAPP(U_3341,U_3340,U_3338,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))
    | hAPP(U_3341,U_3341,U_3336,hAPP(U_3341,U_3341,U_3337,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))) != ti(U_3341,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))
    | ~ hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),hAPP(U_3341,U_3341,U_3337,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))),U_3335))
    | hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3338),U_3334) = hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3339),U_3335)
    | hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331)),U_3335))
    | ~ hBOOL(hAPP(fun(U_3341,bool),bool,finite_finite_1(U_3341),U_3334))
    | ~ hBOOL(hAPP(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool,hAPP(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool),hAPP(fun(U_3340,fun(U_3340,U_3340)),fun(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool)),finite_folding_image(U_3340,U_3341),U_3333),U_3332),U_3331)) ),
    inference(clausify,[status(thm)],[f_847_4]) ).

cnf(f_847_7,plain,
    ( hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331)),U_3334))
    | hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3338),U_3334) = hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3339),U_3335)
    | hAPP(U_3341,U_3341,U_3337,hAPP(U_3341,U_3341,U_3336,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))) != ti(U_3341,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))
    | ~ hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),hAPP(U_3341,U_3341,U_3336,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))),U_3334))
    | ~ hBOOL(hAPP(fun(U_3341,bool),bool,finite_finite_1(U_3341),U_3334))
    | ~ hBOOL(hAPP(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool,hAPP(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool),hAPP(fun(U_3340,fun(U_3340,U_3340)),fun(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool)),finite_folding_image(U_3340,U_3341),U_3333),U_3332),U_3331)) ),
    inference(clausify,[status(thm)],[f_847_4]) ).

cnf(f_847_8,plain,
    ( hAPP(U_3341,U_3340,U_3339,hAPP(U_3341,U_3341,U_3337,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))) != hAPP(U_3341,U_3340,U_3338,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))
    | hAPP(U_3341,U_3341,U_3336,hAPP(U_3341,U_3341,U_3337,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))) != ti(U_3341,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))
    | ~ hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),hAPP(U_3341,U_3341,U_3337,sK164(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))),U_3335))
    | hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3338),U_3334) = hAPP(fun(U_3341,bool),U_3340,hAPP(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340),U_3331,U_3339),U_3335)
    | hAPP(U_3341,U_3341,U_3337,hAPP(U_3341,U_3341,U_3336,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))) != ti(U_3341,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))
    | ~ hBOOL(hAPP(fun(U_3341,bool),bool,hAPP(U_3341,fun(fun(U_3341,bool),bool),member(U_3341),hAPP(U_3341,U_3341,U_3336,sK163(U_3341,U_3340,U_3339,U_3338,U_3337,U_3336,U_3335,U_3334,U_3333,U_3332,U_3331))),U_3334))
    | ~ hBOOL(hAPP(fun(U_3341,bool),bool,finite_finite_1(U_3341),U_3334))
    | ~ hBOOL(hAPP(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool,hAPP(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool),hAPP(fun(U_3340,fun(U_3340,U_3340)),fun(U_3340,fun(fun(fun(U_3341,U_3340),fun(fun(U_3341,bool),U_3340)),bool)),finite_folding_image(U_3340,U_3341),U_3333),U_3332),U_3331)) ),
    inference(clausify,[status(thm)],[f_847_4]) ).

fof(f_848_1,plain,
    ! [X_b,X_a,Ha,G,S,R_2,F,Z_1,Fa] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,Ha),S)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),Fa,G),S)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(X_b,X_a,Ha,X_1)),hAPP(X_b,X_a,G,X_1)))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),S)) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S))
      | ? [X1,Y1,X2,Y2] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X2),Y2)))
          & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,Y1),Y2))
          & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,X1),X2)) )
      | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,Z_1),Z_1))
      | ~ hBOOL(hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool,hAPP(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),bool)),finite_folding_image(X_a,X_b),F),Z_1),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_758_folding__image_Orelated]) ).

fof(f_848_2,plain,
    ! [U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347] :
      ( hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
      | ? [U_3346] :
          ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3355,U_3354,U_3353,U_3346)),hAPP(U_3355,U_3354,U_3352,U_3346)))
          & hBOOL(hAPP(fun(U_3355,bool),bool,hAPP(U_3355,fun(fun(U_3355,bool),bool),member(U_3355),U_3346),U_3351)) )
      | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
      | ? [U_3345,U_3344,U_3343,U_3342] :
          ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,U_3345),U_3344)),hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,U_3343),U_3342)))
          & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3344),U_3342))
          & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3345),U_3343)) )
      | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
      | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

fof(f_848_3,plain,
    ! [U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347] :
      ( hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
      | ? [U_3346] :
          ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3355,U_3354,U_3353,U_3346)),hAPP(U_3355,U_3354,U_3352,U_3346)))
          & hBOOL(hAPP(fun(U_3355,bool),bool,hAPP(U_3355,fun(fun(U_3355,bool),bool),member(U_3355),U_3346),U_3351)) )
      | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
      | ? [U_3344,U_3343,U_3342] :
          ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),U_3344)),hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,U_3343),U_3342)))
          & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3344),U_3342))
          & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),U_3343)) )
      | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
      | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_3345,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))],[f_848_2]) ).

fof(f_848_4,plain,
    ! [U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347] :
      ( hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
      | ? [U_3346] :
          ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3355,U_3354,U_3353,U_3346)),hAPP(U_3355,U_3354,U_3352,U_3346)))
          & hBOOL(hAPP(fun(U_3355,bool),bool,hAPP(U_3355,fun(fun(U_3355,bool),bool),member(U_3355),U_3346),U_3351)) )
      | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
      | ? [U_3343,U_3342] :
          ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))),hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,U_3343),U_3342)))
          & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),U_3342))
          & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),U_3343)) )
      | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
      | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_3344,sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))],[f_848_3]) ).

fof(f_848_5,plain,
    ! [U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347] :
      ( hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
      | ? [U_3346] :
          ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3355,U_3354,U_3353,U_3346)),hAPP(U_3355,U_3354,U_3352,U_3346)))
          & hBOOL(hAPP(fun(U_3355,bool),bool,hAPP(U_3355,fun(fun(U_3355,bool),bool),member(U_3355),U_3346),U_3351)) )
      | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
      | ? [U_3342] :
          ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))),hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),U_3342)))
          & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),U_3342))
          & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))) )
      | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
      | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_3343,sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))],[f_848_4]) ).

fof(f_848_6,plain,
    ! [U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347] :
      ( hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
      | ? [U_3346] :
          ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3355,U_3354,U_3353,U_3346)),hAPP(U_3355,U_3354,U_3352,U_3346)))
          & hBOOL(hAPP(fun(U_3355,bool),bool,hAPP(U_3355,fun(fun(U_3355,bool),bool),member(U_3355),U_3346),U_3351)) )
      | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
      | ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))),hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK168(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))))
        & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK168(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)))
        & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))) )
      | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
      | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_3342,sK168(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))],[f_848_5]) ).

fof(f_848_7,plain,
    ! [U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347] :
      ( hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
      | ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3355,U_3354,U_3353,sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))),hAPP(U_3355,U_3354,U_3352,sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))))
        & hBOOL(hAPP(fun(U_3355,bool),bool,hAPP(U_3355,fun(fun(U_3355,bool),bool),member(U_3355),sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),U_3351)) )
      | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
      | ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))),hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK168(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))))
        & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK168(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)))
        & hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))) )
      | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
      | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_3346,sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))],[f_848_6]) ).

cnf(f_848_8,plain,
    ( hBOOL(hAPP(fun(U_3355,bool),bool,hAPP(U_3355,fun(fun(U_3355,bool),bool),member(U_3355),sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),U_3351))
    | hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
    | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
    | hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)))
    | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
    | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(clausify,[status(thm)],[f_848_7]) ).

cnf(f_848_9,plain,
    ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3355,U_3354,U_3353,sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))),hAPP(U_3355,U_3354,U_3352,sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))))
    | hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
    | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
    | hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)))
    | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
    | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(clausify,[status(thm)],[f_848_7]) ).

cnf(f_848_10,plain,
    ( hBOOL(hAPP(fun(U_3355,bool),bool,hAPP(U_3355,fun(fun(U_3355,bool),bool),member(U_3355),sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),U_3351))
    | hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
    | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
    | hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK168(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)))
    | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
    | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(clausify,[status(thm)],[f_848_7]) ).

cnf(f_848_11,plain,
    ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3355,U_3354,U_3353,sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))),hAPP(U_3355,U_3354,U_3352,sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))))
    | hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
    | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
    | hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK168(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)))
    | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
    | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(clausify,[status(thm)],[f_848_7]) ).

cnf(f_848_12,plain,
    ( hBOOL(hAPP(fun(U_3355,bool),bool,hAPP(U_3355,fun(fun(U_3355,bool),bool),member(U_3355),sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),U_3351))
    | hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
    | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
    | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))),hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK168(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))))
    | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
    | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(clausify,[status(thm)],[f_848_7]) ).

cnf(f_848_13,plain,
    ( ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3355,U_3354,U_3353,sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))),hAPP(U_3355,U_3354,U_3352,sK169(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))))
    | hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3353),U_3351)),hAPP(fun(U_3355,bool),U_3354,hAPP(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354),U_3347,U_3352),U_3351)))
    | ~ hBOOL(hAPP(fun(U_3355,bool),bool,finite_finite_1(U_3355),U_3351))
    | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK165(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK166(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))),hAPP(U_3354,U_3354,hAPP(U_3354,fun(U_3354,U_3354),U_3349,sK167(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347)),sK168(U_3355,U_3354,U_3353,U_3352,U_3351,U_3350,U_3349,U_3348,U_3347))))
    | ~ hBOOL(hAPP(U_3354,bool,hAPP(U_3354,fun(U_3354,bool),U_3350,U_3348),U_3348))
    | ~ hBOOL(hAPP(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool,hAPP(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool),hAPP(fun(U_3354,fun(U_3354,U_3354)),fun(U_3354,fun(fun(fun(U_3355,U_3354),fun(fun(U_3355,bool),U_3354)),bool)),finite_folding_image(U_3354,U_3355),U_3349),U_3348),U_3347)) ),
    inference(clausify,[status(thm)],[f_848_7]) ).

fof(f_849_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da))) ) )
      | ~ dense_linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_759_greaterThanLessThan__subseteq__atLeastAtMost__iff]) ).

fof(f_849_2,plain,
    ! [U_3360] :
      ( ! [U_3359,U_3358,U_3357,U_3356] :
          ( ( hBOOL(hAPP(fun(U_3360,bool),bool,hAPP(fun(U_3360,bool),fun(fun(U_3360,bool),bool),ord_less_eq(fun(U_3360,bool)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_gr676655987ssThan(U_3360),U_3359),U_3358)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_atLeastAtMost(U_3360),U_3357),U_3356)))
            | ( ( ~ hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3358),U_3356))
                | ~ hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3357),U_3359)) )
              & hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less(U_3360),U_3359),U_3358)) ) )
          & ( ( hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3358),U_3356))
              & hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3357),U_3359)) )
            | ~ hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less(U_3360),U_3359),U_3358))
            | ~ hBOOL(hAPP(fun(U_3360,bool),bool,hAPP(fun(U_3360,bool),fun(fun(U_3360,bool),bool),ord_less_eq(fun(U_3360,bool)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_gr676655987ssThan(U_3360),U_3359),U_3358)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_atLeastAtMost(U_3360),U_3357),U_3356))) ) )
      | ~ dense_linorder(U_3360) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ! [U_3360] :
      ( ( ! [U_3368,U_3366,U_3364,U_3362] :
            ( hBOOL(hAPP(fun(U_3360,bool),bool,hAPP(fun(U_3360,bool),fun(fun(U_3360,bool),bool),ord_less_eq(fun(U_3360,bool)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_gr676655987ssThan(U_3360),U_3368),U_3366)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_atLeastAtMost(U_3360),U_3364),U_3362)))
            | ( ( ~ hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3366),U_3362))
                | ~ hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3364),U_3368)) )
              & hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less(U_3360),U_3368),U_3366)) ) )
        & ! [U_3367,U_3365,U_3363,U_3361] :
            ( ( hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3365),U_3361))
              & hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3363),U_3367)) )
            | ~ hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less(U_3360),U_3367),U_3365))
            | ~ hBOOL(hAPP(fun(U_3360,bool),bool,hAPP(fun(U_3360,bool),fun(fun(U_3360,bool),bool),ord_less_eq(fun(U_3360,bool)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_gr676655987ssThan(U_3360),U_3367),U_3365)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_atLeastAtMost(U_3360),U_3363),U_3361))) ) )
      | ~ dense_linorder(U_3360) ),
    inference(miniscope,[status(thm)],[f_849_2]) ).

cnf(f_849_4,plain,
    ( hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3363),U_3367))
    | ~ hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less(U_3360),U_3367),U_3365))
    | ~ hBOOL(hAPP(fun(U_3360,bool),bool,hAPP(fun(U_3360,bool),fun(fun(U_3360,bool),bool),ord_less_eq(fun(U_3360,bool)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_gr676655987ssThan(U_3360),U_3367),U_3365)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_atLeastAtMost(U_3360),U_3363),U_3361)))
    | ~ dense_linorder(U_3360) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

cnf(f_849_5,plain,
    ( hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3365),U_3361))
    | ~ hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less(U_3360),U_3367),U_3365))
    | ~ hBOOL(hAPP(fun(U_3360,bool),bool,hAPP(fun(U_3360,bool),fun(fun(U_3360,bool),bool),ord_less_eq(fun(U_3360,bool)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_gr676655987ssThan(U_3360),U_3367),U_3365)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_atLeastAtMost(U_3360),U_3363),U_3361)))
    | ~ dense_linorder(U_3360) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

cnf(f_849_6,plain,
    ( hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less(U_3360),U_3368),U_3366))
    | hBOOL(hAPP(fun(U_3360,bool),bool,hAPP(fun(U_3360,bool),fun(fun(U_3360,bool),bool),ord_less_eq(fun(U_3360,bool)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_gr676655987ssThan(U_3360),U_3368),U_3366)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_atLeastAtMost(U_3360),U_3364),U_3362)))
    | ~ dense_linorder(U_3360) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

cnf(f_849_7,plain,
    ( ~ hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3366),U_3362))
    | ~ hBOOL(hAPP(U_3360,bool,hAPP(U_3360,fun(U_3360,bool),ord_less_eq(U_3360),U_3364),U_3368))
    | hBOOL(hAPP(fun(U_3360,bool),bool,hAPP(fun(U_3360,bool),fun(fun(U_3360,bool),bool),ord_less_eq(fun(U_3360,bool)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_gr676655987ssThan(U_3360),U_3368),U_3366)),hAPP(U_3360,fun(U_3360,bool),hAPP(U_3360,fun(U_3360,fun(U_3360,bool)),ord_atLeastAtMost(U_3360),U_3364),U_3362)))
    | ~ dense_linorder(U_3360) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

fof(f_850_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da))) ) )
      | ~ dense_linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_760_greaterThanAtMost__subseteq__atLeastAtMost__iff]) ).

fof(f_850_2,plain,
    ! [U_3373] :
      ( ! [U_3372,U_3371,U_3370,U_3369] :
          ( ( hBOOL(hAPP(fun(U_3373,bool),bool,hAPP(fun(U_3373,bool),fun(fun(U_3373,bool),bool),ord_less_eq(fun(U_3373,bool)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_gr1471790799AtMost(U_3373),U_3372),U_3371)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_atLeastAtMost(U_3373),U_3370),U_3369)))
            | ( ( ~ hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3371),U_3369))
                | ~ hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3370),U_3372)) )
              & hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less(U_3373),U_3372),U_3371)) ) )
          & ( ( hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3371),U_3369))
              & hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3370),U_3372)) )
            | ~ hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less(U_3373),U_3372),U_3371))
            | ~ hBOOL(hAPP(fun(U_3373,bool),bool,hAPP(fun(U_3373,bool),fun(fun(U_3373,bool),bool),ord_less_eq(fun(U_3373,bool)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_gr1471790799AtMost(U_3373),U_3372),U_3371)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_atLeastAtMost(U_3373),U_3370),U_3369))) ) )
      | ~ dense_linorder(U_3373) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ! [U_3373] :
      ( ( ! [U_3381,U_3379,U_3377,U_3375] :
            ( hBOOL(hAPP(fun(U_3373,bool),bool,hAPP(fun(U_3373,bool),fun(fun(U_3373,bool),bool),ord_less_eq(fun(U_3373,bool)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_gr1471790799AtMost(U_3373),U_3381),U_3379)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_atLeastAtMost(U_3373),U_3377),U_3375)))
            | ( ( ~ hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3379),U_3375))
                | ~ hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3377),U_3381)) )
              & hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less(U_3373),U_3381),U_3379)) ) )
        & ! [U_3380,U_3378,U_3376,U_3374] :
            ( ( hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3378),U_3374))
              & hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3376),U_3380)) )
            | ~ hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less(U_3373),U_3380),U_3378))
            | ~ hBOOL(hAPP(fun(U_3373,bool),bool,hAPP(fun(U_3373,bool),fun(fun(U_3373,bool),bool),ord_less_eq(fun(U_3373,bool)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_gr1471790799AtMost(U_3373),U_3380),U_3378)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_atLeastAtMost(U_3373),U_3376),U_3374))) ) )
      | ~ dense_linorder(U_3373) ),
    inference(miniscope,[status(thm)],[f_850_2]) ).

cnf(f_850_4,plain,
    ( hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3376),U_3380))
    | ~ hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less(U_3373),U_3380),U_3378))
    | ~ hBOOL(hAPP(fun(U_3373,bool),bool,hAPP(fun(U_3373,bool),fun(fun(U_3373,bool),bool),ord_less_eq(fun(U_3373,bool)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_gr1471790799AtMost(U_3373),U_3380),U_3378)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_atLeastAtMost(U_3373),U_3376),U_3374)))
    | ~ dense_linorder(U_3373) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_5,plain,
    ( hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3378),U_3374))
    | ~ hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less(U_3373),U_3380),U_3378))
    | ~ hBOOL(hAPP(fun(U_3373,bool),bool,hAPP(fun(U_3373,bool),fun(fun(U_3373,bool),bool),ord_less_eq(fun(U_3373,bool)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_gr1471790799AtMost(U_3373),U_3380),U_3378)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_atLeastAtMost(U_3373),U_3376),U_3374)))
    | ~ dense_linorder(U_3373) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_6,plain,
    ( hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less(U_3373),U_3381),U_3379))
    | hBOOL(hAPP(fun(U_3373,bool),bool,hAPP(fun(U_3373,bool),fun(fun(U_3373,bool),bool),ord_less_eq(fun(U_3373,bool)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_gr1471790799AtMost(U_3373),U_3381),U_3379)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_atLeastAtMost(U_3373),U_3377),U_3375)))
    | ~ dense_linorder(U_3373) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_7,plain,
    ( ~ hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3379),U_3375))
    | ~ hBOOL(hAPP(U_3373,bool,hAPP(U_3373,fun(U_3373,bool),ord_less_eq(U_3373),U_3377),U_3381))
    | hBOOL(hAPP(fun(U_3373,bool),bool,hAPP(fun(U_3373,bool),fun(fun(U_3373,bool),bool),ord_less_eq(fun(U_3373,bool)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_gr1471790799AtMost(U_3373),U_3381),U_3379)),hAPP(U_3373,fun(U_3373,bool),hAPP(U_3373,fun(U_3373,fun(U_3373,bool)),ord_atLeastAtMost(U_3373),U_3377),U_3375)))
    | ~ dense_linorder(U_3373) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

fof(f_851_1,plain,
    ! [L,U] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U))),
    inference(fof_nnf,[status(thm)],[fact_761_finite__atLeastAtMost]) ).

fof(f_851_2,plain,
    ! [U_3383,U_3382] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3383),U_3382))),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

cnf(f_851_3,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3383),U_3382))),
    inference(clausify,[status(thm)],[f_851_2]) ).

fof(f_852_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da))) ) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_762_atLeastatMost__subset__iff]) ).

fof(f_852_2,plain,
    ! [U_3388] :
      ( ! [U_3387,U_3386,U_3385,U_3384] :
          ( ( hBOOL(hAPP(fun(U_3388,bool),bool,hAPP(fun(U_3388,bool),fun(fun(U_3388,bool),bool),ord_less_eq(fun(U_3388,bool)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3387),U_3386)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3385),U_3384)))
            | ( ( ~ hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3386),U_3384))
                | ~ hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3385),U_3387)) )
              & hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3387),U_3386)) ) )
          & ( ( hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3386),U_3384))
              & hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3385),U_3387)) )
            | ~ hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3387),U_3386))
            | ~ hBOOL(hAPP(fun(U_3388,bool),bool,hAPP(fun(U_3388,bool),fun(fun(U_3388,bool),bool),ord_less_eq(fun(U_3388,bool)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3387),U_3386)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3385),U_3384))) ) )
      | ~ order(U_3388) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ! [U_3388] :
      ( ( ! [U_3396,U_3394,U_3392,U_3390] :
            ( hBOOL(hAPP(fun(U_3388,bool),bool,hAPP(fun(U_3388,bool),fun(fun(U_3388,bool),bool),ord_less_eq(fun(U_3388,bool)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3396),U_3394)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3392),U_3390)))
            | ( ( ~ hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3394),U_3390))
                | ~ hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3392),U_3396)) )
              & hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3396),U_3394)) ) )
        & ! [U_3395,U_3393,U_3391,U_3389] :
            ( ( hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3393),U_3389))
              & hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3391),U_3395)) )
            | ~ hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3395),U_3393))
            | ~ hBOOL(hAPP(fun(U_3388,bool),bool,hAPP(fun(U_3388,bool),fun(fun(U_3388,bool),bool),ord_less_eq(fun(U_3388,bool)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3395),U_3393)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3391),U_3389))) ) )
      | ~ order(U_3388) ),
    inference(miniscope,[status(thm)],[f_852_2]) ).

cnf(f_852_4,plain,
    ( hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3391),U_3395))
    | ~ hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3395),U_3393))
    | ~ hBOOL(hAPP(fun(U_3388,bool),bool,hAPP(fun(U_3388,bool),fun(fun(U_3388,bool),bool),ord_less_eq(fun(U_3388,bool)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3395),U_3393)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3391),U_3389)))
    | ~ order(U_3388) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

cnf(f_852_5,plain,
    ( hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3393),U_3389))
    | ~ hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3395),U_3393))
    | ~ hBOOL(hAPP(fun(U_3388,bool),bool,hAPP(fun(U_3388,bool),fun(fun(U_3388,bool),bool),ord_less_eq(fun(U_3388,bool)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3395),U_3393)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3391),U_3389)))
    | ~ order(U_3388) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

cnf(f_852_6,plain,
    ( hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3396),U_3394))
    | hBOOL(hAPP(fun(U_3388,bool),bool,hAPP(fun(U_3388,bool),fun(fun(U_3388,bool),bool),ord_less_eq(fun(U_3388,bool)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3396),U_3394)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3392),U_3390)))
    | ~ order(U_3388) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

cnf(f_852_7,plain,
    ( ~ hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3394),U_3390))
    | ~ hBOOL(hAPP(U_3388,bool,hAPP(U_3388,fun(U_3388,bool),ord_less_eq(U_3388),U_3392),U_3396))
    | hBOOL(hAPP(fun(U_3388,bool),bool,hAPP(fun(U_3388,bool),fun(fun(U_3388,bool),bool),ord_less_eq(fun(U_3388,bool)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3396),U_3394)),hAPP(U_3388,fun(U_3388,bool),hAPP(U_3388,fun(U_3388,fun(U_3388,bool)),ord_atLeastAtMost(U_3388),U_3392),U_3390)))
    | ~ order(U_3388) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

fof(f_853_1,plain,
    ! [L,U] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),hAPP(nat,nat,suc,U)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U),
    inference(fof_nnf,[status(thm)],[fact_763_atLeastLessThanSuc__atLeastAtMost]) ).

fof(f_853_2,plain,
    ! [U_3398,U_3397] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_3398),hAPP(nat,nat,suc,U_3397)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3398),U_3397),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

cnf(f_853_3,plain,
    hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_3398),hAPP(nat,nat,suc,U_3397)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3398),U_3397),
    inference(clausify,[status(thm)],[f_853_2]) ).

fof(f_854_1,plain,
    ! [Pa,Na] :
      ( ( ? [M_1] :
            ( hBOOL(hAPP(nat,bool,Pa,M_1))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) )
        | ! [X_1] :
            ( ~ hBOOL(hAPP(nat,bool,Pa,X_1))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),Na))) ) )
      & ( ? [X_1] :
            ( hBOOL(hAPP(nat,bool,Pa,X_1))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),Na))) )
        | ! [M_1] :
            ( ~ hBOOL(hAPP(nat,bool,Pa,M_1))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_764_ex__nat__less]) ).

fof(f_854_2,plain,
    ! [U_3404,U_3403] :
      ( ( ? [U_3402] :
            ( hBOOL(hAPP(nat,bool,U_3404,U_3402))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3402),U_3403)) )
        | ! [U_3401] :
            ( ~ hBOOL(hAPP(nat,bool,U_3404,U_3401))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3401),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3403))) ) )
      & ( ? [U_3400] :
            ( hBOOL(hAPP(nat,bool,U_3404,U_3400))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3400),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3403))) )
        | ! [U_3399] :
            ( ~ hBOOL(hAPP(nat,bool,U_3404,U_3399))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3399),U_3403)) ) ) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

fof(f_854_3,plain,
    ( ! [U_3408,U_3406] :
        ( ? [U_3402] :
            ( hBOOL(hAPP(nat,bool,U_3408,U_3402))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3402),U_3406)) )
        | ! [U_3401] :
            ( ~ hBOOL(hAPP(nat,bool,U_3408,U_3401))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3401),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3406))) ) )
    & ! [U_3407,U_3405] :
        ( ? [U_3400] :
            ( hBOOL(hAPP(nat,bool,U_3407,U_3400))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3400),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3405))) )
        | ! [U_3399] :
            ( ~ hBOOL(hAPP(nat,bool,U_3407,U_3399))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3399),U_3405)) ) ) ),
    inference(miniscope,[status(thm)],[f_854_2]) ).

fof(f_854_4,plain,
    ( ! [U_3408,U_3406] :
        ( ? [U_3402] :
            ( hBOOL(hAPP(nat,bool,U_3408,U_3402))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3402),U_3406)) )
        | ! [U_3401] :
            ( ~ hBOOL(hAPP(nat,bool,U_3408,U_3401))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3401),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3406))) ) )
    & ! [U_3407,U_3405] :
        ( ( hBOOL(hAPP(nat,bool,U_3407,sK170(U_3407,U_3405)))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK170(U_3407,U_3405)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3405))) )
        | ! [U_3399] :
            ( ~ hBOOL(hAPP(nat,bool,U_3407,U_3399))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3399),U_3405)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_3400,sK170(U_3407,U_3405))],[f_854_3]) ).

fof(f_854_5,plain,
    ( ! [U_3408,U_3406] :
        ( ( hBOOL(hAPP(nat,bool,U_3408,sK171(U_3408,U_3406)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK171(U_3408,U_3406)),U_3406)) )
        | ! [U_3401] :
            ( ~ hBOOL(hAPP(nat,bool,U_3408,U_3401))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3401),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3406))) ) )
    & ! [U_3407,U_3405] :
        ( ( hBOOL(hAPP(nat,bool,U_3407,sK170(U_3407,U_3405)))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK170(U_3407,U_3405)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3405))) )
        | ! [U_3399] :
            ( ~ hBOOL(hAPP(nat,bool,U_3407,U_3399))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3399),U_3405)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_3402,sK171(U_3408,U_3406))],[f_854_4]) ).

cnf(f_854_6,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK170(U_3407,U_3405)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3405)))
    | ~ hBOOL(hAPP(nat,bool,U_3407,U_3399))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3399),U_3405)) ),
    inference(clausify,[status(thm)],[f_854_5]) ).

cnf(f_854_7,plain,
    ( hBOOL(hAPP(nat,bool,U_3407,sK170(U_3407,U_3405)))
    | ~ hBOOL(hAPP(nat,bool,U_3407,U_3399))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3399),U_3405)) ),
    inference(clausify,[status(thm)],[f_854_5]) ).

cnf(f_854_8,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK171(U_3408,U_3406)),U_3406))
    | ~ hBOOL(hAPP(nat,bool,U_3408,U_3401))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3401),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3406))) ),
    inference(clausify,[status(thm)],[f_854_5]) ).

cnf(f_854_9,plain,
    ( hBOOL(hAPP(nat,bool,U_3408,sK171(U_3408,U_3406)))
    | ~ hBOOL(hAPP(nat,bool,U_3408,U_3401))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3401),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3406))) ),
    inference(clausify,[status(thm)],[f_854_5]) ).

fof(f_855_1,plain,
    ! [Pa,Na] :
      ( ( ! [M_1] :
            ( hBOOL(hAPP(nat,bool,Pa,M_1))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) )
        | ? [X_1] :
            ( ~ hBOOL(hAPP(nat,bool,Pa,X_1))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),Na))) ) )
      & ( ! [X_1] :
            ( hBOOL(hAPP(nat,bool,Pa,X_1))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),Na))) )
        | ? [M_1] :
            ( ~ hBOOL(hAPP(nat,bool,Pa,M_1))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_765_all__nat__less]) ).

fof(f_855_2,plain,
    ! [U_3414,U_3413] :
      ( ( ! [U_3412] :
            ( hBOOL(hAPP(nat,bool,U_3414,U_3412))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3412),U_3413)) )
        | ? [U_3411] :
            ( ~ hBOOL(hAPP(nat,bool,U_3414,U_3411))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3411),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3413))) ) )
      & ( ! [U_3410] :
            ( hBOOL(hAPP(nat,bool,U_3414,U_3410))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3410),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3413))) )
        | ? [U_3409] :
            ( ~ hBOOL(hAPP(nat,bool,U_3414,U_3409))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3409),U_3413)) ) ) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

fof(f_855_3,plain,
    ( ! [U_3418,U_3416] :
        ( ! [U_3412] :
            ( hBOOL(hAPP(nat,bool,U_3418,U_3412))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3412),U_3416)) )
        | ? [U_3411] :
            ( ~ hBOOL(hAPP(nat,bool,U_3418,U_3411))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3411),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3416))) ) )
    & ! [U_3417,U_3415] :
        ( ! [U_3410] :
            ( hBOOL(hAPP(nat,bool,U_3417,U_3410))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3410),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3415))) )
        | ? [U_3409] :
            ( ~ hBOOL(hAPP(nat,bool,U_3417,U_3409))
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3409),U_3415)) ) ) ),
    inference(miniscope,[status(thm)],[f_855_2]) ).

fof(f_855_4,plain,
    ( ! [U_3418,U_3416] :
        ( ! [U_3412] :
            ( hBOOL(hAPP(nat,bool,U_3418,U_3412))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3412),U_3416)) )
        | ? [U_3411] :
            ( ~ hBOOL(hAPP(nat,bool,U_3418,U_3411))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3411),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3416))) ) )
    & ! [U_3417,U_3415] :
        ( ! [U_3410] :
            ( hBOOL(hAPP(nat,bool,U_3417,U_3410))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3410),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3415))) )
        | ( ~ hBOOL(hAPP(nat,bool,U_3417,sK172(U_3417,U_3415)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK172(U_3417,U_3415)),U_3415)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_3409,sK172(U_3417,U_3415))],[f_855_3]) ).

fof(f_855_5,plain,
    ( ! [U_3418,U_3416] :
        ( ! [U_3412] :
            ( hBOOL(hAPP(nat,bool,U_3418,U_3412))
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3412),U_3416)) )
        | ( ~ hBOOL(hAPP(nat,bool,U_3418,sK173(U_3418,U_3416)))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK173(U_3418,U_3416)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3416))) ) )
    & ! [U_3417,U_3415] :
        ( ! [U_3410] :
            ( hBOOL(hAPP(nat,bool,U_3417,U_3410))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3410),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3415))) )
        | ( ~ hBOOL(hAPP(nat,bool,U_3417,sK172(U_3417,U_3415)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK172(U_3417,U_3415)),U_3415)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_3411,sK173(U_3418,U_3416))],[f_855_4]) ).

cnf(f_855_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK172(U_3417,U_3415)),U_3415))
    | hBOOL(hAPP(nat,bool,U_3417,U_3410))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3410),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3415))) ),
    inference(clausify,[status(thm)],[f_855_5]) ).

cnf(f_855_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_3417,sK172(U_3417,U_3415)))
    | hBOOL(hAPP(nat,bool,U_3417,U_3410))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_3410),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3415))) ),
    inference(clausify,[status(thm)],[f_855_5]) ).

cnf(f_855_8,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK173(U_3418,U_3416)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_3416)))
    | hBOOL(hAPP(nat,bool,U_3418,U_3412))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3412),U_3416)) ),
    inference(clausify,[status(thm)],[f_855_5]) ).

cnf(f_855_9,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_3418,sK173(U_3418,U_3416)))
    | hBOOL(hAPP(nat,bool,U_3418,U_3412))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3412),U_3416)) ),
    inference(clausify,[status(thm)],[f_855_5]) ).

fof(f_856_1,plain,
    ! [I,J] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J)),
    inference(fof_nnf,[status(thm)],[fact_766_image__Suc__atLeastAtMost]) ).

fof(f_856_2,plain,
    ! [U_3420,U_3419] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3420),U_3419)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,U_3420)),hAPP(nat,nat,suc,U_3419)),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

cnf(f_856_3,plain,
    hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3420),U_3419)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,U_3420)),hAPP(nat,nat,suc,U_3419)),
    inference(clausify,[status(thm)],[f_856_2]) ).

fof(f_857_1,plain,
    ! [L,U] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,L)),U) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),L),U),
    inference(fof_nnf,[status(thm)],[fact_767_atLeastSucAtMost__greaterThanAtMost]) ).

fof(f_857_2,plain,
    ! [U_3422,U_3421] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,U_3422)),U_3421) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),U_3422),U_3421),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

cnf(f_857_3,plain,
    hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,U_3422)),U_3421) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),U_3422),U_3421),
    inference(clausify,[status(thm)],[f_857_2]) ).

fof(f_858_1,plain,
    ! [K,I,J] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(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_768_image__add__atLeastAtMost]) ).

fof(f_858_2,plain,
    ! [U_3425,U_3424,U_3423] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),U_3425)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3424),U_3423)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3424),U_3425)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3423),U_3425)),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

cnf(f_858_3,plain,
    hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),U_3425)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3424),U_3423)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3424),U_3425)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3423),U_3425)),
    inference(clausify,[status(thm)],[f_858_2]) ).

fof(f_859_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Da))
            | ( ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Da))
                  & ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Aa)) )
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Da))
              & ( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Da))
                    | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ca),Aa)) )
                  & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
                  & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) )
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da))) ) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_769_atLeastatMost__psubset__iff]) ).

fof(f_859_2,plain,
    ! [U_3430] :
      ( ! [U_3429,U_3428,U_3427,U_3426] :
          ( ( hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3429),U_3428)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3427),U_3426)))
            | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3427),U_3426))
            | ( ( ( ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3428),U_3426))
                  & ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3427),U_3429)) )
                | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3428),U_3426))
                | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3427),U_3429)) )
              & hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3429),U_3428)) ) )
          & ( ( hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3427),U_3426))
              & ( ( ( hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3428),U_3426))
                    | hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3427),U_3429)) )
                  & hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3428),U_3426))
                  & hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3427),U_3429)) )
                | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3429),U_3428)) ) )
            | ~ hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3429),U_3428)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3427),U_3426))) ) )
      | ~ order(U_3430) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ! [U_3430] :
      ( ( ! [U_3438,U_3436,U_3434,U_3432] :
            ( hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3438),U_3436)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3434),U_3432)))
            | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3434),U_3432))
            | ( ( ( ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3436),U_3432))
                  & ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3434),U_3438)) )
                | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3436),U_3432))
                | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3434),U_3438)) )
              & hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3438),U_3436)) ) )
        & ! [U_3437,U_3435,U_3433,U_3431] :
            ( ( hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3433),U_3431))
              & ( ( ( hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3435),U_3431))
                    | hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3433),U_3437)) )
                  & hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3435),U_3431))
                  & hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3433),U_3437)) )
                | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3437),U_3435)) ) )
            | ~ hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3437),U_3435)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3433),U_3431))) ) )
      | ~ order(U_3430) ),
    inference(miniscope,[status(thm)],[f_859_2]) ).

cnf(f_859_4,plain,
    ( hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3433),U_3437))
    | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3437),U_3435))
    | ~ hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3437),U_3435)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3433),U_3431)))
    | ~ order(U_3430) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

cnf(f_859_5,plain,
    ( hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3435),U_3431))
    | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3437),U_3435))
    | ~ hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3437),U_3435)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3433),U_3431)))
    | ~ order(U_3430) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

cnf(f_859_6,plain,
    ( hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3435),U_3431))
    | hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3433),U_3437))
    | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3437),U_3435))
    | ~ hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3437),U_3435)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3433),U_3431)))
    | ~ order(U_3430) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

cnf(f_859_7,plain,
    ( hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3433),U_3431))
    | ~ hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3437),U_3435)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3433),U_3431)))
    | ~ order(U_3430) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

cnf(f_859_8,plain,
    ( hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3438),U_3436))
    | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3434),U_3432))
    | hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3438),U_3436)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3434),U_3432)))
    | ~ order(U_3430) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

cnf(f_859_9,plain,
    ( ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3434),U_3438))
    | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3436),U_3432))
    | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3434),U_3438))
    | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3434),U_3432))
    | hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3438),U_3436)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3434),U_3432)))
    | ~ order(U_3430) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

cnf(f_859_10,plain,
    ( ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less(U_3430),U_3436),U_3432))
    | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3436),U_3432))
    | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3434),U_3438))
    | ~ hBOOL(hAPP(U_3430,bool,hAPP(U_3430,fun(U_3430,bool),ord_less_eq(U_3430),U_3434),U_3432))
    | hBOOL(hAPP(fun(U_3430,bool),bool,hAPP(fun(U_3430,bool),fun(fun(U_3430,bool),bool),ord_less(fun(U_3430,bool)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3438),U_3436)),hAPP(U_3430,fun(U_3430,bool),hAPP(U_3430,fun(U_3430,fun(U_3430,bool)),ord_atLeastAtMost(U_3430),U_3434),U_3432)))
    | ~ order(U_3430) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

fof(f_860_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Da))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Ca),Da))) ) )
      | ~ dense_linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_770_atLeastAtMost__subseteq__atLeastLessThan__iff]) ).

fof(f_860_2,plain,
    ! [U_3443] :
      ( ! [U_3442,U_3441,U_3440,U_3439] :
          ( ( hBOOL(hAPP(fun(U_3443,bool),bool,hAPP(fun(U_3443,bool),fun(fun(U_3443,bool),bool),ord_less_eq(fun(U_3443,bool)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastAtMost(U_3443),U_3442),U_3441)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastLessThan(U_3443),U_3440),U_3439)))
            | ( ( ~ hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less(U_3443),U_3441),U_3439))
                | ~ hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3440),U_3442)) )
              & hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3442),U_3441)) ) )
          & ( ( hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less(U_3443),U_3441),U_3439))
              & hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3440),U_3442)) )
            | ~ hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3442),U_3441))
            | ~ hBOOL(hAPP(fun(U_3443,bool),bool,hAPP(fun(U_3443,bool),fun(fun(U_3443,bool),bool),ord_less_eq(fun(U_3443,bool)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastAtMost(U_3443),U_3442),U_3441)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastLessThan(U_3443),U_3440),U_3439))) ) )
      | ~ dense_linorder(U_3443) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ! [U_3443] :
      ( ( ! [U_3451,U_3449,U_3447,U_3445] :
            ( hBOOL(hAPP(fun(U_3443,bool),bool,hAPP(fun(U_3443,bool),fun(fun(U_3443,bool),bool),ord_less_eq(fun(U_3443,bool)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastAtMost(U_3443),U_3451),U_3449)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastLessThan(U_3443),U_3447),U_3445)))
            | ( ( ~ hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less(U_3443),U_3449),U_3445))
                | ~ hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3447),U_3451)) )
              & hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3451),U_3449)) ) )
        & ! [U_3450,U_3448,U_3446,U_3444] :
            ( ( hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less(U_3443),U_3448),U_3444))
              & hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3446),U_3450)) )
            | ~ hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3450),U_3448))
            | ~ hBOOL(hAPP(fun(U_3443,bool),bool,hAPP(fun(U_3443,bool),fun(fun(U_3443,bool),bool),ord_less_eq(fun(U_3443,bool)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastAtMost(U_3443),U_3450),U_3448)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastLessThan(U_3443),U_3446),U_3444))) ) )
      | ~ dense_linorder(U_3443) ),
    inference(miniscope,[status(thm)],[f_860_2]) ).

cnf(f_860_4,plain,
    ( hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3446),U_3450))
    | ~ hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3450),U_3448))
    | ~ hBOOL(hAPP(fun(U_3443,bool),bool,hAPP(fun(U_3443,bool),fun(fun(U_3443,bool),bool),ord_less_eq(fun(U_3443,bool)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastAtMost(U_3443),U_3450),U_3448)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastLessThan(U_3443),U_3446),U_3444)))
    | ~ dense_linorder(U_3443) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

cnf(f_860_5,plain,
    ( hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less(U_3443),U_3448),U_3444))
    | ~ hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3450),U_3448))
    | ~ hBOOL(hAPP(fun(U_3443,bool),bool,hAPP(fun(U_3443,bool),fun(fun(U_3443,bool),bool),ord_less_eq(fun(U_3443,bool)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastAtMost(U_3443),U_3450),U_3448)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastLessThan(U_3443),U_3446),U_3444)))
    | ~ dense_linorder(U_3443) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

cnf(f_860_6,plain,
    ( hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3451),U_3449))
    | hBOOL(hAPP(fun(U_3443,bool),bool,hAPP(fun(U_3443,bool),fun(fun(U_3443,bool),bool),ord_less_eq(fun(U_3443,bool)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastAtMost(U_3443),U_3451),U_3449)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastLessThan(U_3443),U_3447),U_3445)))
    | ~ dense_linorder(U_3443) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

cnf(f_860_7,plain,
    ( ~ hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less(U_3443),U_3449),U_3445))
    | ~ hBOOL(hAPP(U_3443,bool,hAPP(U_3443,fun(U_3443,bool),ord_less_eq(U_3443),U_3447),U_3451))
    | hBOOL(hAPP(fun(U_3443,bool),bool,hAPP(fun(U_3443,bool),fun(fun(U_3443,bool),bool),ord_less_eq(fun(U_3443,bool)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastAtMost(U_3443),U_3451),U_3449)),hAPP(U_3443,fun(U_3443,bool),hAPP(U_3443,fun(U_3443,fun(U_3443,bool)),ord_atLeastLessThan(U_3443),U_3447),U_3445)))
    | ~ dense_linorder(U_3443) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

fof(f_861_1,plain,
    ! [X_a] :
      ( ! [Aa,Ba,Ca,Da] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da)))
            | ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
                | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) ) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Da))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ca),Aa)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Ca),Da))) ) )
      | ~ dense_linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_771_atLeastLessThan__subseteq__atLeastAtMost__iff]) ).

fof(f_861_2,plain,
    ! [U_3456] :
      ( ! [U_3455,U_3454,U_3453,U_3452] :
          ( ( hBOOL(hAPP(fun(U_3456,bool),bool,hAPP(fun(U_3456,bool),fun(fun(U_3456,bool),bool),ord_less_eq(fun(U_3456,bool)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastLessThan(U_3456),U_3455),U_3454)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastAtMost(U_3456),U_3453),U_3452)))
            | ( ( ~ hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3454),U_3452))
                | ~ hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3453),U_3455)) )
              & hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less(U_3456),U_3455),U_3454)) ) )
          & ( ( hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3454),U_3452))
              & hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3453),U_3455)) )
            | ~ hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less(U_3456),U_3455),U_3454))
            | ~ hBOOL(hAPP(fun(U_3456,bool),bool,hAPP(fun(U_3456,bool),fun(fun(U_3456,bool),bool),ord_less_eq(fun(U_3456,bool)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastLessThan(U_3456),U_3455),U_3454)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastAtMost(U_3456),U_3453),U_3452))) ) )
      | ~ dense_linorder(U_3456) ),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

fof(f_861_3,plain,
    ! [U_3456] :
      ( ( ! [U_3464,U_3462,U_3460,U_3458] :
            ( hBOOL(hAPP(fun(U_3456,bool),bool,hAPP(fun(U_3456,bool),fun(fun(U_3456,bool),bool),ord_less_eq(fun(U_3456,bool)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastLessThan(U_3456),U_3464),U_3462)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastAtMost(U_3456),U_3460),U_3458)))
            | ( ( ~ hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3462),U_3458))
                | ~ hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3460),U_3464)) )
              & hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less(U_3456),U_3464),U_3462)) ) )
        & ! [U_3463,U_3461,U_3459,U_3457] :
            ( ( hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3461),U_3457))
              & hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3459),U_3463)) )
            | ~ hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less(U_3456),U_3463),U_3461))
            | ~ hBOOL(hAPP(fun(U_3456,bool),bool,hAPP(fun(U_3456,bool),fun(fun(U_3456,bool),bool),ord_less_eq(fun(U_3456,bool)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastLessThan(U_3456),U_3463),U_3461)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastAtMost(U_3456),U_3459),U_3457))) ) )
      | ~ dense_linorder(U_3456) ),
    inference(miniscope,[status(thm)],[f_861_2]) ).

cnf(f_861_4,plain,
    ( hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3459),U_3463))
    | ~ hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less(U_3456),U_3463),U_3461))
    | ~ hBOOL(hAPP(fun(U_3456,bool),bool,hAPP(fun(U_3456,bool),fun(fun(U_3456,bool),bool),ord_less_eq(fun(U_3456,bool)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastLessThan(U_3456),U_3463),U_3461)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastAtMost(U_3456),U_3459),U_3457)))
    | ~ dense_linorder(U_3456) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

cnf(f_861_5,plain,
    ( hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3461),U_3457))
    | ~ hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less(U_3456),U_3463),U_3461))
    | ~ hBOOL(hAPP(fun(U_3456,bool),bool,hAPP(fun(U_3456,bool),fun(fun(U_3456,bool),bool),ord_less_eq(fun(U_3456,bool)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastLessThan(U_3456),U_3463),U_3461)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastAtMost(U_3456),U_3459),U_3457)))
    | ~ dense_linorder(U_3456) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

cnf(f_861_6,plain,
    ( hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less(U_3456),U_3464),U_3462))
    | hBOOL(hAPP(fun(U_3456,bool),bool,hAPP(fun(U_3456,bool),fun(fun(U_3456,bool),bool),ord_less_eq(fun(U_3456,bool)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastLessThan(U_3456),U_3464),U_3462)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastAtMost(U_3456),U_3460),U_3458)))
    | ~ dense_linorder(U_3456) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

cnf(f_861_7,plain,
    ( ~ hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3462),U_3458))
    | ~ hBOOL(hAPP(U_3456,bool,hAPP(U_3456,fun(U_3456,bool),ord_less_eq(U_3456),U_3460),U_3464))
    | hBOOL(hAPP(fun(U_3456,bool),bool,hAPP(fun(U_3456,bool),fun(fun(U_3456,bool),bool),ord_less_eq(fun(U_3456,bool)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastLessThan(U_3456),U_3464),U_3462)),hAPP(U_3456,fun(U_3456,bool),hAPP(U_3456,fun(U_3456,fun(U_3456,bool)),ord_atLeastAtMost(U_3456),U_3460),U_3458)))
    | ~ dense_linorder(U_3456) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

fof(f_862_1,plain,
    ! [X_a] :
      ( ! [U,L,M] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),L),U)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),L),M)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_772_ivl__disj__un_I19_J]) ).

fof(f_862_2,plain,
    ! [U_3468] :
      ( ! [U_3467,U_3466,U_3465] :
          ( hAPP(fun(U_3468,bool),fun(U_3468,bool),hAPP(fun(U_3468,bool),fun(fun(U_3468,bool),fun(U_3468,bool)),semilattice_sup_sup(fun(U_3468,bool)),hAPP(U_3468,fun(U_3468,bool),hAPP(U_3468,fun(U_3468,fun(U_3468,bool)),ord_gr676655987ssThan(U_3468),U_3466),U_3465)),hAPP(U_3468,fun(U_3468,bool),hAPP(U_3468,fun(U_3468,fun(U_3468,bool)),ord_atLeastAtMost(U_3468),U_3465),U_3467)) = hAPP(U_3468,fun(U_3468,bool),hAPP(U_3468,fun(U_3468,fun(U_3468,bool)),ord_gr1471790799AtMost(U_3468),U_3466),U_3467)
          | ~ hBOOL(hAPP(U_3468,bool,hAPP(U_3468,fun(U_3468,bool),ord_less_eq(U_3468),U_3465),U_3467))
          | ~ hBOOL(hAPP(U_3468,bool,hAPP(U_3468,fun(U_3468,bool),ord_less(U_3468),U_3466),U_3465)) )
      | ~ linorder(U_3468) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

cnf(f_862_3,plain,
    ( hAPP(fun(U_3468,bool),fun(U_3468,bool),hAPP(fun(U_3468,bool),fun(fun(U_3468,bool),fun(U_3468,bool)),semilattice_sup_sup(fun(U_3468,bool)),hAPP(U_3468,fun(U_3468,bool),hAPP(U_3468,fun(U_3468,fun(U_3468,bool)),ord_gr676655987ssThan(U_3468),U_3466),U_3465)),hAPP(U_3468,fun(U_3468,bool),hAPP(U_3468,fun(U_3468,fun(U_3468,bool)),ord_atLeastAtMost(U_3468),U_3465),U_3467)) = hAPP(U_3468,fun(U_3468,bool),hAPP(U_3468,fun(U_3468,fun(U_3468,bool)),ord_gr1471790799AtMost(U_3468),U_3466),U_3467)
    | ~ hBOOL(hAPP(U_3468,bool,hAPP(U_3468,fun(U_3468,bool),ord_less_eq(U_3468),U_3465),U_3467))
    | ~ hBOOL(hAPP(U_3468,bool,hAPP(U_3468,fun(U_3468,bool),ord_less(U_3468),U_3466),U_3465))
    | ~ linorder(U_3468) ),
    inference(clausify,[status(thm)],[f_862_2]) ).

fof(f_863_1,plain,
    ! [X_a] :
      ( ! [U,L,M] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),L),U)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),M),U))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_773_ivl__disj__un_I18_J]) ).

fof(f_863_2,plain,
    ! [U_3472] :
      ( ! [U_3471,U_3470,U_3469] :
          ( hAPP(fun(U_3472,bool),fun(U_3472,bool),hAPP(fun(U_3472,bool),fun(fun(U_3472,bool),fun(U_3472,bool)),semilattice_sup_sup(fun(U_3472,bool)),hAPP(U_3472,fun(U_3472,bool),hAPP(U_3472,fun(U_3472,fun(U_3472,bool)),ord_atLeastAtMost(U_3472),U_3470),U_3469)),hAPP(U_3472,fun(U_3472,bool),hAPP(U_3472,fun(U_3472,fun(U_3472,bool)),ord_gr676655987ssThan(U_3472),U_3469),U_3471)) = hAPP(U_3472,fun(U_3472,bool),hAPP(U_3472,fun(U_3472,fun(U_3472,bool)),ord_atLeastLessThan(U_3472),U_3470),U_3471)
          | ~ hBOOL(hAPP(U_3472,bool,hAPP(U_3472,fun(U_3472,bool),ord_less(U_3472),U_3469),U_3471))
          | ~ hBOOL(hAPP(U_3472,bool,hAPP(U_3472,fun(U_3472,bool),ord_less_eq(U_3472),U_3470),U_3469)) )
      | ~ linorder(U_3472) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

cnf(f_863_3,plain,
    ( hAPP(fun(U_3472,bool),fun(U_3472,bool),hAPP(fun(U_3472,bool),fun(fun(U_3472,bool),fun(U_3472,bool)),semilattice_sup_sup(fun(U_3472,bool)),hAPP(U_3472,fun(U_3472,bool),hAPP(U_3472,fun(U_3472,fun(U_3472,bool)),ord_atLeastAtMost(U_3472),U_3470),U_3469)),hAPP(U_3472,fun(U_3472,bool),hAPP(U_3472,fun(U_3472,fun(U_3472,bool)),ord_gr676655987ssThan(U_3472),U_3469),U_3471)) = hAPP(U_3472,fun(U_3472,bool),hAPP(U_3472,fun(U_3472,fun(U_3472,bool)),ord_atLeastLessThan(U_3472),U_3470),U_3471)
    | ~ hBOOL(hAPP(U_3472,bool,hAPP(U_3472,fun(U_3472,bool),ord_less(U_3472),U_3469),U_3471))
    | ~ hBOOL(hAPP(U_3472,bool,hAPP(U_3472,fun(U_3472,bool),ord_less_eq(U_3472),U_3470),U_3469))
    | ~ linorder(U_3472) ),
    inference(clausify,[status(thm)],[f_863_2]) ).

fof(f_864_1,plain,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
      | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) ),
    inference(fof_nnf,[status(thm)],[fact_774_UnE]) ).

fof(f_864_2,plain,
    ! [U_3476,U_3475,U_3474,U_3473] :
      ( hBOOL(hAPP(fun(U_3476,bool),bool,hAPP(U_3476,fun(fun(U_3476,bool),bool),member(U_3476),U_3475),U_3473))
      | hBOOL(hAPP(fun(U_3476,bool),bool,hAPP(U_3476,fun(fun(U_3476,bool),bool),member(U_3476),U_3475),U_3474))
      | ~ hBOOL(hAPP(fun(U_3476,bool),bool,hAPP(U_3476,fun(fun(U_3476,bool),bool),member(U_3476),U_3475),hAPP(fun(U_3476,bool),fun(U_3476,bool),hAPP(fun(U_3476,bool),fun(fun(U_3476,bool),fun(U_3476,bool)),semilattice_sup_sup(fun(U_3476,bool)),U_3474),U_3473))) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

cnf(f_864_3,plain,
    ( hBOOL(hAPP(fun(U_3476,bool),bool,hAPP(U_3476,fun(fun(U_3476,bool),bool),member(U_3476),U_3475),U_3473))
    | hBOOL(hAPP(fun(U_3476,bool),bool,hAPP(U_3476,fun(fun(U_3476,bool),bool),member(U_3476),U_3475),U_3474))
    | ~ hBOOL(hAPP(fun(U_3476,bool),bool,hAPP(U_3476,fun(fun(U_3476,bool),bool),member(U_3476),U_3475),hAPP(fun(U_3476,bool),fun(U_3476,bool),hAPP(fun(U_3476,bool),fun(fun(U_3476,bool),fun(U_3476,bool)),semilattice_sup_sup(fun(U_3476,bool)),U_3474),U_3473))) ),
    inference(clausify,[status(thm)],[f_864_2]) ).

fof(f_865_1,plain,
    ! [X_a,A_1,B,X_2] :
      ( hBOOL(hAPP(X_a,bool,B,X_2))
      | hBOOL(hAPP(X_a,bool,A_1,X_2))
      | ~ hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_775_sup1E]) ).

fof(f_865_2,plain,
    ! [U_3480,U_3479,U_3478,U_3477] :
      ( hBOOL(hAPP(U_3480,bool,U_3478,U_3477))
      | hBOOL(hAPP(U_3480,bool,U_3479,U_3477))
      | ~ hBOOL(hAPP(U_3480,bool,hAPP(fun(U_3480,bool),fun(U_3480,bool),hAPP(fun(U_3480,bool),fun(fun(U_3480,bool),fun(U_3480,bool)),semilattice_sup_sup(fun(U_3480,bool)),U_3479),U_3478),U_3477)) ),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

cnf(f_865_3,plain,
    ( hBOOL(hAPP(U_3480,bool,U_3478,U_3477))
    | hBOOL(hAPP(U_3480,bool,U_3479,U_3477))
    | ~ hBOOL(hAPP(U_3480,bool,hAPP(fun(U_3480,bool),fun(U_3480,bool),hAPP(fun(U_3480,bool),fun(fun(U_3480,bool),fun(U_3480,bool)),semilattice_sup_sup(fun(U_3480,bool)),U_3479),U_3478),U_3477)) ),
    inference(clausify,[status(thm)],[f_865_2]) ).

fof(f_866_1,plain,
    ! [X_a,A_1,B,X_2] :
      ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2))
      | ( ~ hBOOL(hAPP(X_a,bool,A_1,X_2))
        & ~ hBOOL(hAPP(X_a,bool,B,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_776_sup1CI]) ).

fof(f_866_2,plain,
    ! [U_3484,U_3483,U_3482,U_3481] :
      ( hBOOL(hAPP(U_3484,bool,hAPP(fun(U_3484,bool),fun(U_3484,bool),hAPP(fun(U_3484,bool),fun(fun(U_3484,bool),fun(U_3484,bool)),semilattice_sup_sup(fun(U_3484,bool)),U_3483),U_3482),U_3481))
      | ( ~ hBOOL(hAPP(U_3484,bool,U_3483,U_3481))
        & ~ hBOOL(hAPP(U_3484,bool,U_3482,U_3481)) ) ),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

cnf(f_866_3,plain,
    ( ~ hBOOL(hAPP(U_3484,bool,U_3482,U_3481))
    | hBOOL(hAPP(U_3484,bool,hAPP(fun(U_3484,bool),fun(U_3484,bool),hAPP(fun(U_3484,bool),fun(fun(U_3484,bool),fun(U_3484,bool)),semilattice_sup_sup(fun(U_3484,bool)),U_3483),U_3482),U_3481)) ),
    inference(clausify,[status(thm)],[f_866_2]) ).

cnf(f_866_4,plain,
    ( ~ hBOOL(hAPP(U_3484,bool,U_3483,U_3481))
    | hBOOL(hAPP(U_3484,bool,hAPP(fun(U_3484,bool),fun(U_3484,bool),hAPP(fun(U_3484,bool),fun(fun(U_3484,bool),fun(U_3484,bool)),semilattice_sup_sup(fun(U_3484,bool)),U_3483),U_3482),U_3481)) ),
    inference(clausify,[status(thm)],[f_866_2]) ).

fof(f_867_1,plain,
    ! [X_a,A_1,Ca,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)))
      | ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
        & ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_777_UnCI]) ).

fof(f_867_2,plain,
    ! [U_3488,U_3487,U_3486,U_3485] :
      ( hBOOL(hAPP(fun(U_3488,bool),bool,hAPP(U_3488,fun(fun(U_3488,bool),bool),member(U_3488),U_3486),hAPP(fun(U_3488,bool),fun(U_3488,bool),hAPP(fun(U_3488,bool),fun(fun(U_3488,bool),fun(U_3488,bool)),semilattice_sup_sup(fun(U_3488,bool)),U_3487),U_3485)))
      | ( ~ hBOOL(hAPP(fun(U_3488,bool),bool,hAPP(U_3488,fun(fun(U_3488,bool),bool),member(U_3488),U_3486),U_3487))
        & ~ hBOOL(hAPP(fun(U_3488,bool),bool,hAPP(U_3488,fun(fun(U_3488,bool),bool),member(U_3488),U_3486),U_3485)) ) ),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

cnf(f_867_3,plain,
    ( ~ hBOOL(hAPP(fun(U_3488,bool),bool,hAPP(U_3488,fun(fun(U_3488,bool),bool),member(U_3488),U_3486),U_3485))
    | hBOOL(hAPP(fun(U_3488,bool),bool,hAPP(U_3488,fun(fun(U_3488,bool),bool),member(U_3488),U_3486),hAPP(fun(U_3488,bool),fun(U_3488,bool),hAPP(fun(U_3488,bool),fun(fun(U_3488,bool),fun(U_3488,bool)),semilattice_sup_sup(fun(U_3488,bool)),U_3487),U_3485))) ),
    inference(clausify,[status(thm)],[f_867_2]) ).

cnf(f_867_4,plain,
    ( ~ hBOOL(hAPP(fun(U_3488,bool),bool,hAPP(U_3488,fun(fun(U_3488,bool),bool),member(U_3488),U_3486),U_3487))
    | hBOOL(hAPP(fun(U_3488,bool),bool,hAPP(U_3488,fun(fun(U_3488,bool),bool),member(U_3488),U_3486),hAPP(fun(U_3488,bool),fun(U_3488,bool),hAPP(fun(U_3488,bool),fun(fun(U_3488,bool),fun(U_3488,bool)),semilattice_sup_sup(fun(U_3488,bool)),U_3487),U_3485))) ),
    inference(clausify,[status(thm)],[f_867_2]) ).

fof(f_868_1,plain,
    ! [X_a] :
      ( ! [U,L,M] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),L),U)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_778_ivl__disj__un_I20_J]) ).

fof(f_868_2,plain,
    ! [U_3492] :
      ( ! [U_3491,U_3490,U_3489] :
          ( hAPP(fun(U_3492,bool),fun(U_3492,bool),hAPP(fun(U_3492,bool),fun(fun(U_3492,bool),fun(U_3492,bool)),semilattice_sup_sup(fun(U_3492,bool)),hAPP(U_3492,fun(U_3492,bool),hAPP(U_3492,fun(U_3492,fun(U_3492,bool)),ord_gr1471790799AtMost(U_3492),U_3490),U_3489)),hAPP(U_3492,fun(U_3492,bool),hAPP(U_3492,fun(U_3492,fun(U_3492,bool)),ord_gr1471790799AtMost(U_3492),U_3489),U_3491)) = hAPP(U_3492,fun(U_3492,bool),hAPP(U_3492,fun(U_3492,fun(U_3492,bool)),ord_gr1471790799AtMost(U_3492),U_3490),U_3491)
          | ~ hBOOL(hAPP(U_3492,bool,hAPP(U_3492,fun(U_3492,bool),ord_less_eq(U_3492),U_3489),U_3491))
          | ~ hBOOL(hAPP(U_3492,bool,hAPP(U_3492,fun(U_3492,bool),ord_less_eq(U_3492),U_3490),U_3489)) )
      | ~ linorder(U_3492) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

cnf(f_868_3,plain,
    ( hAPP(fun(U_3492,bool),fun(U_3492,bool),hAPP(fun(U_3492,bool),fun(fun(U_3492,bool),fun(U_3492,bool)),semilattice_sup_sup(fun(U_3492,bool)),hAPP(U_3492,fun(U_3492,bool),hAPP(U_3492,fun(U_3492,fun(U_3492,bool)),ord_gr1471790799AtMost(U_3492),U_3490),U_3489)),hAPP(U_3492,fun(U_3492,bool),hAPP(U_3492,fun(U_3492,fun(U_3492,bool)),ord_gr1471790799AtMost(U_3492),U_3489),U_3491)) = hAPP(U_3492,fun(U_3492,bool),hAPP(U_3492,fun(U_3492,fun(U_3492,bool)),ord_gr1471790799AtMost(U_3492),U_3490),U_3491)
    | ~ hBOOL(hAPP(U_3492,bool,hAPP(U_3492,fun(U_3492,bool),ord_less_eq(U_3492),U_3489),U_3491))
    | ~ hBOOL(hAPP(U_3492,bool,hAPP(U_3492,fun(U_3492,bool),ord_less_eq(U_3492),U_3490),U_3489))
    | ~ linorder(U_3492) ),
    inference(clausify,[status(thm)],[f_868_2]) ).

fof(f_869_1,plain,
    ! [X_a] :
      ( ! [U,L,M] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),L),U)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_779_ivl__disj__un_I17_J]) ).

fof(f_869_2,plain,
    ! [U_3496] :
      ( ! [U_3495,U_3494,U_3493] :
          ( hAPP(fun(U_3496,bool),fun(U_3496,bool),hAPP(fun(U_3496,bool),fun(fun(U_3496,bool),fun(U_3496,bool)),semilattice_sup_sup(fun(U_3496,bool)),hAPP(U_3496,fun(U_3496,bool),hAPP(U_3496,fun(U_3496,fun(U_3496,bool)),ord_atLeastLessThan(U_3496),U_3494),U_3493)),hAPP(U_3496,fun(U_3496,bool),hAPP(U_3496,fun(U_3496,fun(U_3496,bool)),ord_atLeastLessThan(U_3496),U_3493),U_3495)) = hAPP(U_3496,fun(U_3496,bool),hAPP(U_3496,fun(U_3496,fun(U_3496,bool)),ord_atLeastLessThan(U_3496),U_3494),U_3495)
          | ~ hBOOL(hAPP(U_3496,bool,hAPP(U_3496,fun(U_3496,bool),ord_less_eq(U_3496),U_3493),U_3495))
          | ~ hBOOL(hAPP(U_3496,bool,hAPP(U_3496,fun(U_3496,bool),ord_less_eq(U_3496),U_3494),U_3493)) )
      | ~ linorder(U_3496) ),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

cnf(f_869_3,plain,
    ( hAPP(fun(U_3496,bool),fun(U_3496,bool),hAPP(fun(U_3496,bool),fun(fun(U_3496,bool),fun(U_3496,bool)),semilattice_sup_sup(fun(U_3496,bool)),hAPP(U_3496,fun(U_3496,bool),hAPP(U_3496,fun(U_3496,fun(U_3496,bool)),ord_atLeastLessThan(U_3496),U_3494),U_3493)),hAPP(U_3496,fun(U_3496,bool),hAPP(U_3496,fun(U_3496,fun(U_3496,bool)),ord_atLeastLessThan(U_3496),U_3493),U_3495)) = hAPP(U_3496,fun(U_3496,bool),hAPP(U_3496,fun(U_3496,fun(U_3496,bool)),ord_atLeastLessThan(U_3496),U_3494),U_3495)
    | ~ hBOOL(hAPP(U_3496,bool,hAPP(U_3496,fun(U_3496,bool),ord_less_eq(U_3496),U_3493),U_3495))
    | ~ hBOOL(hAPP(U_3496,bool,hAPP(U_3496,fun(U_3496,bool),ord_less_eq(U_3496),U_3494),U_3493))
    | ~ linorder(U_3496) ),
    inference(clausify,[status(thm)],[f_869_2]) ).

fof(f_870_1,plain,
    ! [X_a,X_b,F,A_1,B] :
      ( ( ( hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)
          | ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) )
        & ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
          | hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) != hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) ),
    inference(fof_nnf,[status(thm)],[fact_780_inj__on__Un__image__eq__iff]) ).

fof(f_870_2,plain,
    ! [U_3501,U_3500,U_3499,U_3498,U_3497] :
      ( ( ( hAPP(fun(U_3501,bool),fun(U_3500,bool),hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),fun(U_3500,bool)),image(U_3501,U_3500),U_3499),U_3498) = hAPP(fun(U_3501,bool),fun(U_3500,bool),hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),fun(U_3500,bool)),image(U_3501,U_3500),U_3499),U_3497)
          | ti(fun(U_3501,bool),U_3498) != ti(fun(U_3501,bool),U_3497) )
        & ( ti(fun(U_3501,bool),U_3498) = ti(fun(U_3501,bool),U_3497)
          | hAPP(fun(U_3501,bool),fun(U_3500,bool),hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),fun(U_3500,bool)),image(U_3501,U_3500),U_3499),U_3498) != hAPP(fun(U_3501,bool),fun(U_3500,bool),hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),fun(U_3500,bool)),image(U_3501,U_3500),U_3499),U_3497) ) )
      | ~ hBOOL(hAPP(fun(U_3501,bool),bool,hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),bool),inj_on(U_3501,U_3500),U_3499),hAPP(fun(U_3501,bool),fun(U_3501,bool),hAPP(fun(U_3501,bool),fun(fun(U_3501,bool),fun(U_3501,bool)),semilattice_sup_sup(fun(U_3501,bool)),U_3498),U_3497))) ),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

cnf(f_870_3,plain,
    ( ti(fun(U_3501,bool),U_3498) = ti(fun(U_3501,bool),U_3497)
    | hAPP(fun(U_3501,bool),fun(U_3500,bool),hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),fun(U_3500,bool)),image(U_3501,U_3500),U_3499),U_3498) != hAPP(fun(U_3501,bool),fun(U_3500,bool),hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),fun(U_3500,bool)),image(U_3501,U_3500),U_3499),U_3497)
    | ~ hBOOL(hAPP(fun(U_3501,bool),bool,hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),bool),inj_on(U_3501,U_3500),U_3499),hAPP(fun(U_3501,bool),fun(U_3501,bool),hAPP(fun(U_3501,bool),fun(fun(U_3501,bool),fun(U_3501,bool)),semilattice_sup_sup(fun(U_3501,bool)),U_3498),U_3497))) ),
    inference(clausify,[status(thm)],[f_870_2]) ).

cnf(f_870_4,plain,
    ( hAPP(fun(U_3501,bool),fun(U_3500,bool),hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),fun(U_3500,bool)),image(U_3501,U_3500),U_3499),U_3498) = hAPP(fun(U_3501,bool),fun(U_3500,bool),hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),fun(U_3500,bool)),image(U_3501,U_3500),U_3499),U_3497)
    | ti(fun(U_3501,bool),U_3498) != ti(fun(U_3501,bool),U_3497)
    | ~ hBOOL(hAPP(fun(U_3501,bool),bool,hAPP(fun(U_3501,U_3500),fun(fun(U_3501,bool),bool),inj_on(U_3501,U_3500),U_3499),hAPP(fun(U_3501,bool),fun(U_3501,bool),hAPP(fun(U_3501,bool),fun(fun(U_3501,bool),fun(U_3501,bool)),semilattice_sup_sup(fun(U_3501,bool)),U_3498),U_3497))) ),
    inference(clausify,[status(thm)],[f_870_2]) ).

fof(f_871_1,plain,
    ! [X_b,X_a,F,A_1,B] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B)),
    inference(fof_nnf,[status(thm)],[fact_781_image__Un]) ).

fof(f_871_2,plain,
    ! [U_3506,U_3505,U_3504,U_3503,U_3502] : hAPP(fun(U_3506,bool),fun(U_3505,bool),hAPP(fun(U_3506,U_3505),fun(fun(U_3506,bool),fun(U_3505,bool)),image(U_3506,U_3505),U_3504),hAPP(fun(U_3506,bool),fun(U_3506,bool),hAPP(fun(U_3506,bool),fun(fun(U_3506,bool),fun(U_3506,bool)),semilattice_sup_sup(fun(U_3506,bool)),U_3503),U_3502)) = hAPP(fun(U_3505,bool),fun(U_3505,bool),hAPP(fun(U_3505,bool),fun(fun(U_3505,bool),fun(U_3505,bool)),semilattice_sup_sup(fun(U_3505,bool)),hAPP(fun(U_3506,bool),fun(U_3505,bool),hAPP(fun(U_3506,U_3505),fun(fun(U_3506,bool),fun(U_3505,bool)),image(U_3506,U_3505),U_3504),U_3503)),hAPP(fun(U_3506,bool),fun(U_3505,bool),hAPP(fun(U_3506,U_3505),fun(fun(U_3506,bool),fun(U_3505,bool)),image(U_3506,U_3505),U_3504),U_3502)),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

cnf(f_871_3,plain,
    hAPP(fun(U_3506,bool),fun(U_3505,bool),hAPP(fun(U_3506,U_3505),fun(fun(U_3506,bool),fun(U_3505,bool)),image(U_3506,U_3505),U_3504),hAPP(fun(U_3506,bool),fun(U_3506,bool),hAPP(fun(U_3506,bool),fun(fun(U_3506,bool),fun(U_3506,bool)),semilattice_sup_sup(fun(U_3506,bool)),U_3503),U_3502)) = hAPP(fun(U_3505,bool),fun(U_3505,bool),hAPP(fun(U_3505,bool),fun(fun(U_3505,bool),fun(U_3505,bool)),semilattice_sup_sup(fun(U_3505,bool)),hAPP(fun(U_3506,bool),fun(U_3505,bool),hAPP(fun(U_3506,U_3505),fun(fun(U_3506,bool),fun(U_3505,bool)),image(U_3506,U_3505),U_3504),U_3503)),hAPP(fun(U_3506,bool),fun(U_3505,bool),hAPP(fun(U_3506,U_3505),fun(fun(U_3506,bool),fun(U_3505,bool)),image(U_3506,U_3505),U_3504),U_3502)),
    inference(clausify,[status(thm)],[f_871_2]) ).

fof(f_872_1,plain,
    ! [X_a,A_1,B] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),
    inference(fof_nnf,[status(thm)],[fact_782_Un__upper1]) ).

fof(f_872_2,plain,
    ! [U_3509,U_3508,U_3507] : hBOOL(hAPP(fun(U_3509,bool),bool,hAPP(fun(U_3509,bool),fun(fun(U_3509,bool),bool),ord_less_eq(fun(U_3509,bool)),U_3508),hAPP(fun(U_3509,bool),fun(U_3509,bool),hAPP(fun(U_3509,bool),fun(fun(U_3509,bool),fun(U_3509,bool)),semilattice_sup_sup(fun(U_3509,bool)),U_3508),U_3507))),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

cnf(f_872_3,plain,
    hBOOL(hAPP(fun(U_3509,bool),bool,hAPP(fun(U_3509,bool),fun(fun(U_3509,bool),bool),ord_less_eq(fun(U_3509,bool)),U_3508),hAPP(fun(U_3509,bool),fun(U_3509,bool),hAPP(fun(U_3509,bool),fun(fun(U_3509,bool),fun(U_3509,bool)),semilattice_sup_sup(fun(U_3509,bool)),U_3508),U_3507))),
    inference(clausify,[status(thm)],[f_872_2]) ).

fof(f_873_1,plain,
    ! [X_a,B,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),
    inference(fof_nnf,[status(thm)],[fact_783_Un__upper2]) ).

fof(f_873_2,plain,
    ! [U_3512,U_3511,U_3510] : hBOOL(hAPP(fun(U_3512,bool),bool,hAPP(fun(U_3512,bool),fun(fun(U_3512,bool),bool),ord_less_eq(fun(U_3512,bool)),U_3511),hAPP(fun(U_3512,bool),fun(U_3512,bool),hAPP(fun(U_3512,bool),fun(fun(U_3512,bool),fun(U_3512,bool)),semilattice_sup_sup(fun(U_3512,bool)),U_3510),U_3511))),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

cnf(f_873_3,plain,
    hBOOL(hAPP(fun(U_3512,bool),bool,hAPP(fun(U_3512,bool),fun(fun(U_3512,bool),bool),ord_less_eq(fun(U_3512,bool)),U_3511),hAPP(fun(U_3512,bool),fun(U_3512,bool),hAPP(fun(U_3512,bool),fun(fun(U_3512,bool),fun(U_3512,bool)),semilattice_sup_sup(fun(U_3512,bool)),U_3510),U_3511))),
    inference(clausify,[status(thm)],[f_873_2]) ).

fof(f_874_1,plain,
    ! [X_a,A_1,B] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
        | hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) != ti(fun(X_a,bool),B) )
      & ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),B)
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_784_subset__Un__eq]) ).

fof(f_874_2,plain,
    ! [U_3515,U_3514,U_3513] :
      ( ( hBOOL(hAPP(fun(U_3515,bool),bool,hAPP(fun(U_3515,bool),fun(fun(U_3515,bool),bool),ord_less_eq(fun(U_3515,bool)),U_3514),U_3513))
        | hAPP(fun(U_3515,bool),fun(U_3515,bool),hAPP(fun(U_3515,bool),fun(fun(U_3515,bool),fun(U_3515,bool)),semilattice_sup_sup(fun(U_3515,bool)),U_3514),U_3513) != ti(fun(U_3515,bool),U_3513) )
      & ( hAPP(fun(U_3515,bool),fun(U_3515,bool),hAPP(fun(U_3515,bool),fun(fun(U_3515,bool),fun(U_3515,bool)),semilattice_sup_sup(fun(U_3515,bool)),U_3514),U_3513) = ti(fun(U_3515,bool),U_3513)
        | ~ hBOOL(hAPP(fun(U_3515,bool),bool,hAPP(fun(U_3515,bool),fun(fun(U_3515,bool),bool),ord_less_eq(fun(U_3515,bool)),U_3514),U_3513)) ) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ( ! [U_3521,U_3519,U_3517] :
        ( hBOOL(hAPP(fun(U_3521,bool),bool,hAPP(fun(U_3521,bool),fun(fun(U_3521,bool),bool),ord_less_eq(fun(U_3521,bool)),U_3519),U_3517))
        | hAPP(fun(U_3521,bool),fun(U_3521,bool),hAPP(fun(U_3521,bool),fun(fun(U_3521,bool),fun(U_3521,bool)),semilattice_sup_sup(fun(U_3521,bool)),U_3519),U_3517) != ti(fun(U_3521,bool),U_3517) )
    & ! [U_3520,U_3518,U_3516] :
        ( hAPP(fun(U_3520,bool),fun(U_3520,bool),hAPP(fun(U_3520,bool),fun(fun(U_3520,bool),fun(U_3520,bool)),semilattice_sup_sup(fun(U_3520,bool)),U_3518),U_3516) = ti(fun(U_3520,bool),U_3516)
        | ~ hBOOL(hAPP(fun(U_3520,bool),bool,hAPP(fun(U_3520,bool),fun(fun(U_3520,bool),bool),ord_less_eq(fun(U_3520,bool)),U_3518),U_3516)) ) ),
    inference(miniscope,[status(thm)],[f_874_2]) ).

cnf(f_874_4,plain,
    ( hAPP(fun(U_3520,bool),fun(U_3520,bool),hAPP(fun(U_3520,bool),fun(fun(U_3520,bool),fun(U_3520,bool)),semilattice_sup_sup(fun(U_3520,bool)),U_3518),U_3516) = ti(fun(U_3520,bool),U_3516)
    | ~ hBOOL(hAPP(fun(U_3520,bool),bool,hAPP(fun(U_3520,bool),fun(fun(U_3520,bool),bool),ord_less_eq(fun(U_3520,bool)),U_3518),U_3516)) ),
    inference(clausify,[status(thm)],[f_874_3]) ).

cnf(f_874_5,plain,
    ( hBOOL(hAPP(fun(U_3521,bool),bool,hAPP(fun(U_3521,bool),fun(fun(U_3521,bool),bool),ord_less_eq(fun(U_3521,bool)),U_3519),U_3517))
    | hAPP(fun(U_3521,bool),fun(U_3521,bool),hAPP(fun(U_3521,bool),fun(fun(U_3521,bool),fun(U_3521,bool)),semilattice_sup_sup(fun(U_3521,bool)),U_3519),U_3517) != ti(fun(U_3521,bool),U_3517) ),
    inference(clausify,[status(thm)],[f_874_3]) ).

fof(f_875_1,plain,
    ! [X_a,A_1,B] :
      ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),B)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_785_Un__absorb1]) ).

fof(f_875_2,plain,
    ! [U_3524,U_3523,U_3522] :
      ( hAPP(fun(U_3524,bool),fun(U_3524,bool),hAPP(fun(U_3524,bool),fun(fun(U_3524,bool),fun(U_3524,bool)),semilattice_sup_sup(fun(U_3524,bool)),U_3523),U_3522) = ti(fun(U_3524,bool),U_3522)
      | ~ hBOOL(hAPP(fun(U_3524,bool),bool,hAPP(fun(U_3524,bool),fun(fun(U_3524,bool),bool),ord_less_eq(fun(U_3524,bool)),U_3523),U_3522)) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

cnf(f_875_3,plain,
    ( hAPP(fun(U_3524,bool),fun(U_3524,bool),hAPP(fun(U_3524,bool),fun(fun(U_3524,bool),fun(U_3524,bool)),semilattice_sup_sup(fun(U_3524,bool)),U_3523),U_3522) = ti(fun(U_3524,bool),U_3522)
    | ~ hBOOL(hAPP(fun(U_3524,bool),bool,hAPP(fun(U_3524,bool),fun(fun(U_3524,bool),bool),ord_less_eq(fun(U_3524,bool)),U_3523),U_3522)) ),
    inference(clausify,[status(thm)],[f_875_2]) ).

fof(f_876_1,plain,
    ! [X_a,B,A_1] :
      ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),A_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_786_Un__absorb2]) ).

fof(f_876_2,plain,
    ! [U_3527,U_3526,U_3525] :
      ( hAPP(fun(U_3527,bool),fun(U_3527,bool),hAPP(fun(U_3527,bool),fun(fun(U_3527,bool),fun(U_3527,bool)),semilattice_sup_sup(fun(U_3527,bool)),U_3525),U_3526) = ti(fun(U_3527,bool),U_3525)
      | ~ hBOOL(hAPP(fun(U_3527,bool),bool,hAPP(fun(U_3527,bool),fun(fun(U_3527,bool),bool),ord_less_eq(fun(U_3527,bool)),U_3526),U_3525)) ),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

cnf(f_876_3,plain,
    ( hAPP(fun(U_3527,bool),fun(U_3527,bool),hAPP(fun(U_3527,bool),fun(fun(U_3527,bool),fun(U_3527,bool)),semilattice_sup_sup(fun(U_3527,bool)),U_3525),U_3526) = ti(fun(U_3527,bool),U_3525)
    | ~ hBOOL(hAPP(fun(U_3527,bool),bool,hAPP(fun(U_3527,bool),fun(fun(U_3527,bool),bool),ord_less_eq(fun(U_3527,bool)),U_3526),U_3525)) ),
    inference(clausify,[status(thm)],[f_876_2]) ).

fof(f_877_1,plain,
    ! [X_a,B,A_1,C] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C)) ),
    inference(fof_nnf,[status(thm)],[fact_787_Un__least]) ).

fof(f_877_2,plain,
    ! [U_3531,U_3530,U_3529,U_3528] :
      ( hBOOL(hAPP(fun(U_3531,bool),bool,hAPP(fun(U_3531,bool),fun(fun(U_3531,bool),bool),ord_less_eq(fun(U_3531,bool)),hAPP(fun(U_3531,bool),fun(U_3531,bool),hAPP(fun(U_3531,bool),fun(fun(U_3531,bool),fun(U_3531,bool)),semilattice_sup_sup(fun(U_3531,bool)),U_3529),U_3530)),U_3528))
      | ~ hBOOL(hAPP(fun(U_3531,bool),bool,hAPP(fun(U_3531,bool),fun(fun(U_3531,bool),bool),ord_less_eq(fun(U_3531,bool)),U_3530),U_3528))
      | ~ hBOOL(hAPP(fun(U_3531,bool),bool,hAPP(fun(U_3531,bool),fun(fun(U_3531,bool),bool),ord_less_eq(fun(U_3531,bool)),U_3529),U_3528)) ),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

cnf(f_877_3,plain,
    ( hBOOL(hAPP(fun(U_3531,bool),bool,hAPP(fun(U_3531,bool),fun(fun(U_3531,bool),bool),ord_less_eq(fun(U_3531,bool)),hAPP(fun(U_3531,bool),fun(U_3531,bool),hAPP(fun(U_3531,bool),fun(fun(U_3531,bool),fun(U_3531,bool)),semilattice_sup_sup(fun(U_3531,bool)),U_3529),U_3530)),U_3528))
    | ~ hBOOL(hAPP(fun(U_3531,bool),bool,hAPP(fun(U_3531,bool),fun(fun(U_3531,bool),bool),ord_less_eq(fun(U_3531,bool)),U_3530),U_3528))
    | ~ hBOOL(hAPP(fun(U_3531,bool),bool,hAPP(fun(U_3531,bool),fun(fun(U_3531,bool),bool),ord_less_eq(fun(U_3531,bool)),U_3529),U_3528)) ),
    inference(clausify,[status(thm)],[f_877_2]) ).

fof(f_878_1,plain,
    ! [X_a,B,D_1,A_1,C] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C),D_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),D_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C)) ),
    inference(fof_nnf,[status(thm)],[fact_788_Un__mono]) ).

fof(f_878_2,plain,
    ! [U_3536,U_3535,U_3534,U_3533,U_3532] :
      ( hBOOL(hAPP(fun(U_3536,bool),bool,hAPP(fun(U_3536,bool),fun(fun(U_3536,bool),bool),ord_less_eq(fun(U_3536,bool)),hAPP(fun(U_3536,bool),fun(U_3536,bool),hAPP(fun(U_3536,bool),fun(fun(U_3536,bool),fun(U_3536,bool)),semilattice_sup_sup(fun(U_3536,bool)),U_3533),U_3535)),hAPP(fun(U_3536,bool),fun(U_3536,bool),hAPP(fun(U_3536,bool),fun(fun(U_3536,bool),fun(U_3536,bool)),semilattice_sup_sup(fun(U_3536,bool)),U_3532),U_3534)))
      | ~ hBOOL(hAPP(fun(U_3536,bool),bool,hAPP(fun(U_3536,bool),fun(fun(U_3536,bool),bool),ord_less_eq(fun(U_3536,bool)),U_3535),U_3534))
      | ~ hBOOL(hAPP(fun(U_3536,bool),bool,hAPP(fun(U_3536,bool),fun(fun(U_3536,bool),bool),ord_less_eq(fun(U_3536,bool)),U_3533),U_3532)) ),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

cnf(f_878_3,plain,
    ( hBOOL(hAPP(fun(U_3536,bool),bool,hAPP(fun(U_3536,bool),fun(fun(U_3536,bool),bool),ord_less_eq(fun(U_3536,bool)),hAPP(fun(U_3536,bool),fun(U_3536,bool),hAPP(fun(U_3536,bool),fun(fun(U_3536,bool),fun(U_3536,bool)),semilattice_sup_sup(fun(U_3536,bool)),U_3533),U_3535)),hAPP(fun(U_3536,bool),fun(U_3536,bool),hAPP(fun(U_3536,bool),fun(fun(U_3536,bool),fun(U_3536,bool)),semilattice_sup_sup(fun(U_3536,bool)),U_3532),U_3534)))
    | ~ hBOOL(hAPP(fun(U_3536,bool),bool,hAPP(fun(U_3536,bool),fun(fun(U_3536,bool),bool),ord_less_eq(fun(U_3536,bool)),U_3535),U_3534))
    | ~ hBOOL(hAPP(fun(U_3536,bool),bool,hAPP(fun(U_3536,bool),fun(fun(U_3536,bool),bool),ord_less_eq(fun(U_3536,bool)),U_3533),U_3532)) ),
    inference(clausify,[status(thm)],[f_878_2]) ).

fof(f_879_1,plain,
    ! [X_a,G_1,Fa] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),Fa),G_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),G_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_789_finite__UnI]) ).

fof(f_879_2,plain,
    ! [U_3539,U_3538,U_3537] :
      ( hBOOL(hAPP(fun(U_3539,bool),bool,finite_finite_1(U_3539),hAPP(fun(U_3539,bool),fun(U_3539,bool),hAPP(fun(U_3539,bool),fun(fun(U_3539,bool),fun(U_3539,bool)),semilattice_sup_sup(fun(U_3539,bool)),U_3537),U_3538)))
      | ~ hBOOL(hAPP(fun(U_3539,bool),bool,finite_finite_1(U_3539),U_3538))
      | ~ hBOOL(hAPP(fun(U_3539,bool),bool,finite_finite_1(U_3539),U_3537)) ),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

cnf(f_879_3,plain,
    ( hBOOL(hAPP(fun(U_3539,bool),bool,finite_finite_1(U_3539),hAPP(fun(U_3539,bool),fun(U_3539,bool),hAPP(fun(U_3539,bool),fun(fun(U_3539,bool),fun(U_3539,bool)),semilattice_sup_sup(fun(U_3539,bool)),U_3537),U_3538)))
    | ~ hBOOL(hAPP(fun(U_3539,bool),bool,finite_finite_1(U_3539),U_3538))
    | ~ hBOOL(hAPP(fun(U_3539,bool),bool,finite_finite_1(U_3539),U_3537)) ),
    inference(clausify,[status(thm)],[f_879_2]) ).

fof(f_880_1,plain,
    ! [X_a,Fa,G_1] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),Fa),G_1)))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),G_1))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa)) )
      & ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),G_1))
          & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa)) )
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),Fa),G_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_790_finite__Un]) ).

fof(f_880_2,plain,
    ! [U_3542,U_3541,U_3540] :
      ( ( hBOOL(hAPP(fun(U_3542,bool),bool,finite_finite_1(U_3542),hAPP(fun(U_3542,bool),fun(U_3542,bool),hAPP(fun(U_3542,bool),fun(fun(U_3542,bool),fun(U_3542,bool)),semilattice_sup_sup(fun(U_3542,bool)),U_3541),U_3540)))
        | ~ hBOOL(hAPP(fun(U_3542,bool),bool,finite_finite_1(U_3542),U_3540))
        | ~ hBOOL(hAPP(fun(U_3542,bool),bool,finite_finite_1(U_3542),U_3541)) )
      & ( ( hBOOL(hAPP(fun(U_3542,bool),bool,finite_finite_1(U_3542),U_3540))
          & hBOOL(hAPP(fun(U_3542,bool),bool,finite_finite_1(U_3542),U_3541)) )
        | ~ hBOOL(hAPP(fun(U_3542,bool),bool,finite_finite_1(U_3542),hAPP(fun(U_3542,bool),fun(U_3542,bool),hAPP(fun(U_3542,bool),fun(fun(U_3542,bool),fun(U_3542,bool)),semilattice_sup_sup(fun(U_3542,bool)),U_3541),U_3540))) ) ),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ( ! [U_3548,U_3546,U_3544] :
        ( hBOOL(hAPP(fun(U_3548,bool),bool,finite_finite_1(U_3548),hAPP(fun(U_3548,bool),fun(U_3548,bool),hAPP(fun(U_3548,bool),fun(fun(U_3548,bool),fun(U_3548,bool)),semilattice_sup_sup(fun(U_3548,bool)),U_3546),U_3544)))
        | ~ hBOOL(hAPP(fun(U_3548,bool),bool,finite_finite_1(U_3548),U_3544))
        | ~ hBOOL(hAPP(fun(U_3548,bool),bool,finite_finite_1(U_3548),U_3546)) )
    & ! [U_3547,U_3545,U_3543] :
        ( ( hBOOL(hAPP(fun(U_3547,bool),bool,finite_finite_1(U_3547),U_3543))
          & hBOOL(hAPP(fun(U_3547,bool),bool,finite_finite_1(U_3547),U_3545)) )
        | ~ hBOOL(hAPP(fun(U_3547,bool),bool,finite_finite_1(U_3547),hAPP(fun(U_3547,bool),fun(U_3547,bool),hAPP(fun(U_3547,bool),fun(fun(U_3547,bool),fun(U_3547,bool)),semilattice_sup_sup(fun(U_3547,bool)),U_3545),U_3543))) ) ),
    inference(miniscope,[status(thm)],[f_880_2]) ).

cnf(f_880_4,plain,
    ( hBOOL(hAPP(fun(U_3547,bool),bool,finite_finite_1(U_3547),U_3545))
    | ~ hBOOL(hAPP(fun(U_3547,bool),bool,finite_finite_1(U_3547),hAPP(fun(U_3547,bool),fun(U_3547,bool),hAPP(fun(U_3547,bool),fun(fun(U_3547,bool),fun(U_3547,bool)),semilattice_sup_sup(fun(U_3547,bool)),U_3545),U_3543))) ),
    inference(clausify,[status(thm)],[f_880_3]) ).

cnf(f_880_5,plain,
    ( hBOOL(hAPP(fun(U_3547,bool),bool,finite_finite_1(U_3547),U_3543))
    | ~ hBOOL(hAPP(fun(U_3547,bool),bool,finite_finite_1(U_3547),hAPP(fun(U_3547,bool),fun(U_3547,bool),hAPP(fun(U_3547,bool),fun(fun(U_3547,bool),fun(U_3547,bool)),semilattice_sup_sup(fun(U_3547,bool)),U_3545),U_3543))) ),
    inference(clausify,[status(thm)],[f_880_3]) ).

cnf(f_880_6,plain,
    ( hBOOL(hAPP(fun(U_3548,bool),bool,finite_finite_1(U_3548),hAPP(fun(U_3548,bool),fun(U_3548,bool),hAPP(fun(U_3548,bool),fun(fun(U_3548,bool),fun(U_3548,bool)),semilattice_sup_sup(fun(U_3548,bool)),U_3546),U_3544)))
    | ~ hBOOL(hAPP(fun(U_3548,bool),bool,finite_finite_1(U_3548),U_3544))
    | ~ hBOOL(hAPP(fun(U_3548,bool),bool,finite_finite_1(U_3548),U_3546)) ),
    inference(clausify,[status(thm)],[f_880_3]) ).

fof(f_881_1,plain,
    ! [X_a,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),A_1) = ti(fun(X_a,bool),A_1),
    inference(fof_nnf,[status(thm)],[fact_791_Un__absorb]) ).

fof(f_881_2,plain,
    ! [U_3550,U_3549] : hAPP(fun(U_3550,bool),fun(U_3550,bool),hAPP(fun(U_3550,bool),fun(fun(U_3550,bool),fun(U_3550,bool)),semilattice_sup_sup(fun(U_3550,bool)),U_3549),U_3549) = ti(fun(U_3550,bool),U_3549),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

cnf(f_881_3,plain,
    hAPP(fun(U_3550,bool),fun(U_3550,bool),hAPP(fun(U_3550,bool),fun(fun(U_3550,bool),fun(U_3550,bool)),semilattice_sup_sup(fun(U_3550,bool)),U_3549),U_3549) = ti(fun(U_3550,bool),U_3549),
    inference(clausify,[status(thm)],[f_881_2]) ).

fof(f_882_1,plain,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))),
    inference(fof_nnf,[status(thm)],[fact_792_Un__def]) ).

fof(f_882_2,plain,
    ! [U_3553,U_3552,U_3551] : hAPP(fun(U_3553,bool),fun(U_3553,bool),hAPP(fun(U_3553,bool),fun(fun(U_3553,bool),fun(U_3553,bool)),semilattice_sup_sup(fun(U_3553,bool)),U_3552),U_3551) = hAPP(fun(U_3553,bool),fun(U_3553,bool),collect(U_3553),hAPP(fun(U_3553,bool),fun(U_3553,bool),hAPP(fun(U_3553,fun(bool,bool)),fun(fun(U_3553,bool),fun(U_3553,bool)),combs(U_3553,bool,bool),hAPP(fun(U_3553,bool),fun(U_3553,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_3553,bool),fun(U_3553,fun(bool,bool))),combb(bool,fun(bool,bool),U_3553),fdisj),hAPP(fun(U_3553,bool),fun(U_3553,bool),hAPP(fun(U_3553,fun(fun(U_3553,bool),bool)),fun(fun(U_3553,bool),fun(U_3553,bool)),combc(U_3553,fun(U_3553,bool),bool),member(U_3553)),U_3552))),hAPP(fun(U_3553,bool),fun(U_3553,bool),hAPP(fun(U_3553,fun(fun(U_3553,bool),bool)),fun(fun(U_3553,bool),fun(U_3553,bool)),combc(U_3553,fun(U_3553,bool),bool),member(U_3553)),U_3551))),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

cnf(f_882_3,plain,
    hAPP(fun(U_3553,bool),fun(U_3553,bool),hAPP(fun(U_3553,bool),fun(fun(U_3553,bool),fun(U_3553,bool)),semilattice_sup_sup(fun(U_3553,bool)),U_3552),U_3551) = hAPP(fun(U_3553,bool),fun(U_3553,bool),collect(U_3553),hAPP(fun(U_3553,bool),fun(U_3553,bool),hAPP(fun(U_3553,fun(bool,bool)),fun(fun(U_3553,bool),fun(U_3553,bool)),combs(U_3553,bool,bool),hAPP(fun(U_3553,bool),fun(U_3553,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_3553,bool),fun(U_3553,fun(bool,bool))),combb(bool,fun(bool,bool),U_3553),fdisj),hAPP(fun(U_3553,bool),fun(U_3553,bool),hAPP(fun(U_3553,fun(fun(U_3553,bool),bool)),fun(fun(U_3553,bool),fun(U_3553,bool)),combc(U_3553,fun(U_3553,bool),bool),member(U_3553)),U_3552))),hAPP(fun(U_3553,bool),fun(U_3553,bool),hAPP(fun(U_3553,fun(fun(U_3553,bool),bool)),fun(fun(U_3553,bool),fun(U_3553,bool)),combc(U_3553,fun(U_3553,bool),bool),member(U_3553)),U_3551))),
    inference(clausify,[status(thm)],[f_882_2]) ).

fof(f_883_1,plain,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),A_1),
    inference(fof_nnf,[status(thm)],[fact_793_Un__commute]) ).

fof(f_883_2,plain,
    ! [U_3556,U_3555,U_3554] : hAPP(fun(U_3556,bool),fun(U_3556,bool),hAPP(fun(U_3556,bool),fun(fun(U_3556,bool),fun(U_3556,bool)),semilattice_sup_sup(fun(U_3556,bool)),U_3555),U_3554) = hAPP(fun(U_3556,bool),fun(U_3556,bool),hAPP(fun(U_3556,bool),fun(fun(U_3556,bool),fun(U_3556,bool)),semilattice_sup_sup(fun(U_3556,bool)),U_3554),U_3555),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

cnf(f_883_3,plain,
    hAPP(fun(U_3556,bool),fun(U_3556,bool),hAPP(fun(U_3556,bool),fun(fun(U_3556,bool),fun(U_3556,bool)),semilattice_sup_sup(fun(U_3556,bool)),U_3555),U_3554) = hAPP(fun(U_3556,bool),fun(U_3556,bool),hAPP(fun(U_3556,bool),fun(fun(U_3556,bool),fun(U_3556,bool)),semilattice_sup_sup(fun(U_3556,bool)),U_3554),U_3555),
    inference(clausify,[status(thm)],[f_883_2]) ).

fof(f_884_1,plain,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),
    inference(fof_nnf,[status(thm)],[fact_794_Un__left__absorb]) ).

fof(f_884_2,plain,
    ! [U_3559,U_3558,U_3557] : hAPP(fun(U_3559,bool),fun(U_3559,bool),hAPP(fun(U_3559,bool),fun(fun(U_3559,bool),fun(U_3559,bool)),semilattice_sup_sup(fun(U_3559,bool)),U_3558),hAPP(fun(U_3559,bool),fun(U_3559,bool),hAPP(fun(U_3559,bool),fun(fun(U_3559,bool),fun(U_3559,bool)),semilattice_sup_sup(fun(U_3559,bool)),U_3558),U_3557)) = hAPP(fun(U_3559,bool),fun(U_3559,bool),hAPP(fun(U_3559,bool),fun(fun(U_3559,bool),fun(U_3559,bool)),semilattice_sup_sup(fun(U_3559,bool)),U_3558),U_3557),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

cnf(f_884_3,plain,
    hAPP(fun(U_3559,bool),fun(U_3559,bool),hAPP(fun(U_3559,bool),fun(fun(U_3559,bool),fun(U_3559,bool)),semilattice_sup_sup(fun(U_3559,bool)),U_3558),hAPP(fun(U_3559,bool),fun(U_3559,bool),hAPP(fun(U_3559,bool),fun(fun(U_3559,bool),fun(U_3559,bool)),semilattice_sup_sup(fun(U_3559,bool)),U_3558),U_3557)) = hAPP(fun(U_3559,bool),fun(U_3559,bool),hAPP(fun(U_3559,bool),fun(fun(U_3559,bool),fun(U_3559,bool)),semilattice_sup_sup(fun(U_3559,bool)),U_3558),U_3557),
    inference(clausify,[status(thm)],[f_884_2]) ).

fof(f_885_1,plain,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),C)),
    inference(fof_nnf,[status(thm)],[fact_795_Un__left__commute]) ).

fof(f_885_2,plain,
    ! [U_3563,U_3562,U_3561,U_3560] : hAPP(fun(U_3563,bool),fun(U_3563,bool),hAPP(fun(U_3563,bool),fun(fun(U_3563,bool),fun(U_3563,bool)),semilattice_sup_sup(fun(U_3563,bool)),U_3562),hAPP(fun(U_3563,bool),fun(U_3563,bool),hAPP(fun(U_3563,bool),fun(fun(U_3563,bool),fun(U_3563,bool)),semilattice_sup_sup(fun(U_3563,bool)),U_3561),U_3560)) = hAPP(fun(U_3563,bool),fun(U_3563,bool),hAPP(fun(U_3563,bool),fun(fun(U_3563,bool),fun(U_3563,bool)),semilattice_sup_sup(fun(U_3563,bool)),U_3561),hAPP(fun(U_3563,bool),fun(U_3563,bool),hAPP(fun(U_3563,bool),fun(fun(U_3563,bool),fun(U_3563,bool)),semilattice_sup_sup(fun(U_3563,bool)),U_3562),U_3560)),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

cnf(f_885_3,plain,
    hAPP(fun(U_3563,bool),fun(U_3563,bool),hAPP(fun(U_3563,bool),fun(fun(U_3563,bool),fun(U_3563,bool)),semilattice_sup_sup(fun(U_3563,bool)),U_3562),hAPP(fun(U_3563,bool),fun(U_3563,bool),hAPP(fun(U_3563,bool),fun(fun(U_3563,bool),fun(U_3563,bool)),semilattice_sup_sup(fun(U_3563,bool)),U_3561),U_3560)) = hAPP(fun(U_3563,bool),fun(U_3563,bool),hAPP(fun(U_3563,bool),fun(fun(U_3563,bool),fun(U_3563,bool)),semilattice_sup_sup(fun(U_3563,bool)),U_3561),hAPP(fun(U_3563,bool),fun(U_3563,bool),hAPP(fun(U_3563,bool),fun(fun(U_3563,bool),fun(U_3563,bool)),semilattice_sup_sup(fun(U_3563,bool)),U_3562),U_3560)),
    inference(clausify,[status(thm)],[f_885_2]) ).

fof(f_886_1,plain,
    ! [X_a,Ca,A_1,B] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)))
        | ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
          & ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) ) )
      & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
        | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_796_Un__iff]) ).

fof(f_886_2,plain,
    ! [U_3567,U_3566,U_3565,U_3564] :
      ( ( hBOOL(hAPP(fun(U_3567,bool),bool,hAPP(U_3567,fun(fun(U_3567,bool),bool),member(U_3567),U_3566),hAPP(fun(U_3567,bool),fun(U_3567,bool),hAPP(fun(U_3567,bool),fun(fun(U_3567,bool),fun(U_3567,bool)),semilattice_sup_sup(fun(U_3567,bool)),U_3565),U_3564)))
        | ( ~ hBOOL(hAPP(fun(U_3567,bool),bool,hAPP(U_3567,fun(fun(U_3567,bool),bool),member(U_3567),U_3566),U_3564))
          & ~ hBOOL(hAPP(fun(U_3567,bool),bool,hAPP(U_3567,fun(fun(U_3567,bool),bool),member(U_3567),U_3566),U_3565)) ) )
      & ( hBOOL(hAPP(fun(U_3567,bool),bool,hAPP(U_3567,fun(fun(U_3567,bool),bool),member(U_3567),U_3566),U_3564))
        | hBOOL(hAPP(fun(U_3567,bool),bool,hAPP(U_3567,fun(fun(U_3567,bool),bool),member(U_3567),U_3566),U_3565))
        | ~ hBOOL(hAPP(fun(U_3567,bool),bool,hAPP(U_3567,fun(fun(U_3567,bool),bool),member(U_3567),U_3566),hAPP(fun(U_3567,bool),fun(U_3567,bool),hAPP(fun(U_3567,bool),fun(fun(U_3567,bool),fun(U_3567,bool)),semilattice_sup_sup(fun(U_3567,bool)),U_3565),U_3564))) ) ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

fof(f_886_3,plain,
    ( ! [U_3575,U_3573,U_3571,U_3569] :
        ( hBOOL(hAPP(fun(U_3575,bool),bool,hAPP(U_3575,fun(fun(U_3575,bool),bool),member(U_3575),U_3573),hAPP(fun(U_3575,bool),fun(U_3575,bool),hAPP(fun(U_3575,bool),fun(fun(U_3575,bool),fun(U_3575,bool)),semilattice_sup_sup(fun(U_3575,bool)),U_3571),U_3569)))
        | ( ~ hBOOL(hAPP(fun(U_3575,bool),bool,hAPP(U_3575,fun(fun(U_3575,bool),bool),member(U_3575),U_3573),U_3569))
          & ~ hBOOL(hAPP(fun(U_3575,bool),bool,hAPP(U_3575,fun(fun(U_3575,bool),bool),member(U_3575),U_3573),U_3571)) ) )
    & ! [U_3574,U_3572,U_3570,U_3568] :
        ( hBOOL(hAPP(fun(U_3574,bool),bool,hAPP(U_3574,fun(fun(U_3574,bool),bool),member(U_3574),U_3572),U_3568))
        | hBOOL(hAPP(fun(U_3574,bool),bool,hAPP(U_3574,fun(fun(U_3574,bool),bool),member(U_3574),U_3572),U_3570))
        | ~ hBOOL(hAPP(fun(U_3574,bool),bool,hAPP(U_3574,fun(fun(U_3574,bool),bool),member(U_3574),U_3572),hAPP(fun(U_3574,bool),fun(U_3574,bool),hAPP(fun(U_3574,bool),fun(fun(U_3574,bool),fun(U_3574,bool)),semilattice_sup_sup(fun(U_3574,bool)),U_3570),U_3568))) ) ),
    inference(miniscope,[status(thm)],[f_886_2]) ).

cnf(f_886_4,plain,
    ( hBOOL(hAPP(fun(U_3574,bool),bool,hAPP(U_3574,fun(fun(U_3574,bool),bool),member(U_3574),U_3572),U_3568))
    | hBOOL(hAPP(fun(U_3574,bool),bool,hAPP(U_3574,fun(fun(U_3574,bool),bool),member(U_3574),U_3572),U_3570))
    | ~ hBOOL(hAPP(fun(U_3574,bool),bool,hAPP(U_3574,fun(fun(U_3574,bool),bool),member(U_3574),U_3572),hAPP(fun(U_3574,bool),fun(U_3574,bool),hAPP(fun(U_3574,bool),fun(fun(U_3574,bool),fun(U_3574,bool)),semilattice_sup_sup(fun(U_3574,bool)),U_3570),U_3568))) ),
    inference(clausify,[status(thm)],[f_886_3]) ).

cnf(f_886_5,plain,
    ( ~ hBOOL(hAPP(fun(U_3575,bool),bool,hAPP(U_3575,fun(fun(U_3575,bool),bool),member(U_3575),U_3573),U_3571))
    | hBOOL(hAPP(fun(U_3575,bool),bool,hAPP(U_3575,fun(fun(U_3575,bool),bool),member(U_3575),U_3573),hAPP(fun(U_3575,bool),fun(U_3575,bool),hAPP(fun(U_3575,bool),fun(fun(U_3575,bool),fun(U_3575,bool)),semilattice_sup_sup(fun(U_3575,bool)),U_3571),U_3569))) ),
    inference(clausify,[status(thm)],[f_886_3]) ).

cnf(f_886_6,plain,
    ( ~ hBOOL(hAPP(fun(U_3575,bool),bool,hAPP(U_3575,fun(fun(U_3575,bool),bool),member(U_3575),U_3573),U_3569))
    | hBOOL(hAPP(fun(U_3575,bool),bool,hAPP(U_3575,fun(fun(U_3575,bool),bool),member(U_3575),U_3573),hAPP(fun(U_3575,bool),fun(U_3575,bool),hAPP(fun(U_3575,bool),fun(fun(U_3575,bool),fun(U_3575,bool)),semilattice_sup_sup(fun(U_3575,bool)),U_3571),U_3569))) ),
    inference(clausify,[status(thm)],[f_886_3]) ).

fof(f_887_1,plain,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)),
    inference(fof_nnf,[status(thm)],[fact_797_Un__assoc]) ).

fof(f_887_2,plain,
    ! [U_3579,U_3578,U_3577,U_3576] : hAPP(fun(U_3579,bool),fun(U_3579,bool),hAPP(fun(U_3579,bool),fun(fun(U_3579,bool),fun(U_3579,bool)),semilattice_sup_sup(fun(U_3579,bool)),hAPP(fun(U_3579,bool),fun(U_3579,bool),hAPP(fun(U_3579,bool),fun(fun(U_3579,bool),fun(U_3579,bool)),semilattice_sup_sup(fun(U_3579,bool)),U_3578),U_3577)),U_3576) = hAPP(fun(U_3579,bool),fun(U_3579,bool),hAPP(fun(U_3579,bool),fun(fun(U_3579,bool),fun(U_3579,bool)),semilattice_sup_sup(fun(U_3579,bool)),U_3578),hAPP(fun(U_3579,bool),fun(U_3579,bool),hAPP(fun(U_3579,bool),fun(fun(U_3579,bool),fun(U_3579,bool)),semilattice_sup_sup(fun(U_3579,bool)),U_3577),U_3576)),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

cnf(f_887_3,plain,
    hAPP(fun(U_3579,bool),fun(U_3579,bool),hAPP(fun(U_3579,bool),fun(fun(U_3579,bool),fun(U_3579,bool)),semilattice_sup_sup(fun(U_3579,bool)),hAPP(fun(U_3579,bool),fun(U_3579,bool),hAPP(fun(U_3579,bool),fun(fun(U_3579,bool),fun(U_3579,bool)),semilattice_sup_sup(fun(U_3579,bool)),U_3578),U_3577)),U_3576) = hAPP(fun(U_3579,bool),fun(U_3579,bool),hAPP(fun(U_3579,bool),fun(fun(U_3579,bool),fun(U_3579,bool)),semilattice_sup_sup(fun(U_3579,bool)),U_3578),hAPP(fun(U_3579,bool),fun(U_3579,bool),hAPP(fun(U_3579,bool),fun(fun(U_3579,bool),fun(U_3579,bool)),semilattice_sup_sup(fun(U_3579,bool)),U_3577),U_3576)),
    inference(clausify,[status(thm)],[f_887_2]) ).

fof(f_888_1,plain,
    ! [X_a,Pa,A_1,B] :
      ( ( ? [X_1] :
            ( hBOOL(hAPP(X_a,bool,Pa,X_1))
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) )
        | ( ! [X_1] :
              ( ~ hBOOL(hAPP(X_a,bool,Pa,X_1))
              | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) )
          & ! [X_1] :
              ( ~ hBOOL(hAPP(X_a,bool,Pa,X_1))
              | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ) )
      & ( ? [X_1] :
            ( hBOOL(hAPP(X_a,bool,Pa,X_1))
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) )
        | ? [X_1] :
            ( hBOOL(hAPP(X_a,bool,Pa,X_1))
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) )
        | ! [X_1] :
            ( ~ hBOOL(hAPP(X_a,bool,Pa,X_1))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_798_bex__Un]) ).

fof(f_888_2,plain,
    ! [U_3589,U_3588,U_3587,U_3586] :
      ( ( ? [U_3585] :
            ( hBOOL(hAPP(U_3589,bool,U_3588,U_3585))
            & hBOOL(hAPP(fun(U_3589,bool),bool,hAPP(U_3589,fun(fun(U_3589,bool),bool),member(U_3589),U_3585),hAPP(fun(U_3589,bool),fun(U_3589,bool),hAPP(fun(U_3589,bool),fun(fun(U_3589,bool),fun(U_3589,bool)),semilattice_sup_sup(fun(U_3589,bool)),U_3587),U_3586))) )
        | ( ! [U_3584] :
              ( ~ hBOOL(hAPP(U_3589,bool,U_3588,U_3584))
              | ~ hBOOL(hAPP(fun(U_3589,bool),bool,hAPP(U_3589,fun(fun(U_3589,bool),bool),member(U_3589),U_3584),U_3586)) )
          & ! [U_3583] :
              ( ~ hBOOL(hAPP(U_3589,bool,U_3588,U_3583))
              | ~ hBOOL(hAPP(fun(U_3589,bool),bool,hAPP(U_3589,fun(fun(U_3589,bool),bool),member(U_3589),U_3583),U_3587)) ) ) )
      & ( ? [U_3582] :
            ( hBOOL(hAPP(U_3589,bool,U_3588,U_3582))
            & hBOOL(hAPP(fun(U_3589,bool),bool,hAPP(U_3589,fun(fun(U_3589,bool),bool),member(U_3589),U_3582),U_3586)) )
        | ? [U_3581] :
            ( hBOOL(hAPP(U_3589,bool,U_3588,U_3581))
            & hBOOL(hAPP(fun(U_3589,bool),bool,hAPP(U_3589,fun(fun(U_3589,bool),bool),member(U_3589),U_3581),U_3587)) )
        | ! [U_3580] :
            ( ~ hBOOL(hAPP(U_3589,bool,U_3588,U_3580))
            | ~ hBOOL(hAPP(fun(U_3589,bool),bool,hAPP(U_3589,fun(fun(U_3589,bool),bool),member(U_3589),U_3580),hAPP(fun(U_3589,bool),fun(U_3589,bool),hAPP(fun(U_3589,bool),fun(fun(U_3589,bool),fun(U_3589,bool)),semilattice_sup_sup(fun(U_3589,bool)),U_3587),U_3586))) ) ) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ( ! [U_3597,U_3595,U_3593,U_3591] :
        ( ? [U_3585] :
            ( hBOOL(hAPP(U_3597,bool,U_3595,U_3585))
            & hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3585),hAPP(fun(U_3597,bool),fun(U_3597,bool),hAPP(fun(U_3597,bool),fun(fun(U_3597,bool),fun(U_3597,bool)),semilattice_sup_sup(fun(U_3597,bool)),U_3593),U_3591))) )
        | ( ! [U_3584] :
              ( ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3584))
              | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3584),U_3591)) )
          & ! [U_3583] :
              ( ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3583))
              | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3583),U_3593)) ) ) )
    & ! [U_3596,U_3594,U_3592,U_3590] :
        ( ? [U_3582] :
            ( hBOOL(hAPP(U_3596,bool,U_3594,U_3582))
            & hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3582),U_3590)) )
        | ? [U_3581] :
            ( hBOOL(hAPP(U_3596,bool,U_3594,U_3581))
            & hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3581),U_3592)) )
        | ! [U_3580] :
            ( ~ hBOOL(hAPP(U_3596,bool,U_3594,U_3580))
            | ~ hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3580),hAPP(fun(U_3596,bool),fun(U_3596,bool),hAPP(fun(U_3596,bool),fun(fun(U_3596,bool),fun(U_3596,bool)),semilattice_sup_sup(fun(U_3596,bool)),U_3592),U_3590))) ) ) ),
    inference(miniscope,[status(thm)],[f_888_2]) ).

fof(f_888_4,plain,
    ( ! [U_3597,U_3595,U_3593,U_3591] :
        ( ? [U_3585] :
            ( hBOOL(hAPP(U_3597,bool,U_3595,U_3585))
            & hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3585),hAPP(fun(U_3597,bool),fun(U_3597,bool),hAPP(fun(U_3597,bool),fun(fun(U_3597,bool),fun(U_3597,bool)),semilattice_sup_sup(fun(U_3597,bool)),U_3593),U_3591))) )
        | ( ! [U_3584] :
              ( ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3584))
              | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3584),U_3591)) )
          & ! [U_3583] :
              ( ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3583))
              | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3583),U_3593)) ) ) )
    & ! [U_3596,U_3594,U_3592,U_3590] :
        ( ? [U_3582] :
            ( hBOOL(hAPP(U_3596,bool,U_3594,U_3582))
            & hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3582),U_3590)) )
        | ( hBOOL(hAPP(U_3596,bool,U_3594,sK174(U_3596,U_3594,U_3592,U_3590)))
          & hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),sK174(U_3596,U_3594,U_3592,U_3590)),U_3592)) )
        | ! [U_3580] :
            ( ~ hBOOL(hAPP(U_3596,bool,U_3594,U_3580))
            | ~ hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3580),hAPP(fun(U_3596,bool),fun(U_3596,bool),hAPP(fun(U_3596,bool),fun(fun(U_3596,bool),fun(U_3596,bool)),semilattice_sup_sup(fun(U_3596,bool)),U_3592),U_3590))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_3581,sK174(U_3596,U_3594,U_3592,U_3590))],[f_888_3]) ).

fof(f_888_5,plain,
    ( ! [U_3597,U_3595,U_3593,U_3591] :
        ( ? [U_3585] :
            ( hBOOL(hAPP(U_3597,bool,U_3595,U_3585))
            & hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3585),hAPP(fun(U_3597,bool),fun(U_3597,bool),hAPP(fun(U_3597,bool),fun(fun(U_3597,bool),fun(U_3597,bool)),semilattice_sup_sup(fun(U_3597,bool)),U_3593),U_3591))) )
        | ( ! [U_3584] :
              ( ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3584))
              | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3584),U_3591)) )
          & ! [U_3583] :
              ( ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3583))
              | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3583),U_3593)) ) ) )
    & ! [U_3596,U_3594,U_3592,U_3590] :
        ( ( hBOOL(hAPP(U_3596,bool,U_3594,sK175(U_3596,U_3594,U_3592,U_3590)))
          & hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),sK175(U_3596,U_3594,U_3592,U_3590)),U_3590)) )
        | ( hBOOL(hAPP(U_3596,bool,U_3594,sK174(U_3596,U_3594,U_3592,U_3590)))
          & hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),sK174(U_3596,U_3594,U_3592,U_3590)),U_3592)) )
        | ! [U_3580] :
            ( ~ hBOOL(hAPP(U_3596,bool,U_3594,U_3580))
            | ~ hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3580),hAPP(fun(U_3596,bool),fun(U_3596,bool),hAPP(fun(U_3596,bool),fun(fun(U_3596,bool),fun(U_3596,bool)),semilattice_sup_sup(fun(U_3596,bool)),U_3592),U_3590))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_3582,sK175(U_3596,U_3594,U_3592,U_3590))],[f_888_4]) ).

fof(f_888_6,plain,
    ( ! [U_3597,U_3595,U_3593,U_3591] :
        ( ( hBOOL(hAPP(U_3597,bool,U_3595,sK176(U_3597,U_3595,U_3593,U_3591)))
          & hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),sK176(U_3597,U_3595,U_3593,U_3591)),hAPP(fun(U_3597,bool),fun(U_3597,bool),hAPP(fun(U_3597,bool),fun(fun(U_3597,bool),fun(U_3597,bool)),semilattice_sup_sup(fun(U_3597,bool)),U_3593),U_3591))) )
        | ( ! [U_3584] :
              ( ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3584))
              | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3584),U_3591)) )
          & ! [U_3583] :
              ( ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3583))
              | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3583),U_3593)) ) ) )
    & ! [U_3596,U_3594,U_3592,U_3590] :
        ( ( hBOOL(hAPP(U_3596,bool,U_3594,sK175(U_3596,U_3594,U_3592,U_3590)))
          & hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),sK175(U_3596,U_3594,U_3592,U_3590)),U_3590)) )
        | ( hBOOL(hAPP(U_3596,bool,U_3594,sK174(U_3596,U_3594,U_3592,U_3590)))
          & hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),sK174(U_3596,U_3594,U_3592,U_3590)),U_3592)) )
        | ! [U_3580] :
            ( ~ hBOOL(hAPP(U_3596,bool,U_3594,U_3580))
            | ~ hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3580),hAPP(fun(U_3596,bool),fun(U_3596,bool),hAPP(fun(U_3596,bool),fun(fun(U_3596,bool),fun(U_3596,bool)),semilattice_sup_sup(fun(U_3596,bool)),U_3592),U_3590))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_3585,sK176(U_3597,U_3595,U_3593,U_3591))],[f_888_5]) ).

cnf(f_888_7,plain,
    ( hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),sK175(U_3596,U_3594,U_3592,U_3590)),U_3590))
    | hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),sK174(U_3596,U_3594,U_3592,U_3590)),U_3592))
    | ~ hBOOL(hAPP(U_3596,bool,U_3594,U_3580))
    | ~ hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3580),hAPP(fun(U_3596,bool),fun(U_3596,bool),hAPP(fun(U_3596,bool),fun(fun(U_3596,bool),fun(U_3596,bool)),semilattice_sup_sup(fun(U_3596,bool)),U_3592),U_3590))) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_8,plain,
    ( hBOOL(hAPP(U_3596,bool,U_3594,sK175(U_3596,U_3594,U_3592,U_3590)))
    | hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),sK174(U_3596,U_3594,U_3592,U_3590)),U_3592))
    | ~ hBOOL(hAPP(U_3596,bool,U_3594,U_3580))
    | ~ hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3580),hAPP(fun(U_3596,bool),fun(U_3596,bool),hAPP(fun(U_3596,bool),fun(fun(U_3596,bool),fun(U_3596,bool)),semilattice_sup_sup(fun(U_3596,bool)),U_3592),U_3590))) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_9,plain,
    ( hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),sK175(U_3596,U_3594,U_3592,U_3590)),U_3590))
    | hBOOL(hAPP(U_3596,bool,U_3594,sK174(U_3596,U_3594,U_3592,U_3590)))
    | ~ hBOOL(hAPP(U_3596,bool,U_3594,U_3580))
    | ~ hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3580),hAPP(fun(U_3596,bool),fun(U_3596,bool),hAPP(fun(U_3596,bool),fun(fun(U_3596,bool),fun(U_3596,bool)),semilattice_sup_sup(fun(U_3596,bool)),U_3592),U_3590))) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_10,plain,
    ( hBOOL(hAPP(U_3596,bool,U_3594,sK175(U_3596,U_3594,U_3592,U_3590)))
    | hBOOL(hAPP(U_3596,bool,U_3594,sK174(U_3596,U_3594,U_3592,U_3590)))
    | ~ hBOOL(hAPP(U_3596,bool,U_3594,U_3580))
    | ~ hBOOL(hAPP(fun(U_3596,bool),bool,hAPP(U_3596,fun(fun(U_3596,bool),bool),member(U_3596),U_3580),hAPP(fun(U_3596,bool),fun(U_3596,bool),hAPP(fun(U_3596,bool),fun(fun(U_3596,bool),fun(U_3596,bool)),semilattice_sup_sup(fun(U_3596,bool)),U_3592),U_3590))) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_11,plain,
    ( hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),sK176(U_3597,U_3595,U_3593,U_3591)),hAPP(fun(U_3597,bool),fun(U_3597,bool),hAPP(fun(U_3597,bool),fun(fun(U_3597,bool),fun(U_3597,bool)),semilattice_sup_sup(fun(U_3597,bool)),U_3593),U_3591)))
    | ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3583))
    | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3583),U_3593)) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_12,plain,
    ( hBOOL(hAPP(U_3597,bool,U_3595,sK176(U_3597,U_3595,U_3593,U_3591)))
    | ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3583))
    | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3583),U_3593)) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_13,plain,
    ( hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),sK176(U_3597,U_3595,U_3593,U_3591)),hAPP(fun(U_3597,bool),fun(U_3597,bool),hAPP(fun(U_3597,bool),fun(fun(U_3597,bool),fun(U_3597,bool)),semilattice_sup_sup(fun(U_3597,bool)),U_3593),U_3591)))
    | ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3584))
    | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3584),U_3591)) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_14,plain,
    ( hBOOL(hAPP(U_3597,bool,U_3595,sK176(U_3597,U_3595,U_3593,U_3591)))
    | ~ hBOOL(hAPP(U_3597,bool,U_3595,U_3584))
    | ~ hBOOL(hAPP(fun(U_3597,bool),bool,hAPP(U_3597,fun(fun(U_3597,bool),bool),member(U_3597),U_3584),U_3591)) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

fof(f_889_1,plain,
    ! [X_a,Pa,A_1,B] :
      ( ( ! [X_1] :
            ( hBOOL(hAPP(X_a,bool,Pa,X_1))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) )
        | ? [X_1] :
            ( ~ hBOOL(hAPP(X_a,bool,Pa,X_1))
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) )
        | ? [X_1] :
            ( ~ hBOOL(hAPP(X_a,bool,Pa,X_1))
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) )
      & ( ( ! [X_1] :
              ( hBOOL(hAPP(X_a,bool,Pa,X_1))
              | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) )
          & ! [X_1] :
              ( hBOOL(hAPP(X_a,bool,Pa,X_1))
              | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) )
        | ? [X_1] :
            ( ~ hBOOL(hAPP(X_a,bool,Pa,X_1))
            & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_799_ball__Un]) ).

fof(f_889_2,plain,
    ! [U_3607,U_3606,U_3605,U_3604] :
      ( ( ! [U_3603] :
            ( hBOOL(hAPP(U_3607,bool,U_3606,U_3603))
            | ~ hBOOL(hAPP(fun(U_3607,bool),bool,hAPP(U_3607,fun(fun(U_3607,bool),bool),member(U_3607),U_3603),hAPP(fun(U_3607,bool),fun(U_3607,bool),hAPP(fun(U_3607,bool),fun(fun(U_3607,bool),fun(U_3607,bool)),semilattice_sup_sup(fun(U_3607,bool)),U_3605),U_3604))) )
        | ? [U_3602] :
            ( ~ hBOOL(hAPP(U_3607,bool,U_3606,U_3602))
            & hBOOL(hAPP(fun(U_3607,bool),bool,hAPP(U_3607,fun(fun(U_3607,bool),bool),member(U_3607),U_3602),U_3604)) )
        | ? [U_3601] :
            ( ~ hBOOL(hAPP(U_3607,bool,U_3606,U_3601))
            & hBOOL(hAPP(fun(U_3607,bool),bool,hAPP(U_3607,fun(fun(U_3607,bool),bool),member(U_3607),U_3601),U_3605)) ) )
      & ( ( ! [U_3600] :
              ( hBOOL(hAPP(U_3607,bool,U_3606,U_3600))
              | ~ hBOOL(hAPP(fun(U_3607,bool),bool,hAPP(U_3607,fun(fun(U_3607,bool),bool),member(U_3607),U_3600),U_3604)) )
          & ! [U_3599] :
              ( hBOOL(hAPP(U_3607,bool,U_3606,U_3599))
              | ~ hBOOL(hAPP(fun(U_3607,bool),bool,hAPP(U_3607,fun(fun(U_3607,bool),bool),member(U_3607),U_3599),U_3605)) ) )
        | ? [U_3598] :
            ( ~ hBOOL(hAPP(U_3607,bool,U_3606,U_3598))
            & hBOOL(hAPP(fun(U_3607,bool),bool,hAPP(U_3607,fun(fun(U_3607,bool),bool),member(U_3607),U_3598),hAPP(fun(U_3607,bool),fun(U_3607,bool),hAPP(fun(U_3607,bool),fun(fun(U_3607,bool),fun(U_3607,bool)),semilattice_sup_sup(fun(U_3607,bool)),U_3605),U_3604))) ) ) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ( ! [U_3615,U_3613,U_3611,U_3609] :
        ( ! [U_3603] :
            ( hBOOL(hAPP(U_3615,bool,U_3613,U_3603))
            | ~ hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3603),hAPP(fun(U_3615,bool),fun(U_3615,bool),hAPP(fun(U_3615,bool),fun(fun(U_3615,bool),fun(U_3615,bool)),semilattice_sup_sup(fun(U_3615,bool)),U_3611),U_3609))) )
        | ? [U_3602] :
            ( ~ hBOOL(hAPP(U_3615,bool,U_3613,U_3602))
            & hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3602),U_3609)) )
        | ? [U_3601] :
            ( ~ hBOOL(hAPP(U_3615,bool,U_3613,U_3601))
            & hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3601),U_3611)) ) )
    & ! [U_3614,U_3612,U_3610,U_3608] :
        ( ( ! [U_3600] :
              ( hBOOL(hAPP(U_3614,bool,U_3612,U_3600))
              | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3600),U_3608)) )
          & ! [U_3599] :
              ( hBOOL(hAPP(U_3614,bool,U_3612,U_3599))
              | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3599),U_3610)) ) )
        | ? [U_3598] :
            ( ~ hBOOL(hAPP(U_3614,bool,U_3612,U_3598))
            & hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3598),hAPP(fun(U_3614,bool),fun(U_3614,bool),hAPP(fun(U_3614,bool),fun(fun(U_3614,bool),fun(U_3614,bool)),semilattice_sup_sup(fun(U_3614,bool)),U_3610),U_3608))) ) ) ),
    inference(miniscope,[status(thm)],[f_889_2]) ).

fof(f_889_4,plain,
    ( ! [U_3615,U_3613,U_3611,U_3609] :
        ( ! [U_3603] :
            ( hBOOL(hAPP(U_3615,bool,U_3613,U_3603))
            | ~ hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3603),hAPP(fun(U_3615,bool),fun(U_3615,bool),hAPP(fun(U_3615,bool),fun(fun(U_3615,bool),fun(U_3615,bool)),semilattice_sup_sup(fun(U_3615,bool)),U_3611),U_3609))) )
        | ? [U_3602] :
            ( ~ hBOOL(hAPP(U_3615,bool,U_3613,U_3602))
            & hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3602),U_3609)) )
        | ? [U_3601] :
            ( ~ hBOOL(hAPP(U_3615,bool,U_3613,U_3601))
            & hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3601),U_3611)) ) )
    & ! [U_3614,U_3612,U_3610,U_3608] :
        ( ( ! [U_3600] :
              ( hBOOL(hAPP(U_3614,bool,U_3612,U_3600))
              | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3600),U_3608)) )
          & ! [U_3599] :
              ( hBOOL(hAPP(U_3614,bool,U_3612,U_3599))
              | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3599),U_3610)) ) )
        | ( ~ hBOOL(hAPP(U_3614,bool,U_3612,sK177(U_3614,U_3612,U_3610,U_3608)))
          & hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),sK177(U_3614,U_3612,U_3610,U_3608)),hAPP(fun(U_3614,bool),fun(U_3614,bool),hAPP(fun(U_3614,bool),fun(fun(U_3614,bool),fun(U_3614,bool)),semilattice_sup_sup(fun(U_3614,bool)),U_3610),U_3608))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_3598,sK177(U_3614,U_3612,U_3610,U_3608))],[f_889_3]) ).

fof(f_889_5,plain,
    ( ! [U_3615,U_3613,U_3611,U_3609] :
        ( ! [U_3603] :
            ( hBOOL(hAPP(U_3615,bool,U_3613,U_3603))
            | ~ hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3603),hAPP(fun(U_3615,bool),fun(U_3615,bool),hAPP(fun(U_3615,bool),fun(fun(U_3615,bool),fun(U_3615,bool)),semilattice_sup_sup(fun(U_3615,bool)),U_3611),U_3609))) )
        | ? [U_3602] :
            ( ~ hBOOL(hAPP(U_3615,bool,U_3613,U_3602))
            & hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3602),U_3609)) )
        | ( ~ hBOOL(hAPP(U_3615,bool,U_3613,sK178(U_3615,U_3613,U_3611,U_3609)))
          & hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),sK178(U_3615,U_3613,U_3611,U_3609)),U_3611)) ) )
    & ! [U_3614,U_3612,U_3610,U_3608] :
        ( ( ! [U_3600] :
              ( hBOOL(hAPP(U_3614,bool,U_3612,U_3600))
              | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3600),U_3608)) )
          & ! [U_3599] :
              ( hBOOL(hAPP(U_3614,bool,U_3612,U_3599))
              | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3599),U_3610)) ) )
        | ( ~ hBOOL(hAPP(U_3614,bool,U_3612,sK177(U_3614,U_3612,U_3610,U_3608)))
          & hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),sK177(U_3614,U_3612,U_3610,U_3608)),hAPP(fun(U_3614,bool),fun(U_3614,bool),hAPP(fun(U_3614,bool),fun(fun(U_3614,bool),fun(U_3614,bool)),semilattice_sup_sup(fun(U_3614,bool)),U_3610),U_3608))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_3601,sK178(U_3615,U_3613,U_3611,U_3609))],[f_889_4]) ).

fof(f_889_6,plain,
    ( ! [U_3615,U_3613,U_3611,U_3609] :
        ( ! [U_3603] :
            ( hBOOL(hAPP(U_3615,bool,U_3613,U_3603))
            | ~ hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3603),hAPP(fun(U_3615,bool),fun(U_3615,bool),hAPP(fun(U_3615,bool),fun(fun(U_3615,bool),fun(U_3615,bool)),semilattice_sup_sup(fun(U_3615,bool)),U_3611),U_3609))) )
        | ( ~ hBOOL(hAPP(U_3615,bool,U_3613,sK179(U_3615,U_3613,U_3611,U_3609)))
          & hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),sK179(U_3615,U_3613,U_3611,U_3609)),U_3609)) )
        | ( ~ hBOOL(hAPP(U_3615,bool,U_3613,sK178(U_3615,U_3613,U_3611,U_3609)))
          & hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),sK178(U_3615,U_3613,U_3611,U_3609)),U_3611)) ) )
    & ! [U_3614,U_3612,U_3610,U_3608] :
        ( ( ! [U_3600] :
              ( hBOOL(hAPP(U_3614,bool,U_3612,U_3600))
              | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3600),U_3608)) )
          & ! [U_3599] :
              ( hBOOL(hAPP(U_3614,bool,U_3612,U_3599))
              | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3599),U_3610)) ) )
        | ( ~ hBOOL(hAPP(U_3614,bool,U_3612,sK177(U_3614,U_3612,U_3610,U_3608)))
          & hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),sK177(U_3614,U_3612,U_3610,U_3608)),hAPP(fun(U_3614,bool),fun(U_3614,bool),hAPP(fun(U_3614,bool),fun(fun(U_3614,bool),fun(U_3614,bool)),semilattice_sup_sup(fun(U_3614,bool)),U_3610),U_3608))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_3602,sK179(U_3615,U_3613,U_3611,U_3609))],[f_889_5]) ).

cnf(f_889_7,plain,
    ( hBOOL(hAPP(U_3614,bool,U_3612,U_3599))
    | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3599),U_3610))
    | hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),sK177(U_3614,U_3612,U_3610,U_3608)),hAPP(fun(U_3614,bool),fun(U_3614,bool),hAPP(fun(U_3614,bool),fun(fun(U_3614,bool),fun(U_3614,bool)),semilattice_sup_sup(fun(U_3614,bool)),U_3610),U_3608))) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_8,plain,
    ( hBOOL(hAPP(U_3614,bool,U_3612,U_3600))
    | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3600),U_3608))
    | hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),sK177(U_3614,U_3612,U_3610,U_3608)),hAPP(fun(U_3614,bool),fun(U_3614,bool),hAPP(fun(U_3614,bool),fun(fun(U_3614,bool),fun(U_3614,bool)),semilattice_sup_sup(fun(U_3614,bool)),U_3610),U_3608))) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_9,plain,
    ( hBOOL(hAPP(U_3614,bool,U_3612,U_3599))
    | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3599),U_3610))
    | ~ hBOOL(hAPP(U_3614,bool,U_3612,sK177(U_3614,U_3612,U_3610,U_3608))) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_10,plain,
    ( hBOOL(hAPP(U_3614,bool,U_3612,U_3600))
    | ~ hBOOL(hAPP(fun(U_3614,bool),bool,hAPP(U_3614,fun(fun(U_3614,bool),bool),member(U_3614),U_3600),U_3608))
    | ~ hBOOL(hAPP(U_3614,bool,U_3612,sK177(U_3614,U_3612,U_3610,U_3608))) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_11,plain,
    ( hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),sK179(U_3615,U_3613,U_3611,U_3609)),U_3609))
    | hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),sK178(U_3615,U_3613,U_3611,U_3609)),U_3611))
    | hBOOL(hAPP(U_3615,bool,U_3613,U_3603))
    | ~ hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3603),hAPP(fun(U_3615,bool),fun(U_3615,bool),hAPP(fun(U_3615,bool),fun(fun(U_3615,bool),fun(U_3615,bool)),semilattice_sup_sup(fun(U_3615,bool)),U_3611),U_3609))) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_12,plain,
    ( ~ hBOOL(hAPP(U_3615,bool,U_3613,sK179(U_3615,U_3613,U_3611,U_3609)))
    | hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),sK178(U_3615,U_3613,U_3611,U_3609)),U_3611))
    | hBOOL(hAPP(U_3615,bool,U_3613,U_3603))
    | ~ hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3603),hAPP(fun(U_3615,bool),fun(U_3615,bool),hAPP(fun(U_3615,bool),fun(fun(U_3615,bool),fun(U_3615,bool)),semilattice_sup_sup(fun(U_3615,bool)),U_3611),U_3609))) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_13,plain,
    ( hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),sK179(U_3615,U_3613,U_3611,U_3609)),U_3609))
    | ~ hBOOL(hAPP(U_3615,bool,U_3613,sK178(U_3615,U_3613,U_3611,U_3609)))
    | hBOOL(hAPP(U_3615,bool,U_3613,U_3603))
    | ~ hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3603),hAPP(fun(U_3615,bool),fun(U_3615,bool),hAPP(fun(U_3615,bool),fun(fun(U_3615,bool),fun(U_3615,bool)),semilattice_sup_sup(fun(U_3615,bool)),U_3611),U_3609))) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_14,plain,
    ( ~ hBOOL(hAPP(U_3615,bool,U_3613,sK179(U_3615,U_3613,U_3611,U_3609)))
    | ~ hBOOL(hAPP(U_3615,bool,U_3613,sK178(U_3615,U_3613,U_3611,U_3609)))
    | hBOOL(hAPP(U_3615,bool,U_3613,U_3603))
    | ~ hBOOL(hAPP(fun(U_3615,bool),bool,hAPP(U_3615,fun(fun(U_3615,bool),bool),member(U_3615),U_3603),hAPP(fun(U_3615,bool),fun(U_3615,bool),hAPP(fun(U_3615,bool),fun(fun(U_3615,bool),fun(U_3615,bool)),semilattice_sup_sup(fun(U_3615,bool)),U_3611),U_3609))) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

fof(f_890_1,plain,
    ! [X_a,B,A_1,X_2] :
      ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2))
      | ~ hBOOL(hAPP(X_a,bool,A_1,X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_800_sup1I1]) ).

fof(f_890_2,plain,
    ! [U_3619,U_3618,U_3617,U_3616] :
      ( hBOOL(hAPP(U_3619,bool,hAPP(fun(U_3619,bool),fun(U_3619,bool),hAPP(fun(U_3619,bool),fun(fun(U_3619,bool),fun(U_3619,bool)),semilattice_sup_sup(fun(U_3619,bool)),U_3617),U_3618),U_3616))
      | ~ hBOOL(hAPP(U_3619,bool,U_3617,U_3616)) ),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

cnf(f_890_3,plain,
    ( hBOOL(hAPP(U_3619,bool,hAPP(fun(U_3619,bool),fun(U_3619,bool),hAPP(fun(U_3619,bool),fun(fun(U_3619,bool),fun(U_3619,bool)),semilattice_sup_sup(fun(U_3619,bool)),U_3617),U_3618),U_3616))
    | ~ hBOOL(hAPP(U_3619,bool,U_3617,U_3616)) ),
    inference(clausify,[status(thm)],[f_890_2]) ).

fof(f_891_1,plain,
    ! [X_a,A_1,B,X_2] :
      ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2))
      | ~ hBOOL(hAPP(X_a,bool,B,X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_801_sup1I2]) ).

fof(f_891_2,plain,
    ! [U_3623,U_3622,U_3621,U_3620] :
      ( hBOOL(hAPP(U_3623,bool,hAPP(fun(U_3623,bool),fun(U_3623,bool),hAPP(fun(U_3623,bool),fun(fun(U_3623,bool),fun(U_3623,bool)),semilattice_sup_sup(fun(U_3623,bool)),U_3622),U_3621),U_3620))
      | ~ hBOOL(hAPP(U_3623,bool,U_3621,U_3620)) ),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

cnf(f_891_3,plain,
    ( hBOOL(hAPP(U_3623,bool,hAPP(fun(U_3623,bool),fun(U_3623,bool),hAPP(fun(U_3623,bool),fun(fun(U_3623,bool),fun(U_3623,bool)),semilattice_sup_sup(fun(U_3623,bool)),U_3622),U_3621),U_3620))
    | ~ hBOOL(hAPP(U_3623,bool,U_3621,U_3620)) ),
    inference(clausify,[status(thm)],[f_891_2]) ).

fof(f_892_1,plain,
    ! [X_a,B,Ca,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_802_UnI1]) ).

fof(f_892_2,plain,
    ! [U_3627,U_3626,U_3625,U_3624] :
      ( hBOOL(hAPP(fun(U_3627,bool),bool,hAPP(U_3627,fun(fun(U_3627,bool),bool),member(U_3627),U_3625),hAPP(fun(U_3627,bool),fun(U_3627,bool),hAPP(fun(U_3627,bool),fun(fun(U_3627,bool),fun(U_3627,bool)),semilattice_sup_sup(fun(U_3627,bool)),U_3624),U_3626)))
      | ~ hBOOL(hAPP(fun(U_3627,bool),bool,hAPP(U_3627,fun(fun(U_3627,bool),bool),member(U_3627),U_3625),U_3624)) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

cnf(f_892_3,plain,
    ( hBOOL(hAPP(fun(U_3627,bool),bool,hAPP(U_3627,fun(fun(U_3627,bool),bool),member(U_3627),U_3625),hAPP(fun(U_3627,bool),fun(U_3627,bool),hAPP(fun(U_3627,bool),fun(fun(U_3627,bool),fun(U_3627,bool)),semilattice_sup_sup(fun(U_3627,bool)),U_3624),U_3626)))
    | ~ hBOOL(hAPP(fun(U_3627,bool),bool,hAPP(U_3627,fun(fun(U_3627,bool),bool),member(U_3627),U_3625),U_3624)) ),
    inference(clausify,[status(thm)],[f_892_2]) ).

fof(f_893_1,plain,
    ! [X_a,A_1,Ca,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B)) ),
    inference(fof_nnf,[status(thm)],[fact_803_UnI2]) ).

fof(f_893_2,plain,
    ! [U_3631,U_3630,U_3629,U_3628] :
      ( hBOOL(hAPP(fun(U_3631,bool),bool,hAPP(U_3631,fun(fun(U_3631,bool),bool),member(U_3631),U_3629),hAPP(fun(U_3631,bool),fun(U_3631,bool),hAPP(fun(U_3631,bool),fun(fun(U_3631,bool),fun(U_3631,bool)),semilattice_sup_sup(fun(U_3631,bool)),U_3630),U_3628)))
      | ~ hBOOL(hAPP(fun(U_3631,bool),bool,hAPP(U_3631,fun(fun(U_3631,bool),bool),member(U_3631),U_3629),U_3628)) ),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

cnf(f_893_3,plain,
    ( hBOOL(hAPP(fun(U_3631,bool),bool,hAPP(U_3631,fun(fun(U_3631,bool),bool),member(U_3631),U_3629),hAPP(fun(U_3631,bool),fun(U_3631,bool),hAPP(fun(U_3631,bool),fun(fun(U_3631,bool),fun(U_3631,bool)),semilattice_sup_sup(fun(U_3631,bool)),U_3630),U_3628)))
    | ~ hBOOL(hAPP(fun(U_3631,bool),bool,hAPP(U_3631,fun(fun(U_3631,bool),bool),member(U_3631),U_3629),U_3628)) ),
    inference(clausify,[status(thm)],[f_893_2]) ).

fof(f_894_1,plain,
    ! [X_a,R_2,S,X_1] :
      ( ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)),X_1))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),R_2),S))) )
      & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),R_2),S)))
        | ~ hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)),X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_804_sup__Un__eq]) ).

fof(f_894_2,plain,
    ! [U_3635,U_3634,U_3633,U_3632] :
      ( ( hBOOL(hAPP(U_3635,bool,hAPP(fun(U_3635,bool),fun(U_3635,bool),hAPP(fun(U_3635,bool),fun(fun(U_3635,bool),fun(U_3635,bool)),semilattice_sup_sup(fun(U_3635,bool)),hAPP(fun(U_3635,bool),fun(U_3635,bool),hAPP(fun(U_3635,fun(fun(U_3635,bool),bool)),fun(fun(U_3635,bool),fun(U_3635,bool)),combc(U_3635,fun(U_3635,bool),bool),member(U_3635)),U_3634)),hAPP(fun(U_3635,bool),fun(U_3635,bool),hAPP(fun(U_3635,fun(fun(U_3635,bool),bool)),fun(fun(U_3635,bool),fun(U_3635,bool)),combc(U_3635,fun(U_3635,bool),bool),member(U_3635)),U_3633)),U_3632))
        | ~ hBOOL(hAPP(fun(U_3635,bool),bool,hAPP(U_3635,fun(fun(U_3635,bool),bool),member(U_3635),U_3632),hAPP(fun(U_3635,bool),fun(U_3635,bool),hAPP(fun(U_3635,bool),fun(fun(U_3635,bool),fun(U_3635,bool)),semilattice_sup_sup(fun(U_3635,bool)),U_3634),U_3633))) )
      & ( hBOOL(hAPP(fun(U_3635,bool),bool,hAPP(U_3635,fun(fun(U_3635,bool),bool),member(U_3635),U_3632),hAPP(fun(U_3635,bool),fun(U_3635,bool),hAPP(fun(U_3635,bool),fun(fun(U_3635,bool),fun(U_3635,bool)),semilattice_sup_sup(fun(U_3635,bool)),U_3634),U_3633)))
        | ~ hBOOL(hAPP(U_3635,bool,hAPP(fun(U_3635,bool),fun(U_3635,bool),hAPP(fun(U_3635,bool),fun(fun(U_3635,bool),fun(U_3635,bool)),semilattice_sup_sup(fun(U_3635,bool)),hAPP(fun(U_3635,bool),fun(U_3635,bool),hAPP(fun(U_3635,fun(fun(U_3635,bool),bool)),fun(fun(U_3635,bool),fun(U_3635,bool)),combc(U_3635,fun(U_3635,bool),bool),member(U_3635)),U_3634)),hAPP(fun(U_3635,bool),fun(U_3635,bool),hAPP(fun(U_3635,fun(fun(U_3635,bool),bool)),fun(fun(U_3635,bool),fun(U_3635,bool)),combc(U_3635,fun(U_3635,bool),bool),member(U_3635)),U_3633)),U_3632)) ) ),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ( ! [U_3643,U_3641,U_3639,U_3637] :
        ( hBOOL(hAPP(U_3643,bool,hAPP(fun(U_3643,bool),fun(U_3643,bool),hAPP(fun(U_3643,bool),fun(fun(U_3643,bool),fun(U_3643,bool)),semilattice_sup_sup(fun(U_3643,bool)),hAPP(fun(U_3643,bool),fun(U_3643,bool),hAPP(fun(U_3643,fun(fun(U_3643,bool),bool)),fun(fun(U_3643,bool),fun(U_3643,bool)),combc(U_3643,fun(U_3643,bool),bool),member(U_3643)),U_3641)),hAPP(fun(U_3643,bool),fun(U_3643,bool),hAPP(fun(U_3643,fun(fun(U_3643,bool),bool)),fun(fun(U_3643,bool),fun(U_3643,bool)),combc(U_3643,fun(U_3643,bool),bool),member(U_3643)),U_3639)),U_3637))
        | ~ hBOOL(hAPP(fun(U_3643,bool),bool,hAPP(U_3643,fun(fun(U_3643,bool),bool),member(U_3643),U_3637),hAPP(fun(U_3643,bool),fun(U_3643,bool),hAPP(fun(U_3643,bool),fun(fun(U_3643,bool),fun(U_3643,bool)),semilattice_sup_sup(fun(U_3643,bool)),U_3641),U_3639))) )
    & ! [U_3642,U_3640,U_3638,U_3636] :
        ( hBOOL(hAPP(fun(U_3642,bool),bool,hAPP(U_3642,fun(fun(U_3642,bool),bool),member(U_3642),U_3636),hAPP(fun(U_3642,bool),fun(U_3642,bool),hAPP(fun(U_3642,bool),fun(fun(U_3642,bool),fun(U_3642,bool)),semilattice_sup_sup(fun(U_3642,bool)),U_3640),U_3638)))
        | ~ hBOOL(hAPP(U_3642,bool,hAPP(fun(U_3642,bool),fun(U_3642,bool),hAPP(fun(U_3642,bool),fun(fun(U_3642,bool),fun(U_3642,bool)),semilattice_sup_sup(fun(U_3642,bool)),hAPP(fun(U_3642,bool),fun(U_3642,bool),hAPP(fun(U_3642,fun(fun(U_3642,bool),bool)),fun(fun(U_3642,bool),fun(U_3642,bool)),combc(U_3642,fun(U_3642,bool),bool),member(U_3642)),U_3640)),hAPP(fun(U_3642,bool),fun(U_3642,bool),hAPP(fun(U_3642,fun(fun(U_3642,bool),bool)),fun(fun(U_3642,bool),fun(U_3642,bool)),combc(U_3642,fun(U_3642,bool),bool),member(U_3642)),U_3638)),U_3636)) ) ),
    inference(miniscope,[status(thm)],[f_894_2]) ).

cnf(f_894_4,plain,
    ( hBOOL(hAPP(fun(U_3642,bool),bool,hAPP(U_3642,fun(fun(U_3642,bool),bool),member(U_3642),U_3636),hAPP(fun(U_3642,bool),fun(U_3642,bool),hAPP(fun(U_3642,bool),fun(fun(U_3642,bool),fun(U_3642,bool)),semilattice_sup_sup(fun(U_3642,bool)),U_3640),U_3638)))
    | ~ hBOOL(hAPP(U_3642,bool,hAPP(fun(U_3642,bool),fun(U_3642,bool),hAPP(fun(U_3642,bool),fun(fun(U_3642,bool),fun(U_3642,bool)),semilattice_sup_sup(fun(U_3642,bool)),hAPP(fun(U_3642,bool),fun(U_3642,bool),hAPP(fun(U_3642,fun(fun(U_3642,bool),bool)),fun(fun(U_3642,bool),fun(U_3642,bool)),combc(U_3642,fun(U_3642,bool),bool),member(U_3642)),U_3640)),hAPP(fun(U_3642,bool),fun(U_3642,bool),hAPP(fun(U_3642,fun(fun(U_3642,bool),bool)),fun(fun(U_3642,bool),fun(U_3642,bool)),combc(U_3642,fun(U_3642,bool),bool),member(U_3642)),U_3638)),U_3636)) ),
    inference(clausify,[status(thm)],[f_894_3]) ).

cnf(f_894_5,plain,
    ( hBOOL(hAPP(U_3643,bool,hAPP(fun(U_3643,bool),fun(U_3643,bool),hAPP(fun(U_3643,bool),fun(fun(U_3643,bool),fun(U_3643,bool)),semilattice_sup_sup(fun(U_3643,bool)),hAPP(fun(U_3643,bool),fun(U_3643,bool),hAPP(fun(U_3643,fun(fun(U_3643,bool),bool)),fun(fun(U_3643,bool),fun(U_3643,bool)),combc(U_3643,fun(U_3643,bool),bool),member(U_3643)),U_3641)),hAPP(fun(U_3643,bool),fun(U_3643,bool),hAPP(fun(U_3643,fun(fun(U_3643,bool),bool)),fun(fun(U_3643,bool),fun(U_3643,bool)),combc(U_3643,fun(U_3643,bool),bool),member(U_3643)),U_3639)),U_3637))
    | ~ hBOOL(hAPP(fun(U_3643,bool),bool,hAPP(U_3643,fun(fun(U_3643,bool),bool),member(U_3643),U_3637),hAPP(fun(U_3643,bool),fun(U_3643,bool),hAPP(fun(U_3643,bool),fun(fun(U_3643,bool),fun(U_3643,bool)),semilattice_sup_sup(fun(U_3643,bool)),U_3641),U_3639))) ),
    inference(clausify,[status(thm)],[f_894_3]) ).

fof(f_895_1,plain,
    ! [X_a,Pa,Q_1] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),Pa)),Q_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)),
    inference(fof_nnf,[status(thm)],[fact_805_Collect__disj__eq]) ).

fof(f_895_2,plain,
    ! [U_3646,U_3645,U_3644] : hAPP(fun(U_3646,bool),fun(U_3646,bool),collect(U_3646),hAPP(fun(U_3646,bool),fun(U_3646,bool),hAPP(fun(U_3646,fun(bool,bool)),fun(fun(U_3646,bool),fun(U_3646,bool)),combs(U_3646,bool,bool),hAPP(fun(U_3646,bool),fun(U_3646,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_3646,bool),fun(U_3646,fun(bool,bool))),combb(bool,fun(bool,bool),U_3646),fdisj),U_3645)),U_3644)) = hAPP(fun(U_3646,bool),fun(U_3646,bool),hAPP(fun(U_3646,bool),fun(fun(U_3646,bool),fun(U_3646,bool)),semilattice_sup_sup(fun(U_3646,bool)),hAPP(fun(U_3646,bool),fun(U_3646,bool),collect(U_3646),U_3645)),hAPP(fun(U_3646,bool),fun(U_3646,bool),collect(U_3646),U_3644)),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

cnf(f_895_3,plain,
    hAPP(fun(U_3646,bool),fun(U_3646,bool),collect(U_3646),hAPP(fun(U_3646,bool),fun(U_3646,bool),hAPP(fun(U_3646,fun(bool,bool)),fun(fun(U_3646,bool),fun(U_3646,bool)),combs(U_3646,bool,bool),hAPP(fun(U_3646,bool),fun(U_3646,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_3646,bool),fun(U_3646,fun(bool,bool))),combb(bool,fun(bool,bool),U_3646),fdisj),U_3645)),U_3644)) = hAPP(fun(U_3646,bool),fun(U_3646,bool),hAPP(fun(U_3646,bool),fun(fun(U_3646,bool),fun(U_3646,bool)),semilattice_sup_sup(fun(U_3646,bool)),hAPP(fun(U_3646,bool),fun(U_3646,bool),collect(U_3646),U_3645)),hAPP(fun(U_3646,bool),fun(U_3646,bool),collect(U_3646),U_3644)),
    inference(clausify,[status(thm)],[f_895_2]) ).

fof(f_896_1,plain,
    ! [X_a,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),top_top(fun(X_a,bool))),B) = top_top(fun(X_a,bool)),
    inference(fof_nnf,[status(thm)],[fact_806_Un__UNIV__left]) ).

fof(f_896_2,plain,
    ! [U_3648,U_3647] : hAPP(fun(U_3648,bool),fun(U_3648,bool),hAPP(fun(U_3648,bool),fun(fun(U_3648,bool),fun(U_3648,bool)),semilattice_sup_sup(fun(U_3648,bool)),top_top(fun(U_3648,bool))),U_3647) = top_top(fun(U_3648,bool)),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

cnf(f_896_3,plain,
    hAPP(fun(U_3648,bool),fun(U_3648,bool),hAPP(fun(U_3648,bool),fun(fun(U_3648,bool),fun(U_3648,bool)),semilattice_sup_sup(fun(U_3648,bool)),top_top(fun(U_3648,bool))),U_3647) = top_top(fun(U_3648,bool)),
    inference(clausify,[status(thm)],[f_896_2]) ).

fof(f_897_1,plain,
    ! [X_a,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),top_top(fun(X_a,bool))) = top_top(fun(X_a,bool)),
    inference(fof_nnf,[status(thm)],[fact_807_Un__UNIV__right]) ).

fof(f_897_2,plain,
    ! [U_3650,U_3649] : hAPP(fun(U_3650,bool),fun(U_3650,bool),hAPP(fun(U_3650,bool),fun(fun(U_3650,bool),fun(U_3650,bool)),semilattice_sup_sup(fun(U_3650,bool)),U_3649),top_top(fun(U_3650,bool))) = top_top(fun(U_3650,bool)),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

cnf(f_897_3,plain,
    hAPP(fun(U_3650,bool),fun(U_3650,bool),hAPP(fun(U_3650,bool),fun(fun(U_3650,bool),fun(U_3650,bool)),semilattice_sup_sup(fun(U_3650,bool)),U_3649),top_top(fun(U_3650,bool))) = top_top(fun(U_3650,bool)),
    inference(clausify,[status(thm)],[f_897_2]) ).

fof(f_898_1,plain,
    ! [X_b,X_a,B,A_1,F,Z_1,G,Fa] :
      ( hAPP(fun(X_b,bool),X_a,Fa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,A_1)),hAPP(fun(X_b,bool),X_a,Fa,B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z_1),G),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_808_folding__image__simple__idem_Ounion__idem]) ).

fof(f_898_2,plain,
    ! [U_3658,U_3657,U_3656,U_3655,U_3654,U_3653,U_3652,U_3651] :
      ( hAPP(fun(U_3658,bool),U_3657,U_3651,hAPP(fun(U_3658,bool),fun(U_3658,bool),hAPP(fun(U_3658,bool),fun(fun(U_3658,bool),fun(U_3658,bool)),semilattice_sup_sup(fun(U_3658,bool)),U_3655),U_3656)) = hAPP(U_3657,U_3657,hAPP(U_3657,fun(U_3657,U_3657),U_3654,hAPP(fun(U_3658,bool),U_3657,U_3651,U_3655)),hAPP(fun(U_3658,bool),U_3657,U_3651,U_3656))
      | ~ hBOOL(hAPP(fun(U_3658,bool),bool,finite_finite_1(U_3658),U_3656))
      | ~ hBOOL(hAPP(fun(U_3658,bool),bool,finite_finite_1(U_3658),U_3655))
      | ~ hBOOL(hAPP(fun(fun(U_3658,bool),U_3657),bool,hAPP(fun(U_3658,U_3657),fun(fun(fun(U_3658,bool),U_3657),bool),hAPP(U_3657,fun(fun(U_3658,U_3657),fun(fun(fun(U_3658,bool),U_3657),bool)),hAPP(fun(U_3657,fun(U_3657,U_3657)),fun(U_3657,fun(fun(U_3658,U_3657),fun(fun(fun(U_3658,bool),U_3657),bool))),finite908156982e_idem(U_3657,U_3658),U_3654),U_3653),U_3652),U_3651)) ),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

cnf(f_898_3,plain,
    ( hAPP(fun(U_3658,bool),U_3657,U_3651,hAPP(fun(U_3658,bool),fun(U_3658,bool),hAPP(fun(U_3658,bool),fun(fun(U_3658,bool),fun(U_3658,bool)),semilattice_sup_sup(fun(U_3658,bool)),U_3655),U_3656)) = hAPP(U_3657,U_3657,hAPP(U_3657,fun(U_3657,U_3657),U_3654,hAPP(fun(U_3658,bool),U_3657,U_3651,U_3655)),hAPP(fun(U_3658,bool),U_3657,U_3651,U_3656))
    | ~ hBOOL(hAPP(fun(U_3658,bool),bool,finite_finite_1(U_3658),U_3656))
    | ~ hBOOL(hAPP(fun(U_3658,bool),bool,finite_finite_1(U_3658),U_3655))
    | ~ hBOOL(hAPP(fun(fun(U_3658,bool),U_3657),bool,hAPP(fun(U_3658,U_3657),fun(fun(fun(U_3658,bool),U_3657),bool),hAPP(U_3657,fun(fun(U_3658,U_3657),fun(fun(fun(U_3658,bool),U_3657),bool)),hAPP(fun(U_3657,fun(U_3657,U_3657)),fun(U_3657,fun(fun(U_3658,U_3657),fun(fun(fun(U_3658,bool),U_3657),bool))),finite908156982e_idem(U_3657,U_3658),U_3654),U_3653),U_3652),U_3651)) ),
    inference(clausify,[status(thm)],[f_898_2]) ).

fof(f_899_1,plain,
    ! [X_a] :
      ( ! [U,L,M] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),L),U)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_809_ivl__disj__un_I21_J]) ).

fof(f_899_2,plain,
    ! [U_3662] :
      ( ! [U_3661,U_3660,U_3659] :
          ( hAPP(fun(U_3662,bool),fun(U_3662,bool),hAPP(fun(U_3662,bool),fun(fun(U_3662,bool),fun(U_3662,bool)),semilattice_sup_sup(fun(U_3662,bool)),hAPP(U_3662,fun(U_3662,bool),hAPP(U_3662,fun(U_3662,fun(U_3662,bool)),ord_atLeastLessThan(U_3662),U_3660),U_3659)),hAPP(U_3662,fun(U_3662,bool),hAPP(U_3662,fun(U_3662,fun(U_3662,bool)),ord_atLeastAtMost(U_3662),U_3659),U_3661)) = hAPP(U_3662,fun(U_3662,bool),hAPP(U_3662,fun(U_3662,fun(U_3662,bool)),ord_atLeastAtMost(U_3662),U_3660),U_3661)
          | ~ hBOOL(hAPP(U_3662,bool,hAPP(U_3662,fun(U_3662,bool),ord_less_eq(U_3662),U_3659),U_3661))
          | ~ hBOOL(hAPP(U_3662,bool,hAPP(U_3662,fun(U_3662,bool),ord_less_eq(U_3662),U_3660),U_3659)) )
      | ~ linorder(U_3662) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

cnf(f_899_3,plain,
    ( hAPP(fun(U_3662,bool),fun(U_3662,bool),hAPP(fun(U_3662,bool),fun(fun(U_3662,bool),fun(U_3662,bool)),semilattice_sup_sup(fun(U_3662,bool)),hAPP(U_3662,fun(U_3662,bool),hAPP(U_3662,fun(U_3662,fun(U_3662,bool)),ord_atLeastLessThan(U_3662),U_3660),U_3659)),hAPP(U_3662,fun(U_3662,bool),hAPP(U_3662,fun(U_3662,fun(U_3662,bool)),ord_atLeastAtMost(U_3662),U_3659),U_3661)) = hAPP(U_3662,fun(U_3662,bool),hAPP(U_3662,fun(U_3662,fun(U_3662,bool)),ord_atLeastAtMost(U_3662),U_3660),U_3661)
    | ~ hBOOL(hAPP(U_3662,bool,hAPP(U_3662,fun(U_3662,bool),ord_less_eq(U_3662),U_3659),U_3661))
    | ~ hBOOL(hAPP(U_3662,bool,hAPP(U_3662,fun(U_3662,bool),ord_less_eq(U_3662),U_3660),U_3659))
    | ~ linorder(U_3662) ),
    inference(clausify,[status(thm)],[f_899_2]) ).

fof(f_900_1,plain,
    ! [K,I,J] :
      ( hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),J),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) ),
    inference(fof_nnf,[status(thm)],[fact_810_atLeastLessThan__add__Un]) ).

fof(f_900_2,plain,
    ! [U_3665,U_3664,U_3663] :
      ( hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_3664),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3663),U_3665)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_3664),U_3663)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_3663),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3663),U_3665)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3664),U_3663)) ),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

cnf(f_900_3,plain,
    ( hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_3664),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3663),U_3665)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_3664),U_3663)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_3663),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3663),U_3665)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3664),U_3663)) ),
    inference(clausify,[status(thm)],[f_900_2]) ).

fof(f_901_1,plain,
    ! [X_a] :
      ( ! [U,L,M] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),L),U)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_811_ivl__disj__un_I22_J]) ).

fof(f_901_2,plain,
    ! [U_3669] :
      ( ! [U_3668,U_3667,U_3666] :
          ( hAPP(fun(U_3669,bool),fun(U_3669,bool),hAPP(fun(U_3669,bool),fun(fun(U_3669,bool),fun(U_3669,bool)),semilattice_sup_sup(fun(U_3669,bool)),hAPP(U_3669,fun(U_3669,bool),hAPP(U_3669,fun(U_3669,fun(U_3669,bool)),ord_atLeastAtMost(U_3669),U_3667),U_3666)),hAPP(U_3669,fun(U_3669,bool),hAPP(U_3669,fun(U_3669,fun(U_3669,bool)),ord_gr1471790799AtMost(U_3669),U_3666),U_3668)) = hAPP(U_3669,fun(U_3669,bool),hAPP(U_3669,fun(U_3669,fun(U_3669,bool)),ord_atLeastAtMost(U_3669),U_3667),U_3668)
          | ~ hBOOL(hAPP(U_3669,bool,hAPP(U_3669,fun(U_3669,bool),ord_less_eq(U_3669),U_3666),U_3668))
          | ~ hBOOL(hAPP(U_3669,bool,hAPP(U_3669,fun(U_3669,bool),ord_less_eq(U_3669),U_3667),U_3666)) )
      | ~ linorder(U_3669) ),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

cnf(f_901_3,plain,
    ( hAPP(fun(U_3669,bool),fun(U_3669,bool),hAPP(fun(U_3669,bool),fun(fun(U_3669,bool),fun(U_3669,bool)),semilattice_sup_sup(fun(U_3669,bool)),hAPP(U_3669,fun(U_3669,bool),hAPP(U_3669,fun(U_3669,fun(U_3669,bool)),ord_atLeastAtMost(U_3669),U_3667),U_3666)),hAPP(U_3669,fun(U_3669,bool),hAPP(U_3669,fun(U_3669,fun(U_3669,bool)),ord_gr1471790799AtMost(U_3669),U_3666),U_3668)) = hAPP(U_3669,fun(U_3669,bool),hAPP(U_3669,fun(U_3669,fun(U_3669,bool)),ord_atLeastAtMost(U_3669),U_3667),U_3668)
    | ~ hBOOL(hAPP(U_3669,bool,hAPP(U_3669,fun(U_3669,bool),ord_less_eq(U_3669),U_3666),U_3668))
    | ~ hBOOL(hAPP(U_3669,bool,hAPP(U_3669,fun(U_3669,bool),ord_less_eq(U_3669),U_3667),U_3666))
    | ~ linorder(U_3669) ),
    inference(clausify,[status(thm)],[f_901_2]) ).

fof(f_902_1,plain,
    ! [X_a] :
      ( ! [L,U] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),L),U)),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),U)) = hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),L)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),U)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_812_ivl__disj__un_I11_J]) ).

fof(f_902_2,plain,
    ! [U_3672] :
      ( ! [U_3671,U_3670] :
          ( hAPP(fun(U_3672,bool),fun(U_3672,bool),hAPP(fun(U_3672,bool),fun(fun(U_3672,bool),fun(U_3672,bool)),semilattice_sup_sup(fun(U_3672,bool)),hAPP(U_3672,fun(U_3672,bool),hAPP(U_3672,fun(U_3672,fun(U_3672,bool)),ord_gr1471790799AtMost(U_3672),U_3671),U_3670)),hAPP(U_3672,fun(U_3672,bool),ord_greaterThan(U_3672),U_3670)) = hAPP(U_3672,fun(U_3672,bool),ord_greaterThan(U_3672),U_3671)
          | ~ hBOOL(hAPP(U_3672,bool,hAPP(U_3672,fun(U_3672,bool),ord_less_eq(U_3672),U_3671),U_3670)) )
      | ~ linorder(U_3672) ),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

cnf(f_902_3,plain,
    ( hAPP(fun(U_3672,bool),fun(U_3672,bool),hAPP(fun(U_3672,bool),fun(fun(U_3672,bool),fun(U_3672,bool)),semilattice_sup_sup(fun(U_3672,bool)),hAPP(U_3672,fun(U_3672,bool),hAPP(U_3672,fun(U_3672,fun(U_3672,bool)),ord_gr1471790799AtMost(U_3672),U_3671),U_3670)),hAPP(U_3672,fun(U_3672,bool),ord_greaterThan(U_3672),U_3670)) = hAPP(U_3672,fun(U_3672,bool),ord_greaterThan(U_3672),U_3671)
    | ~ hBOOL(hAPP(U_3672,bool,hAPP(U_3672,fun(U_3672,bool),ord_less_eq(U_3672),U_3671),U_3670))
    | ~ linorder(U_3672) ),
    inference(clausify,[status(thm)],[f_902_2]) ).

fof(f_903_1,plain,
    ! [X_a,X_b,B,A_1,F,Fa] :
      ( hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_b,X_b),fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(fun(X_b,X_b),fun(X_b,X_b)),comp(X_b,X_b,X_b),hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,A_1)),hAPP(fun(X_a,bool),fun(X_b,X_b),Fa,B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1))
      | ~ hBOOL(hAPP(fun(fun(X_a,bool),fun(X_b,X_b)),bool,hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(fun(X_a,bool),fun(X_b,X_b)),bool),finite_folding_idem(X_a,X_b),F),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_813_folding__idem_Ounion__idem]) ).

fof(f_903_2,plain,
    ! [U_3678,U_3677,U_3676,U_3675,U_3674,U_3673] :
      ( hAPP(fun(U_3678,bool),fun(U_3677,U_3677),U_3673,hAPP(fun(U_3678,bool),fun(U_3678,bool),hAPP(fun(U_3678,bool),fun(fun(U_3678,bool),fun(U_3678,bool)),semilattice_sup_sup(fun(U_3678,bool)),U_3675),U_3676)) = hAPP(fun(U_3677,U_3677),fun(U_3677,U_3677),hAPP(fun(U_3677,U_3677),fun(fun(U_3677,U_3677),fun(U_3677,U_3677)),comp(U_3677,U_3677,U_3677),hAPP(fun(U_3678,bool),fun(U_3677,U_3677),U_3673,U_3675)),hAPP(fun(U_3678,bool),fun(U_3677,U_3677),U_3673,U_3676))
      | ~ hBOOL(hAPP(fun(U_3678,bool),bool,finite_finite_1(U_3678),U_3676))
      | ~ hBOOL(hAPP(fun(U_3678,bool),bool,finite_finite_1(U_3678),U_3675))
      | ~ hBOOL(hAPP(fun(fun(U_3678,bool),fun(U_3677,U_3677)),bool,hAPP(fun(U_3678,fun(U_3677,U_3677)),fun(fun(fun(U_3678,bool),fun(U_3677,U_3677)),bool),finite_folding_idem(U_3678,U_3677),U_3674),U_3673)) ),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

cnf(f_903_3,plain,
    ( hAPP(fun(U_3678,bool),fun(U_3677,U_3677),U_3673,hAPP(fun(U_3678,bool),fun(U_3678,bool),hAPP(fun(U_3678,bool),fun(fun(U_3678,bool),fun(U_3678,bool)),semilattice_sup_sup(fun(U_3678,bool)),U_3675),U_3676)) = hAPP(fun(U_3677,U_3677),fun(U_3677,U_3677),hAPP(fun(U_3677,U_3677),fun(fun(U_3677,U_3677),fun(U_3677,U_3677)),comp(U_3677,U_3677,U_3677),hAPP(fun(U_3678,bool),fun(U_3677,U_3677),U_3673,U_3675)),hAPP(fun(U_3678,bool),fun(U_3677,U_3677),U_3673,U_3676))
    | ~ hBOOL(hAPP(fun(U_3678,bool),bool,finite_finite_1(U_3678),U_3676))
    | ~ hBOOL(hAPP(fun(U_3678,bool),bool,finite_finite_1(U_3678),U_3675))
    | ~ hBOOL(hAPP(fun(fun(U_3678,bool),fun(U_3677,U_3677)),bool,hAPP(fun(U_3678,fun(U_3677,U_3677)),fun(fun(fun(U_3678,bool),fun(U_3677,U_3677)),bool),finite_folding_idem(U_3678,U_3677),U_3674),U_3673)) ),
    inference(clausify,[status(thm)],[f_903_2]) ).

fof(f_904_1,plain,
    ! [X_a] :
      ( ! [U,L,M] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),L),U)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M),U))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),L),M)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_814_ivl__disj__un_I15_J]) ).

fof(f_904_2,plain,
    ! [U_3682] :
      ( ! [U_3681,U_3680,U_3679] :
          ( hAPP(fun(U_3682,bool),fun(U_3682,bool),hAPP(fun(U_3682,bool),fun(fun(U_3682,bool),fun(U_3682,bool)),semilattice_sup_sup(fun(U_3682,bool)),hAPP(U_3682,fun(U_3682,bool),hAPP(U_3682,fun(U_3682,fun(U_3682,bool)),ord_gr676655987ssThan(U_3682),U_3680),U_3679)),hAPP(U_3682,fun(U_3682,bool),hAPP(U_3682,fun(U_3682,fun(U_3682,bool)),ord_atLeastLessThan(U_3682),U_3679),U_3681)) = hAPP(U_3682,fun(U_3682,bool),hAPP(U_3682,fun(U_3682,fun(U_3682,bool)),ord_gr676655987ssThan(U_3682),U_3680),U_3681)
          | ~ hBOOL(hAPP(U_3682,bool,hAPP(U_3682,fun(U_3682,bool),ord_less_eq(U_3682),U_3679),U_3681))
          | ~ hBOOL(hAPP(U_3682,bool,hAPP(U_3682,fun(U_3682,bool),ord_less(U_3682),U_3680),U_3679)) )
      | ~ linorder(U_3682) ),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

cnf(f_904_3,plain,
    ( hAPP(fun(U_3682,bool),fun(U_3682,bool),hAPP(fun(U_3682,bool),fun(fun(U_3682,bool),fun(U_3682,bool)),semilattice_sup_sup(fun(U_3682,bool)),hAPP(U_3682,fun(U_3682,bool),hAPP(U_3682,fun(U_3682,fun(U_3682,bool)),ord_gr676655987ssThan(U_3682),U_3680),U_3679)),hAPP(U_3682,fun(U_3682,bool),hAPP(U_3682,fun(U_3682,fun(U_3682,bool)),ord_atLeastLessThan(U_3682),U_3679),U_3681)) = hAPP(U_3682,fun(U_3682,bool),hAPP(U_3682,fun(U_3682,fun(U_3682,bool)),ord_gr676655987ssThan(U_3682),U_3680),U_3681)
    | ~ hBOOL(hAPP(U_3682,bool,hAPP(U_3682,fun(U_3682,bool),ord_less_eq(U_3682),U_3679),U_3681))
    | ~ hBOOL(hAPP(U_3682,bool,hAPP(U_3682,fun(U_3682,bool),ord_less(U_3682),U_3680),U_3679))
    | ~ linorder(U_3682) ),
    inference(clausify,[status(thm)],[f_904_2]) ).

fof(f_905_1,plain,
    ! [X_a] :
      ( ! [U,L,M] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr1471790799AtMost(X_a),L),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),M),U)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),L),U)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),M),U))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),M)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_815_ivl__disj__un_I16_J]) ).

fof(f_905_2,plain,
    ! [U_3686] :
      ( ! [U_3685,U_3684,U_3683] :
          ( hAPP(fun(U_3686,bool),fun(U_3686,bool),hAPP(fun(U_3686,bool),fun(fun(U_3686,bool),fun(U_3686,bool)),semilattice_sup_sup(fun(U_3686,bool)),hAPP(U_3686,fun(U_3686,bool),hAPP(U_3686,fun(U_3686,fun(U_3686,bool)),ord_gr1471790799AtMost(U_3686),U_3684),U_3683)),hAPP(U_3686,fun(U_3686,bool),hAPP(U_3686,fun(U_3686,fun(U_3686,bool)),ord_gr676655987ssThan(U_3686),U_3683),U_3685)) = hAPP(U_3686,fun(U_3686,bool),hAPP(U_3686,fun(U_3686,fun(U_3686,bool)),ord_gr676655987ssThan(U_3686),U_3684),U_3685)
          | ~ hBOOL(hAPP(U_3686,bool,hAPP(U_3686,fun(U_3686,bool),ord_less(U_3686),U_3683),U_3685))
          | ~ hBOOL(hAPP(U_3686,bool,hAPP(U_3686,fun(U_3686,bool),ord_less_eq(U_3686),U_3684),U_3683)) )
      | ~ linorder(U_3686) ),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

cnf(f_905_3,plain,
    ( hAPP(fun(U_3686,bool),fun(U_3686,bool),hAPP(fun(U_3686,bool),fun(fun(U_3686,bool),fun(U_3686,bool)),semilattice_sup_sup(fun(U_3686,bool)),hAPP(U_3686,fun(U_3686,bool),hAPP(U_3686,fun(U_3686,fun(U_3686,bool)),ord_gr1471790799AtMost(U_3686),U_3684),U_3683)),hAPP(U_3686,fun(U_3686,bool),hAPP(U_3686,fun(U_3686,fun(U_3686,bool)),ord_gr676655987ssThan(U_3686),U_3683),U_3685)) = hAPP(U_3686,fun(U_3686,bool),hAPP(U_3686,fun(U_3686,fun(U_3686,bool)),ord_gr676655987ssThan(U_3686),U_3684),U_3685)
    | ~ hBOOL(hAPP(U_3686,bool,hAPP(U_3686,fun(U_3686,bool),ord_less(U_3686),U_3683),U_3685))
    | ~ hBOOL(hAPP(U_3686,bool,hAPP(U_3686,fun(U_3686,bool),ord_less_eq(U_3686),U_3684),U_3683))
    | ~ linorder(U_3686) ),
    inference(clausify,[status(thm)],[f_905_2]) ).

fof(f_906_1,plain,
    ! [X_b,X_a] :
      ( ! [F,G,X_2] : hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),semilattice_sup_sup(fun(X_b,X_a)),F),G),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,G,X_2))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_816_sup__apply]) ).

fof(f_906_2,plain,
    ! [U_3691,U_3690] :
      ( ! [U_3689,U_3688,U_3687] : hAPP(U_3691,U_3690,hAPP(fun(U_3691,U_3690),fun(U_3691,U_3690),hAPP(fun(U_3691,U_3690),fun(fun(U_3691,U_3690),fun(U_3691,U_3690)),semilattice_sup_sup(fun(U_3691,U_3690)),U_3689),U_3688),U_3687) = hAPP(U_3690,U_3690,hAPP(U_3690,fun(U_3690,U_3690),semilattice_sup_sup(U_3690),hAPP(U_3691,U_3690,U_3689,U_3687)),hAPP(U_3691,U_3690,U_3688,U_3687))
      | ~ lattice(U_3690) ),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

cnf(f_906_3,plain,
    ( hAPP(U_3691,U_3690,hAPP(fun(U_3691,U_3690),fun(U_3691,U_3690),hAPP(fun(U_3691,U_3690),fun(fun(U_3691,U_3690),fun(U_3691,U_3690)),semilattice_sup_sup(fun(U_3691,U_3690)),U_3689),U_3688),U_3687) = hAPP(U_3690,U_3690,hAPP(U_3690,fun(U_3690,U_3690),semilattice_sup_sup(U_3690),hAPP(U_3691,U_3690,U_3689,U_3687)),hAPP(U_3691,U_3690,U_3688,U_3687))
    | ~ lattice(U_3690) ),
    inference(clausify,[status(thm)],[f_906_2]) ).

fof(f_907_1,plain,
    ! [X_a,X_b] :
      ( ! [F,G,X_1] : hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),semilattice_sup_sup(fun(X_a,X_b)),F),G),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))
      | ~ lattice(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_817_sup__fun__def]) ).

fof(f_907_2,plain,
    ! [U_3696,U_3695] :
      ( ! [U_3694,U_3693,U_3692] : hAPP(U_3696,U_3695,hAPP(fun(U_3696,U_3695),fun(U_3696,U_3695),hAPP(fun(U_3696,U_3695),fun(fun(U_3696,U_3695),fun(U_3696,U_3695)),semilattice_sup_sup(fun(U_3696,U_3695)),U_3694),U_3693),U_3692) = hAPP(U_3695,U_3695,hAPP(U_3695,fun(U_3695,U_3695),semilattice_sup_sup(U_3695),hAPP(U_3696,U_3695,U_3694,U_3692)),hAPP(U_3696,U_3695,U_3693,U_3692))
      | ~ lattice(U_3695) ),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

cnf(f_907_3,plain,
    ( hAPP(U_3696,U_3695,hAPP(fun(U_3696,U_3695),fun(U_3696,U_3695),hAPP(fun(U_3696,U_3695),fun(fun(U_3696,U_3695),fun(U_3696,U_3695)),semilattice_sup_sup(fun(U_3696,U_3695)),U_3694),U_3693),U_3692) = hAPP(U_3695,U_3695,hAPP(U_3695,fun(U_3695,U_3695),semilattice_sup_sup(U_3695),hAPP(U_3696,U_3695,U_3694,U_3692)),hAPP(U_3696,U_3695,U_3693,U_3692))
    | ~ lattice(U_3695) ),
    inference(clausify,[status(thm)],[f_907_2]) ).

fof(f_908_1,plain,
    ! [X_b,X_a,R_2,S,X_1,Xa] :
      ( ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_2)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S)),X_1),Xa))
        | ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool)),semilattice_sup_sup(fun(product_prod(X_a,X_b),bool)),R_2),S))) )
      & ( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool)),semilattice_sup_sup(fun(product_prod(X_a,X_b),bool)),R_2),S)))
        | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_2)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S)),X_1),Xa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_818_sup__Un__eq2]) ).

fof(f_908_2,plain,
    ! [U_3702,U_3701,U_3700,U_3699,U_3698,U_3697] :
      ( ( hBOOL(hAPP(U_3702,bool,hAPP(U_3701,fun(U_3702,bool),hAPP(fun(U_3701,fun(U_3702,bool)),fun(U_3701,fun(U_3702,bool)),hAPP(fun(U_3701,fun(U_3702,bool)),fun(fun(U_3701,fun(U_3702,bool)),fun(U_3701,fun(U_3702,bool))),semilattice_sup_sup(fun(U_3701,fun(U_3702,bool))),hAPP(fun(product_prod(U_3701,U_3702),bool),fun(U_3701,fun(U_3702,bool)),hAPP(fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3701,fun(U_3702,bool))),combc(U_3701,fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)),hAPP(fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),hAPP(fun(fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),fun(fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)))),combb(fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)),U_3701),combc(U_3702,fun(product_prod(U_3701,U_3702),bool),bool)),hAPP(fun(U_3701,fun(U_3702,product_prod(U_3701,U_3702))),fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),hAPP(fun(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(fun(U_3701,fun(U_3702,product_prod(U_3701,U_3702))),fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)))),combb(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),U_3701),hAPP(fun(product_prod(U_3701,U_3702),fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),combb(product_prod(U_3701,U_3702),fun(fun(product_prod(U_3701,U_3702),bool),bool),U_3702),member(product_prod(U_3701,U_3702)))),product_Pair(U_3701,U_3702)))),U_3700)),hAPP(fun(product_prod(U_3701,U_3702),bool),fun(U_3701,fun(U_3702,bool)),hAPP(fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3701,fun(U_3702,bool))),combc(U_3701,fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)),hAPP(fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),hAPP(fun(fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),fun(fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)))),combb(fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)),U_3701),combc(U_3702,fun(product_prod(U_3701,U_3702),bool),bool)),hAPP(fun(U_3701,fun(U_3702,product_prod(U_3701,U_3702))),fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),hAPP(fun(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(fun(U_3701,fun(U_3702,product_prod(U_3701,U_3702))),fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)))),combb(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),U_3701),hAPP(fun(product_prod(U_3701,U_3702),fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),combb(product_prod(U_3701,U_3702),fun(fun(product_prod(U_3701,U_3702),bool),bool),U_3702),member(product_prod(U_3701,U_3702)))),product_Pair(U_3701,U_3702)))),U_3699)),U_3698),U_3697))
        | ~ hBOOL(hAPP(fun(product_prod(U_3701,U_3702),bool),bool,hAPP(product_prod(U_3701,U_3702),fun(fun(product_prod(U_3701,U_3702),bool),bool),member(product_prod(U_3701,U_3702)),hAPP(U_3702,product_prod(U_3701,U_3702),hAPP(U_3701,fun(U_3702,product_prod(U_3701,U_3702)),product_Pair(U_3701,U_3702),U_3698),U_3697)),hAPP(fun(product_prod(U_3701,U_3702),bool),fun(product_prod(U_3701,U_3702),bool),hAPP(fun(product_prod(U_3701,U_3702),bool),fun(fun(product_prod(U_3701,U_3702),bool),fun(product_prod(U_3701,U_3702),bool)),semilattice_sup_sup(fun(product_prod(U_3701,U_3702),bool)),U_3700),U_3699))) )
      & ( hBOOL(hAPP(fun(product_prod(U_3701,U_3702),bool),bool,hAPP(product_prod(U_3701,U_3702),fun(fun(product_prod(U_3701,U_3702),bool),bool),member(product_prod(U_3701,U_3702)),hAPP(U_3702,product_prod(U_3701,U_3702),hAPP(U_3701,fun(U_3702,product_prod(U_3701,U_3702)),product_Pair(U_3701,U_3702),U_3698),U_3697)),hAPP(fun(product_prod(U_3701,U_3702),bool),fun(product_prod(U_3701,U_3702),bool),hAPP(fun(product_prod(U_3701,U_3702),bool),fun(fun(product_prod(U_3701,U_3702),bool),fun(product_prod(U_3701,U_3702),bool)),semilattice_sup_sup(fun(product_prod(U_3701,U_3702),bool)),U_3700),U_3699)))
        | ~ hBOOL(hAPP(U_3702,bool,hAPP(U_3701,fun(U_3702,bool),hAPP(fun(U_3701,fun(U_3702,bool)),fun(U_3701,fun(U_3702,bool)),hAPP(fun(U_3701,fun(U_3702,bool)),fun(fun(U_3701,fun(U_3702,bool)),fun(U_3701,fun(U_3702,bool))),semilattice_sup_sup(fun(U_3701,fun(U_3702,bool))),hAPP(fun(product_prod(U_3701,U_3702),bool),fun(U_3701,fun(U_3702,bool)),hAPP(fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3701,fun(U_3702,bool))),combc(U_3701,fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)),hAPP(fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),hAPP(fun(fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),fun(fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)))),combb(fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)),U_3701),combc(U_3702,fun(product_prod(U_3701,U_3702),bool),bool)),hAPP(fun(U_3701,fun(U_3702,product_prod(U_3701,U_3702))),fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),hAPP(fun(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(fun(U_3701,fun(U_3702,product_prod(U_3701,U_3702))),fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)))),combb(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),U_3701),hAPP(fun(product_prod(U_3701,U_3702),fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),combb(product_prod(U_3701,U_3702),fun(fun(product_prod(U_3701,U_3702),bool),bool),U_3702),member(product_prod(U_3701,U_3702)))),product_Pair(U_3701,U_3702)))),U_3700)),hAPP(fun(product_prod(U_3701,U_3702),bool),fun(U_3701,fun(U_3702,bool)),hAPP(fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3701,fun(U_3702,bool))),combc(U_3701,fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)),hAPP(fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),hAPP(fun(fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool))),fun(fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(U_3701,fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)))),combb(fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(product_prod(U_3701,U_3702),bool),fun(U_3702,bool)),U_3701),combc(U_3702,fun(product_prod(U_3701,U_3702),bool),bool)),hAPP(fun(U_3701,fun(U_3702,product_prod(U_3701,U_3702))),fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),hAPP(fun(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),fun(fun(U_3701,fun(U_3702,product_prod(U_3701,U_3702))),fun(U_3701,fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)))),combb(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool)),U_3701),hAPP(fun(product_prod(U_3701,U_3702),fun(fun(product_prod(U_3701,U_3702),bool),bool)),fun(fun(U_3702,product_prod(U_3701,U_3702)),fun(U_3702,fun(fun(product_prod(U_3701,U_3702),bool),bool))),combb(product_prod(U_3701,U_3702),fun(fun(product_prod(U_3701,U_3702),bool),bool),U_3702),member(product_prod(U_3701,U_3702)))),product_Pair(U_3701,U_3702)))),U_3699)),U_3698),U_3697)) ) ),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

fof(f_908_3,plain,
    ( ! [U_3714,U_3712,U_3710,U_3708,U_3706,U_3704] :
        ( hBOOL(hAPP(U_3714,bool,hAPP(U_3712,fun(U_3714,bool),hAPP(fun(U_3712,fun(U_3714,bool)),fun(U_3712,fun(U_3714,bool)),hAPP(fun(U_3712,fun(U_3714,bool)),fun(fun(U_3712,fun(U_3714,bool)),fun(U_3712,fun(U_3714,bool))),semilattice_sup_sup(fun(U_3712,fun(U_3714,bool))),hAPP(fun(product_prod(U_3712,U_3714),bool),fun(U_3712,fun(U_3714,bool)),hAPP(fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3712,fun(U_3714,bool))),combc(U_3712,fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)),hAPP(fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),hAPP(fun(fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),fun(fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)))),combb(fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)),U_3712),combc(U_3714,fun(product_prod(U_3712,U_3714),bool),bool)),hAPP(fun(U_3712,fun(U_3714,product_prod(U_3712,U_3714))),fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),hAPP(fun(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(fun(U_3712,fun(U_3714,product_prod(U_3712,U_3714))),fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)))),combb(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),U_3712),hAPP(fun(product_prod(U_3712,U_3714),fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),combb(product_prod(U_3712,U_3714),fun(fun(product_prod(U_3712,U_3714),bool),bool),U_3714),member(product_prod(U_3712,U_3714)))),product_Pair(U_3712,U_3714)))),U_3710)),hAPP(fun(product_prod(U_3712,U_3714),bool),fun(U_3712,fun(U_3714,bool)),hAPP(fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3712,fun(U_3714,bool))),combc(U_3712,fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)),hAPP(fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),hAPP(fun(fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),fun(fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)))),combb(fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)),U_3712),combc(U_3714,fun(product_prod(U_3712,U_3714),bool),bool)),hAPP(fun(U_3712,fun(U_3714,product_prod(U_3712,U_3714))),fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),hAPP(fun(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(fun(U_3712,fun(U_3714,product_prod(U_3712,U_3714))),fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)))),combb(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),U_3712),hAPP(fun(product_prod(U_3712,U_3714),fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),combb(product_prod(U_3712,U_3714),fun(fun(product_prod(U_3712,U_3714),bool),bool),U_3714),member(product_prod(U_3712,U_3714)))),product_Pair(U_3712,U_3714)))),U_3708)),U_3706),U_3704))
        | ~ hBOOL(hAPP(fun(product_prod(U_3712,U_3714),bool),bool,hAPP(product_prod(U_3712,U_3714),fun(fun(product_prod(U_3712,U_3714),bool),bool),member(product_prod(U_3712,U_3714)),hAPP(U_3714,product_prod(U_3712,U_3714),hAPP(U_3712,fun(U_3714,product_prod(U_3712,U_3714)),product_Pair(U_3712,U_3714),U_3706),U_3704)),hAPP(fun(product_prod(U_3712,U_3714),bool),fun(product_prod(U_3712,U_3714),bool),hAPP(fun(product_prod(U_3712,U_3714),bool),fun(fun(product_prod(U_3712,U_3714),bool),fun(product_prod(U_3712,U_3714),bool)),semilattice_sup_sup(fun(product_prod(U_3712,U_3714),bool)),U_3710),U_3708))) )
    & ! [U_3713,U_3711,U_3709,U_3707,U_3705,U_3703] :
        ( hBOOL(hAPP(fun(product_prod(U_3711,U_3713),bool),bool,hAPP(product_prod(U_3711,U_3713),fun(fun(product_prod(U_3711,U_3713),bool),bool),member(product_prod(U_3711,U_3713)),hAPP(U_3713,product_prod(U_3711,U_3713),hAPP(U_3711,fun(U_3713,product_prod(U_3711,U_3713)),product_Pair(U_3711,U_3713),U_3705),U_3703)),hAPP(fun(product_prod(U_3711,U_3713),bool),fun(product_prod(U_3711,U_3713),bool),hAPP(fun(product_prod(U_3711,U_3713),bool),fun(fun(product_prod(U_3711,U_3713),bool),fun(product_prod(U_3711,U_3713),bool)),semilattice_sup_sup(fun(product_prod(U_3711,U_3713),bool)),U_3709),U_3707)))
        | ~ hBOOL(hAPP(U_3713,bool,hAPP(U_3711,fun(U_3713,bool),hAPP(fun(U_3711,fun(U_3713,bool)),fun(U_3711,fun(U_3713,bool)),hAPP(fun(U_3711,fun(U_3713,bool)),fun(fun(U_3711,fun(U_3713,bool)),fun(U_3711,fun(U_3713,bool))),semilattice_sup_sup(fun(U_3711,fun(U_3713,bool))),hAPP(fun(product_prod(U_3711,U_3713),bool),fun(U_3711,fun(U_3713,bool)),hAPP(fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3711,fun(U_3713,bool))),combc(U_3711,fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)),hAPP(fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),hAPP(fun(fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),fun(fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)))),combb(fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)),U_3711),combc(U_3713,fun(product_prod(U_3711,U_3713),bool),bool)),hAPP(fun(U_3711,fun(U_3713,product_prod(U_3711,U_3713))),fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),hAPP(fun(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(fun(U_3711,fun(U_3713,product_prod(U_3711,U_3713))),fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)))),combb(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),U_3711),hAPP(fun(product_prod(U_3711,U_3713),fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),combb(product_prod(U_3711,U_3713),fun(fun(product_prod(U_3711,U_3713),bool),bool),U_3713),member(product_prod(U_3711,U_3713)))),product_Pair(U_3711,U_3713)))),U_3709)),hAPP(fun(product_prod(U_3711,U_3713),bool),fun(U_3711,fun(U_3713,bool)),hAPP(fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3711,fun(U_3713,bool))),combc(U_3711,fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)),hAPP(fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),hAPP(fun(fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),fun(fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)))),combb(fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)),U_3711),combc(U_3713,fun(product_prod(U_3711,U_3713),bool),bool)),hAPP(fun(U_3711,fun(U_3713,product_prod(U_3711,U_3713))),fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),hAPP(fun(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(fun(U_3711,fun(U_3713,product_prod(U_3711,U_3713))),fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)))),combb(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),U_3711),hAPP(fun(product_prod(U_3711,U_3713),fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),combb(product_prod(U_3711,U_3713),fun(fun(product_prod(U_3711,U_3713),bool),bool),U_3713),member(product_prod(U_3711,U_3713)))),product_Pair(U_3711,U_3713)))),U_3707)),U_3705),U_3703)) ) ),
    inference(miniscope,[status(thm)],[f_908_2]) ).

cnf(f_908_4,plain,
    ( hBOOL(hAPP(fun(product_prod(U_3711,U_3713),bool),bool,hAPP(product_prod(U_3711,U_3713),fun(fun(product_prod(U_3711,U_3713),bool),bool),member(product_prod(U_3711,U_3713)),hAPP(U_3713,product_prod(U_3711,U_3713),hAPP(U_3711,fun(U_3713,product_prod(U_3711,U_3713)),product_Pair(U_3711,U_3713),U_3705),U_3703)),hAPP(fun(product_prod(U_3711,U_3713),bool),fun(product_prod(U_3711,U_3713),bool),hAPP(fun(product_prod(U_3711,U_3713),bool),fun(fun(product_prod(U_3711,U_3713),bool),fun(product_prod(U_3711,U_3713),bool)),semilattice_sup_sup(fun(product_prod(U_3711,U_3713),bool)),U_3709),U_3707)))
    | ~ hBOOL(hAPP(U_3713,bool,hAPP(U_3711,fun(U_3713,bool),hAPP(fun(U_3711,fun(U_3713,bool)),fun(U_3711,fun(U_3713,bool)),hAPP(fun(U_3711,fun(U_3713,bool)),fun(fun(U_3711,fun(U_3713,bool)),fun(U_3711,fun(U_3713,bool))),semilattice_sup_sup(fun(U_3711,fun(U_3713,bool))),hAPP(fun(product_prod(U_3711,U_3713),bool),fun(U_3711,fun(U_3713,bool)),hAPP(fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3711,fun(U_3713,bool))),combc(U_3711,fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)),hAPP(fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),hAPP(fun(fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),fun(fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)))),combb(fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)),U_3711),combc(U_3713,fun(product_prod(U_3711,U_3713),bool),bool)),hAPP(fun(U_3711,fun(U_3713,product_prod(U_3711,U_3713))),fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),hAPP(fun(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(fun(U_3711,fun(U_3713,product_prod(U_3711,U_3713))),fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)))),combb(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),U_3711),hAPP(fun(product_prod(U_3711,U_3713),fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),combb(product_prod(U_3711,U_3713),fun(fun(product_prod(U_3711,U_3713),bool),bool),U_3713),member(product_prod(U_3711,U_3713)))),product_Pair(U_3711,U_3713)))),U_3709)),hAPP(fun(product_prod(U_3711,U_3713),bool),fun(U_3711,fun(U_3713,bool)),hAPP(fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3711,fun(U_3713,bool))),combc(U_3711,fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)),hAPP(fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),hAPP(fun(fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool))),fun(fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(U_3711,fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)))),combb(fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(product_prod(U_3711,U_3713),bool),fun(U_3713,bool)),U_3711),combc(U_3713,fun(product_prod(U_3711,U_3713),bool),bool)),hAPP(fun(U_3711,fun(U_3713,product_prod(U_3711,U_3713))),fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),hAPP(fun(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),fun(fun(U_3711,fun(U_3713,product_prod(U_3711,U_3713))),fun(U_3711,fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)))),combb(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool)),U_3711),hAPP(fun(product_prod(U_3711,U_3713),fun(fun(product_prod(U_3711,U_3713),bool),bool)),fun(fun(U_3713,product_prod(U_3711,U_3713)),fun(U_3713,fun(fun(product_prod(U_3711,U_3713),bool),bool))),combb(product_prod(U_3711,U_3713),fun(fun(product_prod(U_3711,U_3713),bool),bool),U_3713),member(product_prod(U_3711,U_3713)))),product_Pair(U_3711,U_3713)))),U_3707)),U_3705),U_3703)) ),
    inference(clausify,[status(thm)],[f_908_3]) ).

cnf(f_908_5,plain,
    ( hBOOL(hAPP(U_3714,bool,hAPP(U_3712,fun(U_3714,bool),hAPP(fun(U_3712,fun(U_3714,bool)),fun(U_3712,fun(U_3714,bool)),hAPP(fun(U_3712,fun(U_3714,bool)),fun(fun(U_3712,fun(U_3714,bool)),fun(U_3712,fun(U_3714,bool))),semilattice_sup_sup(fun(U_3712,fun(U_3714,bool))),hAPP(fun(product_prod(U_3712,U_3714),bool),fun(U_3712,fun(U_3714,bool)),hAPP(fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3712,fun(U_3714,bool))),combc(U_3712,fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)),hAPP(fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),hAPP(fun(fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),fun(fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)))),combb(fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)),U_3712),combc(U_3714,fun(product_prod(U_3712,U_3714),bool),bool)),hAPP(fun(U_3712,fun(U_3714,product_prod(U_3712,U_3714))),fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),hAPP(fun(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(fun(U_3712,fun(U_3714,product_prod(U_3712,U_3714))),fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)))),combb(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),U_3712),hAPP(fun(product_prod(U_3712,U_3714),fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),combb(product_prod(U_3712,U_3714),fun(fun(product_prod(U_3712,U_3714),bool),bool),U_3714),member(product_prod(U_3712,U_3714)))),product_Pair(U_3712,U_3714)))),U_3710)),hAPP(fun(product_prod(U_3712,U_3714),bool),fun(U_3712,fun(U_3714,bool)),hAPP(fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3712,fun(U_3714,bool))),combc(U_3712,fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)),hAPP(fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),hAPP(fun(fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool))),fun(fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(U_3712,fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)))),combb(fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(product_prod(U_3712,U_3714),bool),fun(U_3714,bool)),U_3712),combc(U_3714,fun(product_prod(U_3712,U_3714),bool),bool)),hAPP(fun(U_3712,fun(U_3714,product_prod(U_3712,U_3714))),fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),hAPP(fun(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),fun(fun(U_3712,fun(U_3714,product_prod(U_3712,U_3714))),fun(U_3712,fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)))),combb(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool)),U_3712),hAPP(fun(product_prod(U_3712,U_3714),fun(fun(product_prod(U_3712,U_3714),bool),bool)),fun(fun(U_3714,product_prod(U_3712,U_3714)),fun(U_3714,fun(fun(product_prod(U_3712,U_3714),bool),bool))),combb(product_prod(U_3712,U_3714),fun(fun(product_prod(U_3712,U_3714),bool),bool),U_3714),member(product_prod(U_3712,U_3714)))),product_Pair(U_3712,U_3714)))),U_3708)),U_3706),U_3704))
    | ~ hBOOL(hAPP(fun(product_prod(U_3712,U_3714),bool),bool,hAPP(product_prod(U_3712,U_3714),fun(fun(product_prod(U_3712,U_3714),bool),bool),member(product_prod(U_3712,U_3714)),hAPP(U_3714,product_prod(U_3712,U_3714),hAPP(U_3712,fun(U_3714,product_prod(U_3712,U_3714)),product_Pair(U_3712,U_3714),U_3706),U_3704)),hAPP(fun(product_prod(U_3712,U_3714),bool),fun(product_prod(U_3712,U_3714),bool),hAPP(fun(product_prod(U_3712,U_3714),bool),fun(fun(product_prod(U_3712,U_3714),bool),fun(product_prod(U_3712,U_3714),bool)),semilattice_sup_sup(fun(product_prod(U_3712,U_3714),bool)),U_3710),U_3708))) ),
    inference(clausify,[status(thm)],[f_908_3]) ).

fof(f_909_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),A_2) = ti(X_a,A_2)
      | ~ ab_sem1668676832m_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_819_times_Oidem]) ).

fof(f_909_2,plain,
    ! [U_3716] :
      ( ! [U_3715] : hAPP(U_3716,U_3716,hAPP(U_3716,fun(U_3716,U_3716),times_times(U_3716),U_3715),U_3715) = ti(U_3716,U_3715)
      | ~ ab_sem1668676832m_mult(U_3716) ),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

cnf(f_909_3,plain,
    ( hAPP(U_3716,U_3716,hAPP(U_3716,fun(U_3716,U_3716),times_times(U_3716),U_3715),U_3715) = ti(U_3716,U_3715)
    | ~ ab_sem1668676832m_mult(U_3716) ),
    inference(clausify,[status(thm)],[f_909_2]) ).

fof(f_910_1,plain,
    ! [X_a] :
      ( ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X) = ti(X_a,X)
      | ~ ab_sem1668676832m_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_820_mult__idem]) ).

fof(f_910_2,plain,
    ! [U_3718] :
      ( ! [U_3717] : hAPP(U_3718,U_3718,hAPP(U_3718,fun(U_3718,U_3718),times_times(U_3718),U_3717),U_3717) = ti(U_3718,U_3717)
      | ~ ab_sem1668676832m_mult(U_3718) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

cnf(f_910_3,plain,
    ( hAPP(U_3718,U_3718,hAPP(U_3718,fun(U_3718,U_3718),times_times(U_3718),U_3717),U_3717) = ti(U_3718,U_3717)
    | ~ ab_sem1668676832m_mult(U_3718) ),
    inference(clausify,[status(thm)],[f_910_2]) ).

fof(f_911_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)
      | ~ ab_sem1668676832m_mult(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_821_mult__left__idem]) ).

fof(f_911_2,plain,
    ! [U_3721] :
      ( ! [U_3720,U_3719] : hAPP(U_3721,U_3721,hAPP(U_3721,fun(U_3721,U_3721),times_times(U_3721),U_3720),hAPP(U_3721,U_3721,hAPP(U_3721,fun(U_3721,U_3721),times_times(U_3721),U_3720),U_3719)) = hAPP(U_3721,U_3721,hAPP(U_3721,fun(U_3721,U_3721),times_times(U_3721),U_3720),U_3719)
      | ~ ab_sem1668676832m_mult(U_3721) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

cnf(f_911_3,plain,
    ( hAPP(U_3721,U_3721,hAPP(U_3721,fun(U_3721,U_3721),times_times(U_3721),U_3720),hAPP(U_3721,U_3721,hAPP(U_3721,fun(U_3721,U_3721),times_times(U_3721),U_3720),U_3719)) = hAPP(U_3721,U_3721,hAPP(U_3721,fun(U_3721,U_3721),times_times(U_3721),U_3720),U_3719)
    | ~ ab_sem1668676832m_mult(U_3721) ),
    inference(clausify,[status(thm)],[f_911_2]) ).

fof(f_912_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),A_2) = ti(X_a,A_2)
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_822_sup_Oidem]) ).

fof(f_912_2,plain,
    ! [U_3723] :
      ( ! [U_3722] : hAPP(U_3723,U_3723,hAPP(U_3723,fun(U_3723,U_3723),semilattice_sup_sup(U_3723),U_3722),U_3722) = ti(U_3723,U_3722)
      | ~ semilattice_sup(U_3723) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

cnf(f_912_3,plain,
    ( hAPP(U_3723,U_3723,hAPP(U_3723,fun(U_3723,U_3723),semilattice_sup_sup(U_3723),U_3722),U_3722) = ti(U_3723,U_3722)
    | ~ semilattice_sup(U_3723) ),
    inference(clausify,[status(thm)],[f_912_2]) ).

fof(f_913_1,plain,
    ! [X_a] :
      ( ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),X) = ti(X_a,X)
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_823_sup__idem]) ).

fof(f_913_2,plain,
    ! [U_3725] :
      ( ! [U_3724] : hAPP(U_3725,U_3725,hAPP(U_3725,fun(U_3725,U_3725),semilattice_sup_sup(U_3725),U_3724),U_3724) = ti(U_3725,U_3724)
      | ~ semilattice_sup(U_3725) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

cnf(f_913_3,plain,
    ( hAPP(U_3725,U_3725,hAPP(U_3725,fun(U_3725,U_3725),semilattice_sup_sup(U_3725),U_3724),U_3724) = ti(U_3725,U_3724)
    | ~ semilattice_sup(U_3725) ),
    inference(clausify,[status(thm)],[f_913_2]) ).

fof(f_914_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),A_2)
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_824_sup_Ocommute]) ).

fof(f_914_2,plain,
    ! [U_3728] :
      ( ! [U_3727,U_3726] : hAPP(U_3728,U_3728,hAPP(U_3728,fun(U_3728,U_3728),semilattice_sup_sup(U_3728),U_3727),U_3726) = hAPP(U_3728,U_3728,hAPP(U_3728,fun(U_3728,U_3728),semilattice_sup_sup(U_3728),U_3726),U_3727)
      | ~ semilattice_sup(U_3728) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

cnf(f_914_3,plain,
    ( hAPP(U_3728,U_3728,hAPP(U_3728,fun(U_3728,U_3728),semilattice_sup_sup(U_3728),U_3727),U_3726) = hAPP(U_3728,U_3728,hAPP(U_3728,fun(U_3728,U_3728),semilattice_sup_sup(U_3728),U_3726),U_3727)
    | ~ semilattice_sup(U_3728) ),
    inference(clausify,[status(thm)],[f_914_2]) ).

fof(f_915_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X)
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_825_inf__sup__aci_I5_J]) ).

fof(f_915_2,plain,
    ! [U_3731] :
      ( ! [U_3730,U_3729] : hAPP(U_3731,U_3731,hAPP(U_3731,fun(U_3731,U_3731),semilattice_sup_sup(U_3731),U_3730),U_3729) = hAPP(U_3731,U_3731,hAPP(U_3731,fun(U_3731,U_3731),semilattice_sup_sup(U_3731),U_3729),U_3730)
      | ~ lattice(U_3731) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

cnf(f_915_3,plain,
    ( hAPP(U_3731,U_3731,hAPP(U_3731,fun(U_3731,U_3731),semilattice_sup_sup(U_3731),U_3730),U_3729) = hAPP(U_3731,U_3731,hAPP(U_3731,fun(U_3731,U_3731),semilattice_sup_sup(U_3731),U_3729),U_3730)
    | ~ lattice(U_3731) ),
    inference(clausify,[status(thm)],[f_915_2]) ).

fof(f_916_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X)
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_826_sup__commute]) ).

fof(f_916_2,plain,
    ! [U_3734] :
      ( ! [U_3733,U_3732] : hAPP(U_3734,U_3734,hAPP(U_3734,fun(U_3734,U_3734),semilattice_sup_sup(U_3734),U_3733),U_3732) = hAPP(U_3734,U_3734,hAPP(U_3734,fun(U_3734,U_3734),semilattice_sup_sup(U_3734),U_3732),U_3733)
      | ~ semilattice_sup(U_3734) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

cnf(f_916_3,plain,
    ( hAPP(U_3734,U_3734,hAPP(U_3734,fun(U_3734,U_3734),semilattice_sup_sup(U_3734),U_3733),U_3732) = hAPP(U_3734,U_3734,hAPP(U_3734,fun(U_3734,U_3734),semilattice_sup_sup(U_3734),U_3732),U_3733)
    | ~ semilattice_sup(U_3734) ),
    inference(clausify,[status(thm)],[f_916_2]) ).

fof(f_917_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_827_sup_Oleft__idem]) ).

fof(f_917_2,plain,
    ! [U_3737] :
      ( ! [U_3736,U_3735] : hAPP(U_3737,U_3737,hAPP(U_3737,fun(U_3737,U_3737),semilattice_sup_sup(U_3737),U_3736),hAPP(U_3737,U_3737,hAPP(U_3737,fun(U_3737,U_3737),semilattice_sup_sup(U_3737),U_3736),U_3735)) = hAPP(U_3737,U_3737,hAPP(U_3737,fun(U_3737,U_3737),semilattice_sup_sup(U_3737),U_3736),U_3735)
      | ~ semilattice_sup(U_3737) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

cnf(f_917_3,plain,
    ( hAPP(U_3737,U_3737,hAPP(U_3737,fun(U_3737,U_3737),semilattice_sup_sup(U_3737),U_3736),hAPP(U_3737,U_3737,hAPP(U_3737,fun(U_3737,U_3737),semilattice_sup_sup(U_3737),U_3736),U_3735)) = hAPP(U_3737,U_3737,hAPP(U_3737,fun(U_3737,U_3737),semilattice_sup_sup(U_3737),U_3736),U_3735)
    | ~ semilattice_sup(U_3737) ),
    inference(clausify,[status(thm)],[f_917_2]) ).

fof(f_918_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_828_inf__sup__aci_I8_J]) ).

fof(f_918_2,plain,
    ! [U_3740] :
      ( ! [U_3739,U_3738] : hAPP(U_3740,U_3740,hAPP(U_3740,fun(U_3740,U_3740),semilattice_sup_sup(U_3740),U_3739),hAPP(U_3740,U_3740,hAPP(U_3740,fun(U_3740,U_3740),semilattice_sup_sup(U_3740),U_3739),U_3738)) = hAPP(U_3740,U_3740,hAPP(U_3740,fun(U_3740,U_3740),semilattice_sup_sup(U_3740),U_3739),U_3738)
      | ~ lattice(U_3740) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

cnf(f_918_3,plain,
    ( hAPP(U_3740,U_3740,hAPP(U_3740,fun(U_3740,U_3740),semilattice_sup_sup(U_3740),U_3739),hAPP(U_3740,U_3740,hAPP(U_3740,fun(U_3740,U_3740),semilattice_sup_sup(U_3740),U_3739),U_3738)) = hAPP(U_3740,U_3740,hAPP(U_3740,fun(U_3740,U_3740),semilattice_sup_sup(U_3740),U_3739),U_3738)
    | ~ lattice(U_3740) ),
    inference(clausify,[status(thm)],[f_918_2]) ).

fof(f_919_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_829_sup__left__idem]) ).

fof(f_919_2,plain,
    ! [U_3743] :
      ( ! [U_3742,U_3741] : hAPP(U_3743,U_3743,hAPP(U_3743,fun(U_3743,U_3743),semilattice_sup_sup(U_3743),U_3742),hAPP(U_3743,U_3743,hAPP(U_3743,fun(U_3743,U_3743),semilattice_sup_sup(U_3743),U_3742),U_3741)) = hAPP(U_3743,U_3743,hAPP(U_3743,fun(U_3743,U_3743),semilattice_sup_sup(U_3743),U_3742),U_3741)
      | ~ semilattice_sup(U_3743) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

cnf(f_919_3,plain,
    ( hAPP(U_3743,U_3743,hAPP(U_3743,fun(U_3743,U_3743),semilattice_sup_sup(U_3743),U_3742),hAPP(U_3743,U_3743,hAPP(U_3743,fun(U_3743,U_3743),semilattice_sup_sup(U_3743),U_3742),U_3741)) = hAPP(U_3743,U_3743,hAPP(U_3743,fun(U_3743,U_3743),semilattice_sup_sup(U_3743),U_3742),U_3741)
    | ~ semilattice_sup(U_3743) ),
    inference(clausify,[status(thm)],[f_919_2]) ).

fof(f_920_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),C_1))
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_830_sup_Oleft__commute]) ).

fof(f_920_2,plain,
    ! [U_3747] :
      ( ! [U_3746,U_3745,U_3744] : hAPP(U_3747,U_3747,hAPP(U_3747,fun(U_3747,U_3747),semilattice_sup_sup(U_3747),U_3746),hAPP(U_3747,U_3747,hAPP(U_3747,fun(U_3747,U_3747),semilattice_sup_sup(U_3747),U_3745),U_3744)) = hAPP(U_3747,U_3747,hAPP(U_3747,fun(U_3747,U_3747),semilattice_sup_sup(U_3747),U_3745),hAPP(U_3747,U_3747,hAPP(U_3747,fun(U_3747,U_3747),semilattice_sup_sup(U_3747),U_3746),U_3744))
      | ~ semilattice_sup(U_3747) ),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

cnf(f_920_3,plain,
    ( hAPP(U_3747,U_3747,hAPP(U_3747,fun(U_3747,U_3747),semilattice_sup_sup(U_3747),U_3746),hAPP(U_3747,U_3747,hAPP(U_3747,fun(U_3747,U_3747),semilattice_sup_sup(U_3747),U_3745),U_3744)) = hAPP(U_3747,U_3747,hAPP(U_3747,fun(U_3747,U_3747),semilattice_sup_sup(U_3747),U_3745),hAPP(U_3747,U_3747,hAPP(U_3747,fun(U_3747,U_3747),semilattice_sup_sup(U_3747),U_3746),U_3744))
    | ~ semilattice_sup(U_3747) ),
    inference(clausify,[status(thm)],[f_920_2]) ).

fof(f_921_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_831_inf__sup__aci_I7_J]) ).

fof(f_921_2,plain,
    ! [U_3751] :
      ( ! [U_3750,U_3749,U_3748] : hAPP(U_3751,U_3751,hAPP(U_3751,fun(U_3751,U_3751),semilattice_sup_sup(U_3751),U_3750),hAPP(U_3751,U_3751,hAPP(U_3751,fun(U_3751,U_3751),semilattice_sup_sup(U_3751),U_3749),U_3748)) = hAPP(U_3751,U_3751,hAPP(U_3751,fun(U_3751,U_3751),semilattice_sup_sup(U_3751),U_3749),hAPP(U_3751,U_3751,hAPP(U_3751,fun(U_3751,U_3751),semilattice_sup_sup(U_3751),U_3750),U_3748))
      | ~ lattice(U_3751) ),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

cnf(f_921_3,plain,
    ( hAPP(U_3751,U_3751,hAPP(U_3751,fun(U_3751,U_3751),semilattice_sup_sup(U_3751),U_3750),hAPP(U_3751,U_3751,hAPP(U_3751,fun(U_3751,U_3751),semilattice_sup_sup(U_3751),U_3749),U_3748)) = hAPP(U_3751,U_3751,hAPP(U_3751,fun(U_3751,U_3751),semilattice_sup_sup(U_3751),U_3749),hAPP(U_3751,U_3751,hAPP(U_3751,fun(U_3751,U_3751),semilattice_sup_sup(U_3751),U_3750),U_3748))
    | ~ lattice(U_3751) ),
    inference(clausify,[status(thm)],[f_921_2]) ).

fof(f_922_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z))
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_832_sup__left__commute]) ).

fof(f_922_2,plain,
    ! [U_3755] :
      ( ! [U_3754,U_3753,U_3752] : hAPP(U_3755,U_3755,hAPP(U_3755,fun(U_3755,U_3755),semilattice_sup_sup(U_3755),U_3754),hAPP(U_3755,U_3755,hAPP(U_3755,fun(U_3755,U_3755),semilattice_sup_sup(U_3755),U_3753),U_3752)) = hAPP(U_3755,U_3755,hAPP(U_3755,fun(U_3755,U_3755),semilattice_sup_sup(U_3755),U_3753),hAPP(U_3755,U_3755,hAPP(U_3755,fun(U_3755,U_3755),semilattice_sup_sup(U_3755),U_3754),U_3752))
      | ~ semilattice_sup(U_3755) ),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

cnf(f_922_3,plain,
    ( hAPP(U_3755,U_3755,hAPP(U_3755,fun(U_3755,U_3755),semilattice_sup_sup(U_3755),U_3754),hAPP(U_3755,U_3755,hAPP(U_3755,fun(U_3755,U_3755),semilattice_sup_sup(U_3755),U_3753),U_3752)) = hAPP(U_3755,U_3755,hAPP(U_3755,fun(U_3755,U_3755),semilattice_sup_sup(U_3755),U_3753),hAPP(U_3755,U_3755,hAPP(U_3755,fun(U_3755,U_3755),semilattice_sup_sup(U_3755),U_3754),U_3752))
    | ~ semilattice_sup(U_3755) ),
    inference(clausify,[status(thm)],[f_922_2]) ).

fof(f_923_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_1),C_1))
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_833_sup_Oassoc]) ).

fof(f_923_2,plain,
    ! [U_3759] :
      ( ! [U_3758,U_3757,U_3756] : hAPP(U_3759,U_3759,hAPP(U_3759,fun(U_3759,U_3759),semilattice_sup_sup(U_3759),hAPP(U_3759,U_3759,hAPP(U_3759,fun(U_3759,U_3759),semilattice_sup_sup(U_3759),U_3758),U_3757)),U_3756) = hAPP(U_3759,U_3759,hAPP(U_3759,fun(U_3759,U_3759),semilattice_sup_sup(U_3759),U_3758),hAPP(U_3759,U_3759,hAPP(U_3759,fun(U_3759,U_3759),semilattice_sup_sup(U_3759),U_3757),U_3756))
      | ~ semilattice_sup(U_3759) ),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

cnf(f_923_3,plain,
    ( hAPP(U_3759,U_3759,hAPP(U_3759,fun(U_3759,U_3759),semilattice_sup_sup(U_3759),hAPP(U_3759,U_3759,hAPP(U_3759,fun(U_3759,U_3759),semilattice_sup_sup(U_3759),U_3758),U_3757)),U_3756) = hAPP(U_3759,U_3759,hAPP(U_3759,fun(U_3759,U_3759),semilattice_sup_sup(U_3759),U_3758),hAPP(U_3759,U_3759,hAPP(U_3759,fun(U_3759,U_3759),semilattice_sup_sup(U_3759),U_3757),U_3756))
    | ~ semilattice_sup(U_3759) ),
    inference(clausify,[status(thm)],[f_923_2]) ).

fof(f_924_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_834_inf__sup__aci_I6_J]) ).

fof(f_924_2,plain,
    ! [U_3763] :
      ( ! [U_3762,U_3761,U_3760] : hAPP(U_3763,U_3763,hAPP(U_3763,fun(U_3763,U_3763),semilattice_sup_sup(U_3763),hAPP(U_3763,U_3763,hAPP(U_3763,fun(U_3763,U_3763),semilattice_sup_sup(U_3763),U_3762),U_3761)),U_3760) = hAPP(U_3763,U_3763,hAPP(U_3763,fun(U_3763,U_3763),semilattice_sup_sup(U_3763),U_3762),hAPP(U_3763,U_3763,hAPP(U_3763,fun(U_3763,U_3763),semilattice_sup_sup(U_3763),U_3761),U_3760))
      | ~ lattice(U_3763) ),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

cnf(f_924_3,plain,
    ( hAPP(U_3763,U_3763,hAPP(U_3763,fun(U_3763,U_3763),semilattice_sup_sup(U_3763),hAPP(U_3763,U_3763,hAPP(U_3763,fun(U_3763,U_3763),semilattice_sup_sup(U_3763),U_3762),U_3761)),U_3760) = hAPP(U_3763,U_3763,hAPP(U_3763,fun(U_3763,U_3763),semilattice_sup_sup(U_3763),U_3762),hAPP(U_3763,U_3763,hAPP(U_3763,fun(U_3763,U_3763),semilattice_sup_sup(U_3763),U_3761),U_3760))
    | ~ lattice(U_3763) ),
    inference(clausify,[status(thm)],[f_924_2]) ).

fof(f_925_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_835_sup__assoc]) ).

fof(f_925_2,plain,
    ! [U_3767] :
      ( ! [U_3766,U_3765,U_3764] : hAPP(U_3767,U_3767,hAPP(U_3767,fun(U_3767,U_3767),semilattice_sup_sup(U_3767),hAPP(U_3767,U_3767,hAPP(U_3767,fun(U_3767,U_3767),semilattice_sup_sup(U_3767),U_3766),U_3765)),U_3764) = hAPP(U_3767,U_3767,hAPP(U_3767,fun(U_3767,U_3767),semilattice_sup_sup(U_3767),U_3766),hAPP(U_3767,U_3767,hAPP(U_3767,fun(U_3767,U_3767),semilattice_sup_sup(U_3767),U_3765),U_3764))
      | ~ semilattice_sup(U_3767) ),
    inference(variable_rename,[status(thm)],[f_925_1]) ).

cnf(f_925_3,plain,
    ( hAPP(U_3767,U_3767,hAPP(U_3767,fun(U_3767,U_3767),semilattice_sup_sup(U_3767),hAPP(U_3767,U_3767,hAPP(U_3767,fun(U_3767,U_3767),semilattice_sup_sup(U_3767),U_3766),U_3765)),U_3764) = hAPP(U_3767,U_3767,hAPP(U_3767,fun(U_3767,U_3767),semilattice_sup_sup(U_3767),U_3766),hAPP(U_3767,U_3767,hAPP(U_3767,fun(U_3767,U_3767),semilattice_sup_sup(U_3767),U_3765),U_3764))
    | ~ semilattice_sup(U_3767) ),
    inference(clausify,[status(thm)],[f_925_2]) ).

fof(f_926_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_836_inf__sup__ord_I3_J]) ).

fof(f_926_2,plain,
    ! [U_3770] :
      ( ! [U_3769,U_3768] : hBOOL(hAPP(U_3770,bool,hAPP(U_3770,fun(U_3770,bool),ord_less_eq(U_3770),U_3769),hAPP(U_3770,U_3770,hAPP(U_3770,fun(U_3770,U_3770),semilattice_sup_sup(U_3770),U_3769),U_3768)))
      | ~ lattice(U_3770) ),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

cnf(f_926_3,plain,
    ( hBOOL(hAPP(U_3770,bool,hAPP(U_3770,fun(U_3770,bool),ord_less_eq(U_3770),U_3769),hAPP(U_3770,U_3770,hAPP(U_3770,fun(U_3770,U_3770),semilattice_sup_sup(U_3770),U_3769),U_3768)))
    | ~ lattice(U_3770) ),
    inference(clausify,[status(thm)],[f_926_2]) ).

fof(f_927_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_837_sup__ge1]) ).

fof(f_927_2,plain,
    ! [U_3773] :
      ( ! [U_3772,U_3771] : hBOOL(hAPP(U_3773,bool,hAPP(U_3773,fun(U_3773,bool),ord_less_eq(U_3773),U_3772),hAPP(U_3773,U_3773,hAPP(U_3773,fun(U_3773,U_3773),semilattice_sup_sup(U_3773),U_3772),U_3771)))
      | ~ semilattice_sup(U_3773) ),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

cnf(f_927_3,plain,
    ( hBOOL(hAPP(U_3773,bool,hAPP(U_3773,fun(U_3773,bool),ord_less_eq(U_3773),U_3772),hAPP(U_3773,U_3773,hAPP(U_3773,fun(U_3773,U_3773),semilattice_sup_sup(U_3773),U_3772),U_3771)))
    | ~ semilattice_sup(U_3773) ),
    inference(clausify,[status(thm)],[f_927_2]) ).

fof(f_928_1,plain,
    ! [X_a] :
      ( ! [Y,X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_838_inf__sup__ord_I4_J]) ).

fof(f_928_2,plain,
    ! [U_3776] :
      ( ! [U_3775,U_3774] : hBOOL(hAPP(U_3776,bool,hAPP(U_3776,fun(U_3776,bool),ord_less_eq(U_3776),U_3775),hAPP(U_3776,U_3776,hAPP(U_3776,fun(U_3776,U_3776),semilattice_sup_sup(U_3776),U_3774),U_3775)))
      | ~ lattice(U_3776) ),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

cnf(f_928_3,plain,
    ( hBOOL(hAPP(U_3776,bool,hAPP(U_3776,fun(U_3776,bool),ord_less_eq(U_3776),U_3775),hAPP(U_3776,U_3776,hAPP(U_3776,fun(U_3776,U_3776),semilattice_sup_sup(U_3776),U_3774),U_3775)))
    | ~ lattice(U_3776) ),
    inference(clausify,[status(thm)],[f_928_2]) ).

fof(f_929_1,plain,
    ! [X_a] :
      ( ! [Y,X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_839_sup__ge2]) ).

fof(f_929_2,plain,
    ! [U_3779] :
      ( ! [U_3778,U_3777] : hBOOL(hAPP(U_3779,bool,hAPP(U_3779,fun(U_3779,bool),ord_less_eq(U_3779),U_3778),hAPP(U_3779,U_3779,hAPP(U_3779,fun(U_3779,U_3779),semilattice_sup_sup(U_3779),U_3777),U_3778)))
      | ~ semilattice_sup(U_3779) ),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

cnf(f_929_3,plain,
    ( hBOOL(hAPP(U_3779,bool,hAPP(U_3779,fun(U_3779,bool),ord_less_eq(U_3779),U_3778),hAPP(U_3779,U_3779,hAPP(U_3779,fun(U_3779,U_3779),semilattice_sup_sup(U_3779),U_3777),U_3778)))
    | ~ semilattice_sup(U_3779) ),
    inference(clausify,[status(thm)],[f_929_2]) ).

fof(f_930_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
            | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_1) != ti(X_a,Y_1) )
          & ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_1) = ti(X_a,Y_1)
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) ) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_840_le__iff__sup]) ).

fof(f_930_2,plain,
    ! [U_3782] :
      ( ! [U_3781,U_3780] :
          ( ( hBOOL(hAPP(U_3782,bool,hAPP(U_3782,fun(U_3782,bool),ord_less_eq(U_3782),U_3781),U_3780))
            | hAPP(U_3782,U_3782,hAPP(U_3782,fun(U_3782,U_3782),semilattice_sup_sup(U_3782),U_3781),U_3780) != ti(U_3782,U_3780) )
          & ( hAPP(U_3782,U_3782,hAPP(U_3782,fun(U_3782,U_3782),semilattice_sup_sup(U_3782),U_3781),U_3780) = ti(U_3782,U_3780)
            | ~ hBOOL(hAPP(U_3782,bool,hAPP(U_3782,fun(U_3782,bool),ord_less_eq(U_3782),U_3781),U_3780)) ) )
      | ~ semilattice_sup(U_3782) ),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

fof(f_930_3,plain,
    ! [U_3782] :
      ( ( ! [U_3786,U_3784] :
            ( hBOOL(hAPP(U_3782,bool,hAPP(U_3782,fun(U_3782,bool),ord_less_eq(U_3782),U_3786),U_3784))
            | hAPP(U_3782,U_3782,hAPP(U_3782,fun(U_3782,U_3782),semilattice_sup_sup(U_3782),U_3786),U_3784) != ti(U_3782,U_3784) )
        & ! [U_3785,U_3783] :
            ( hAPP(U_3782,U_3782,hAPP(U_3782,fun(U_3782,U_3782),semilattice_sup_sup(U_3782),U_3785),U_3783) = ti(U_3782,U_3783)
            | ~ hBOOL(hAPP(U_3782,bool,hAPP(U_3782,fun(U_3782,bool),ord_less_eq(U_3782),U_3785),U_3783)) ) )
      | ~ semilattice_sup(U_3782) ),
    inference(miniscope,[status(thm)],[f_930_2]) ).

cnf(f_930_4,plain,
    ( hAPP(U_3782,U_3782,hAPP(U_3782,fun(U_3782,U_3782),semilattice_sup_sup(U_3782),U_3785),U_3783) = ti(U_3782,U_3783)
    | ~ hBOOL(hAPP(U_3782,bool,hAPP(U_3782,fun(U_3782,bool),ord_less_eq(U_3782),U_3785),U_3783))
    | ~ semilattice_sup(U_3782) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

cnf(f_930_5,plain,
    ( hBOOL(hAPP(U_3782,bool,hAPP(U_3782,fun(U_3782,bool),ord_less_eq(U_3782),U_3786),U_3784))
    | hAPP(U_3782,U_3782,hAPP(U_3782,fun(U_3782,U_3782),semilattice_sup_sup(U_3782),U_3786),U_3784) != ti(U_3782,U_3784)
    | ~ semilattice_sup(U_3782) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

fof(f_931_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1,Z_1] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_1)),Z_1))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z_1))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z_1))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_1)),Z_1)) ) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_841_le__sup__iff]) ).

fof(f_931_2,plain,
    ! [U_3790] :
      ( ! [U_3789,U_3788,U_3787] :
          ( ( hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),hAPP(U_3790,U_3790,hAPP(U_3790,fun(U_3790,U_3790),semilattice_sup_sup(U_3790),U_3789),U_3788)),U_3787))
            | ~ hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3788),U_3787))
            | ~ hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3789),U_3787)) )
          & ( ( hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3788),U_3787))
              & hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3789),U_3787)) )
            | ~ hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),hAPP(U_3790,U_3790,hAPP(U_3790,fun(U_3790,U_3790),semilattice_sup_sup(U_3790),U_3789),U_3788)),U_3787)) ) )
      | ~ semilattice_sup(U_3790) ),
    inference(variable_rename,[status(thm)],[f_931_1]) ).

fof(f_931_3,plain,
    ! [U_3790] :
      ( ( ! [U_3796,U_3794,U_3792] :
            ( hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),hAPP(U_3790,U_3790,hAPP(U_3790,fun(U_3790,U_3790),semilattice_sup_sup(U_3790),U_3796),U_3794)),U_3792))
            | ~ hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3794),U_3792))
            | ~ hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3796),U_3792)) )
        & ! [U_3795,U_3793,U_3791] :
            ( ( hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3793),U_3791))
              & hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3795),U_3791)) )
            | ~ hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),hAPP(U_3790,U_3790,hAPP(U_3790,fun(U_3790,U_3790),semilattice_sup_sup(U_3790),U_3795),U_3793)),U_3791)) ) )
      | ~ semilattice_sup(U_3790) ),
    inference(miniscope,[status(thm)],[f_931_2]) ).

cnf(f_931_4,plain,
    ( hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3795),U_3791))
    | ~ hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),hAPP(U_3790,U_3790,hAPP(U_3790,fun(U_3790,U_3790),semilattice_sup_sup(U_3790),U_3795),U_3793)),U_3791))
    | ~ semilattice_sup(U_3790) ),
    inference(clausify,[status(thm)],[f_931_3]) ).

cnf(f_931_5,plain,
    ( hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3793),U_3791))
    | ~ hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),hAPP(U_3790,U_3790,hAPP(U_3790,fun(U_3790,U_3790),semilattice_sup_sup(U_3790),U_3795),U_3793)),U_3791))
    | ~ semilattice_sup(U_3790) ),
    inference(clausify,[status(thm)],[f_931_3]) ).

cnf(f_931_6,plain,
    ( hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),hAPP(U_3790,U_3790,hAPP(U_3790,fun(U_3790,U_3790),semilattice_sup_sup(U_3790),U_3796),U_3794)),U_3792))
    | ~ hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3794),U_3792))
    | ~ hBOOL(hAPP(U_3790,bool,hAPP(U_3790,fun(U_3790,bool),ord_less_eq(U_3790),U_3796),U_3792))
    | ~ semilattice_sup(U_3790) ),
    inference(clausify,[status(thm)],[f_931_3]) ).

fof(f_932_1,plain,
    ! [X_a] :
      ( ! [B_1,X,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2)) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_842_le__supI1]) ).

fof(f_932_2,plain,
    ! [U_3800] :
      ( ! [U_3799,U_3798,U_3797] :
          ( hBOOL(hAPP(U_3800,bool,hAPP(U_3800,fun(U_3800,bool),ord_less_eq(U_3800),U_3798),hAPP(U_3800,U_3800,hAPP(U_3800,fun(U_3800,U_3800),semilattice_sup_sup(U_3800),U_3797),U_3799)))
          | ~ hBOOL(hAPP(U_3800,bool,hAPP(U_3800,fun(U_3800,bool),ord_less_eq(U_3800),U_3798),U_3797)) )
      | ~ semilattice_sup(U_3800) ),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

cnf(f_932_3,plain,
    ( hBOOL(hAPP(U_3800,bool,hAPP(U_3800,fun(U_3800,bool),ord_less_eq(U_3800),U_3798),hAPP(U_3800,U_3800,hAPP(U_3800,fun(U_3800,U_3800),semilattice_sup_sup(U_3800),U_3797),U_3799)))
    | ~ hBOOL(hAPP(U_3800,bool,hAPP(U_3800,fun(U_3800,bool),ord_less_eq(U_3800),U_3798),U_3797))
    | ~ semilattice_sup(U_3800) ),
    inference(clausify,[status(thm)],[f_932_2]) ).

fof(f_933_1,plain,
    ! [X_a] :
      ( ! [A_2,X,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_1)) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_843_le__supI2]) ).

fof(f_933_2,plain,
    ! [U_3804] :
      ( ! [U_3803,U_3802,U_3801] :
          ( hBOOL(hAPP(U_3804,bool,hAPP(U_3804,fun(U_3804,bool),ord_less_eq(U_3804),U_3802),hAPP(U_3804,U_3804,hAPP(U_3804,fun(U_3804,U_3804),semilattice_sup_sup(U_3804),U_3803),U_3801)))
          | ~ hBOOL(hAPP(U_3804,bool,hAPP(U_3804,fun(U_3804,bool),ord_less_eq(U_3804),U_3802),U_3801)) )
      | ~ semilattice_sup(U_3804) ),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

cnf(f_933_3,plain,
    ( hBOOL(hAPP(U_3804,bool,hAPP(U_3804,fun(U_3804,bool),ord_less_eq(U_3804),U_3802),hAPP(U_3804,U_3804,hAPP(U_3804,fun(U_3804,U_3804),semilattice_sup_sup(U_3804),U_3803),U_3801)))
    | ~ hBOOL(hAPP(U_3804,bool,hAPP(U_3804,fun(U_3804,bool),ord_less_eq(U_3804),U_3802),U_3801))
    | ~ semilattice_sup(U_3804) ),
    inference(clausify,[status(thm)],[f_933_2]) ).

fof(f_934_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = ti(X_a,Y)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_844_sup__absorb2]) ).

fof(f_934_2,plain,
    ! [U_3807] :
      ( ! [U_3806,U_3805] :
          ( hAPP(U_3807,U_3807,hAPP(U_3807,fun(U_3807,U_3807),semilattice_sup_sup(U_3807),U_3806),U_3805) = ti(U_3807,U_3805)
          | ~ hBOOL(hAPP(U_3807,bool,hAPP(U_3807,fun(U_3807,bool),ord_less_eq(U_3807),U_3806),U_3805)) )
      | ~ semilattice_sup(U_3807) ),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

cnf(f_934_3,plain,
    ( hAPP(U_3807,U_3807,hAPP(U_3807,fun(U_3807,U_3807),semilattice_sup_sup(U_3807),U_3806),U_3805) = ti(U_3807,U_3805)
    | ~ hBOOL(hAPP(U_3807,bool,hAPP(U_3807,fun(U_3807,bool),ord_less_eq(U_3807),U_3806),U_3805))
    | ~ semilattice_sup(U_3807) ),
    inference(clausify,[status(thm)],[f_934_2]) ).

fof(f_935_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = ti(X_a,X)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_845_sup__absorb1]) ).

fof(f_935_2,plain,
    ! [U_3810] :
      ( ! [U_3809,U_3808] :
          ( hAPP(U_3810,U_3810,hAPP(U_3810,fun(U_3810,U_3810),semilattice_sup_sup(U_3810),U_3808),U_3809) = ti(U_3810,U_3808)
          | ~ hBOOL(hAPP(U_3810,bool,hAPP(U_3810,fun(U_3810,bool),ord_less_eq(U_3810),U_3809),U_3808)) )
      | ~ semilattice_sup(U_3810) ),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

cnf(f_935_3,plain,
    ( hAPP(U_3810,U_3810,hAPP(U_3810,fun(U_3810,U_3810),semilattice_sup_sup(U_3810),U_3808),U_3809) = ti(U_3810,U_3808)
    | ~ hBOOL(hAPP(U_3810,bool,hAPP(U_3810,fun(U_3810,bool),ord_less_eq(U_3810),U_3809),U_3808))
    | ~ semilattice_sup(U_3810) ),
    inference(clausify,[status(thm)],[f_935_2]) ).

fof(f_936_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X)) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_846_le__supI]) ).

fof(f_936_2,plain,
    ! [U_3814] :
      ( ! [U_3813,U_3812,U_3811] :
          ( hBOOL(hAPP(U_3814,bool,hAPP(U_3814,fun(U_3814,bool),ord_less_eq(U_3814),hAPP(U_3814,U_3814,hAPP(U_3814,fun(U_3814,U_3814),semilattice_sup_sup(U_3814),U_3812),U_3813)),U_3811))
          | ~ hBOOL(hAPP(U_3814,bool,hAPP(U_3814,fun(U_3814,bool),ord_less_eq(U_3814),U_3813),U_3811))
          | ~ hBOOL(hAPP(U_3814,bool,hAPP(U_3814,fun(U_3814,bool),ord_less_eq(U_3814),U_3812),U_3811)) )
      | ~ semilattice_sup(U_3814) ),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

cnf(f_936_3,plain,
    ( hBOOL(hAPP(U_3814,bool,hAPP(U_3814,fun(U_3814,bool),ord_less_eq(U_3814),hAPP(U_3814,U_3814,hAPP(U_3814,fun(U_3814,U_3814),semilattice_sup_sup(U_3814),U_3812),U_3813)),U_3811))
    | ~ hBOOL(hAPP(U_3814,bool,hAPP(U_3814,fun(U_3814,bool),ord_less_eq(U_3814),U_3813),U_3811))
    | ~ hBOOL(hAPP(U_3814,bool,hAPP(U_3814,fun(U_3814,bool),ord_less_eq(U_3814),U_3812),U_3811))
    | ~ semilattice_sup(U_3814) ),
    inference(clausify,[status(thm)],[f_936_2]) ).

fof(f_937_1,plain,
    ! [X_a] :
      ( ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_847_sup__least]) ).

fof(f_937_2,plain,
    ! [U_3818] :
      ( ! [U_3817,U_3816,U_3815] :
          ( hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less_eq(U_3818),hAPP(U_3818,U_3818,hAPP(U_3818,fun(U_3818,U_3818),semilattice_sup_sup(U_3818),U_3816),U_3817)),U_3815))
          | ~ hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less_eq(U_3818),U_3817),U_3815))
          | ~ hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less_eq(U_3818),U_3816),U_3815)) )
      | ~ semilattice_sup(U_3818) ),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

cnf(f_937_3,plain,
    ( hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less_eq(U_3818),hAPP(U_3818,U_3818,hAPP(U_3818,fun(U_3818,U_3818),semilattice_sup_sup(U_3818),U_3816),U_3817)),U_3815))
    | ~ hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less_eq(U_3818),U_3817),U_3815))
    | ~ hBOOL(hAPP(U_3818,bool,hAPP(U_3818,fun(U_3818,bool),ord_less_eq(U_3818),U_3816),U_3815))
    | ~ semilattice_sup(U_3818) ),
    inference(clausify,[status(thm)],[f_937_2]) ).

fof(f_938_1,plain,
    ! [X_a] :
      ( ! [B_1,D,A_2,C_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),C_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1)) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_848_sup__mono]) ).

fof(f_938_2,plain,
    ! [U_3823] :
      ( ! [U_3822,U_3821,U_3820,U_3819] :
          ( hBOOL(hAPP(U_3823,bool,hAPP(U_3823,fun(U_3823,bool),ord_less_eq(U_3823),hAPP(U_3823,U_3823,hAPP(U_3823,fun(U_3823,U_3823),semilattice_sup_sup(U_3823),U_3820),U_3822)),hAPP(U_3823,U_3823,hAPP(U_3823,fun(U_3823,U_3823),semilattice_sup_sup(U_3823),U_3819),U_3821)))
          | ~ hBOOL(hAPP(U_3823,bool,hAPP(U_3823,fun(U_3823,bool),ord_less_eq(U_3823),U_3822),U_3821))
          | ~ hBOOL(hAPP(U_3823,bool,hAPP(U_3823,fun(U_3823,bool),ord_less_eq(U_3823),U_3820),U_3819)) )
      | ~ semilattice_sup(U_3823) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

cnf(f_938_3,plain,
    ( hBOOL(hAPP(U_3823,bool,hAPP(U_3823,fun(U_3823,bool),ord_less_eq(U_3823),hAPP(U_3823,U_3823,hAPP(U_3823,fun(U_3823,U_3823),semilattice_sup_sup(U_3823),U_3820),U_3822)),hAPP(U_3823,U_3823,hAPP(U_3823,fun(U_3823,U_3823),semilattice_sup_sup(U_3823),U_3819),U_3821)))
    | ~ hBOOL(hAPP(U_3823,bool,hAPP(U_3823,fun(U_3823,bool),ord_less_eq(U_3823),U_3822),U_3821))
    | ~ hBOOL(hAPP(U_3823,bool,hAPP(U_3823,fun(U_3823,bool),ord_less_eq(U_3823),U_3820),U_3819))
    | ~ semilattice_sup(U_3823) ),
    inference(clausify,[status(thm)],[f_938_2]) ).

fof(f_939_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,X] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),X))
            & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X)) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)),X)) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_849_le__supE]) ).

fof(f_939_2,plain,
    ! [U_3827] :
      ( ! [U_3826,U_3825,U_3824] :
          ( ( hBOOL(hAPP(U_3827,bool,hAPP(U_3827,fun(U_3827,bool),ord_less_eq(U_3827),U_3825),U_3824))
            & hBOOL(hAPP(U_3827,bool,hAPP(U_3827,fun(U_3827,bool),ord_less_eq(U_3827),U_3826),U_3824)) )
          | ~ hBOOL(hAPP(U_3827,bool,hAPP(U_3827,fun(U_3827,bool),ord_less_eq(U_3827),hAPP(U_3827,U_3827,hAPP(U_3827,fun(U_3827,U_3827),semilattice_sup_sup(U_3827),U_3826),U_3825)),U_3824)) )
      | ~ semilattice_sup(U_3827) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

cnf(f_939_3,plain,
    ( hBOOL(hAPP(U_3827,bool,hAPP(U_3827,fun(U_3827,bool),ord_less_eq(U_3827),U_3826),U_3824))
    | ~ hBOOL(hAPP(U_3827,bool,hAPP(U_3827,fun(U_3827,bool),ord_less_eq(U_3827),hAPP(U_3827,U_3827,hAPP(U_3827,fun(U_3827,U_3827),semilattice_sup_sup(U_3827),U_3826),U_3825)),U_3824))
    | ~ semilattice_sup(U_3827) ),
    inference(clausify,[status(thm)],[f_939_2]) ).

cnf(f_939_4,plain,
    ( hBOOL(hAPP(U_3827,bool,hAPP(U_3827,fun(U_3827,bool),ord_less_eq(U_3827),U_3825),U_3824))
    | ~ hBOOL(hAPP(U_3827,bool,hAPP(U_3827,fun(U_3827,bool),ord_less_eq(U_3827),hAPP(U_3827,U_3827,hAPP(U_3827,fun(U_3827,U_3827),semilattice_sup_sup(U_3827),U_3826),U_3825)),U_3824))
    | ~ semilattice_sup(U_3827) ),
    inference(clausify,[status(thm)],[f_939_2]) ).

fof(f_940_1,plain,
    ! [X_a] :
      ( ! [A_2,X,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B_1)) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_850_less__supI2]) ).

fof(f_940_2,plain,
    ! [U_3831] :
      ( ! [U_3830,U_3829,U_3828] :
          ( hBOOL(hAPP(U_3831,bool,hAPP(U_3831,fun(U_3831,bool),ord_less(U_3831),U_3829),hAPP(U_3831,U_3831,hAPP(U_3831,fun(U_3831,U_3831),semilattice_sup_sup(U_3831),U_3830),U_3828)))
          | ~ hBOOL(hAPP(U_3831,bool,hAPP(U_3831,fun(U_3831,bool),ord_less(U_3831),U_3829),U_3828)) )
      | ~ semilattice_sup(U_3831) ),
    inference(variable_rename,[status(thm)],[f_940_1]) ).

cnf(f_940_3,plain,
    ( hBOOL(hAPP(U_3831,bool,hAPP(U_3831,fun(U_3831,bool),ord_less(U_3831),U_3829),hAPP(U_3831,U_3831,hAPP(U_3831,fun(U_3831,U_3831),semilattice_sup_sup(U_3831),U_3830),U_3828)))
    | ~ hBOOL(hAPP(U_3831,bool,hAPP(U_3831,fun(U_3831,bool),ord_less(U_3831),U_3829),U_3828))
    | ~ semilattice_sup(U_3831) ),
    inference(clausify,[status(thm)],[f_940_2]) ).

fof(f_941_1,plain,
    ! [X_a] :
      ( ! [B_1,X,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_2)) )
      | ~ semilattice_sup(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_851_less__supI1]) ).

fof(f_941_2,plain,
    ! [U_3835] :
      ( ! [U_3834,U_3833,U_3832] :
          ( hBOOL(hAPP(U_3835,bool,hAPP(U_3835,fun(U_3835,bool),ord_less(U_3835),U_3833),hAPP(U_3835,U_3835,hAPP(U_3835,fun(U_3835,U_3835),semilattice_sup_sup(U_3835),U_3832),U_3834)))
          | ~ hBOOL(hAPP(U_3835,bool,hAPP(U_3835,fun(U_3835,bool),ord_less(U_3835),U_3833),U_3832)) )
      | ~ semilattice_sup(U_3835) ),
    inference(variable_rename,[status(thm)],[f_941_1]) ).

cnf(f_941_3,plain,
    ( hBOOL(hAPP(U_3835,bool,hAPP(U_3835,fun(U_3835,bool),ord_less(U_3835),U_3833),hAPP(U_3835,U_3835,hAPP(U_3835,fun(U_3835,U_3835),semilattice_sup_sup(U_3835),U_3832),U_3834)))
    | ~ hBOOL(hAPP(U_3835,bool,hAPP(U_3835,fun(U_3835,bool),ord_less(U_3835),U_3833),U_3832))
    | ~ semilattice_sup(U_3835) ),
    inference(clausify,[status(thm)],[f_941_2]) ).

fof(f_942_1,plain,
    ! [X_a] :
      ( ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),top_top(X_a)),X) = top_top(X_a)
      | ~ bounded_lattice_top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_852_sup__top__left]) ).

fof(f_942_2,plain,
    ! [U_3837] :
      ( ! [U_3836] : hAPP(U_3837,U_3837,hAPP(U_3837,fun(U_3837,U_3837),semilattice_sup_sup(U_3837),top_top(U_3837)),U_3836) = top_top(U_3837)
      | ~ bounded_lattice_top(U_3837) ),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

cnf(f_942_3,plain,
    ( hAPP(U_3837,U_3837,hAPP(U_3837,fun(U_3837,U_3837),semilattice_sup_sup(U_3837),top_top(U_3837)),U_3836) = top_top(U_3837)
    | ~ bounded_lattice_top(U_3837) ),
    inference(clausify,[status(thm)],[f_942_2]) ).

fof(f_943_1,plain,
    ! [X_a] :
      ( ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),top_top(X_a)) = top_top(X_a)
      | ~ bounded_lattice_top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_853_sup__top__right]) ).

fof(f_943_2,plain,
    ! [U_3839] :
      ( ! [U_3838] : hAPP(U_3839,U_3839,hAPP(U_3839,fun(U_3839,U_3839),semilattice_sup_sup(U_3839),U_3838),top_top(U_3839)) = top_top(U_3839)
      | ~ bounded_lattice_top(U_3839) ),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

cnf(f_943_3,plain,
    ( hAPP(U_3839,U_3839,hAPP(U_3839,fun(U_3839,U_3839),semilattice_sup_sup(U_3839),U_3838),top_top(U_3839)) = top_top(U_3839)
    | ~ bounded_lattice_top(U_3839) ),
    inference(clausify,[status(thm)],[f_943_2]) ).

fof(f_944_1,plain,
    ! [X_a] :
      ( ! [L,U] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),L),U)),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),U)) = hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),L)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),L),U)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_854_ivl__disj__un_I12_J]) ).

fof(f_944_2,plain,
    ! [U_3842] :
      ( ! [U_3841,U_3840] :
          ( hAPP(fun(U_3842,bool),fun(U_3842,bool),hAPP(fun(U_3842,bool),fun(fun(U_3842,bool),fun(U_3842,bool)),semilattice_sup_sup(fun(U_3842,bool)),hAPP(U_3842,fun(U_3842,bool),hAPP(U_3842,fun(U_3842,fun(U_3842,bool)),ord_gr676655987ssThan(U_3842),U_3841),U_3840)),hAPP(U_3842,fun(U_3842,bool),ord_atLeast(U_3842),U_3840)) = hAPP(U_3842,fun(U_3842,bool),ord_greaterThan(U_3842),U_3841)
          | ~ hBOOL(hAPP(U_3842,bool,hAPP(U_3842,fun(U_3842,bool),ord_less(U_3842),U_3841),U_3840)) )
      | ~ linorder(U_3842) ),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

cnf(f_944_3,plain,
    ( hAPP(fun(U_3842,bool),fun(U_3842,bool),hAPP(fun(U_3842,bool),fun(fun(U_3842,bool),fun(U_3842,bool)),semilattice_sup_sup(fun(U_3842,bool)),hAPP(U_3842,fun(U_3842,bool),hAPP(U_3842,fun(U_3842,fun(U_3842,bool)),ord_gr676655987ssThan(U_3842),U_3841),U_3840)),hAPP(U_3842,fun(U_3842,bool),ord_atLeast(U_3842),U_3840)) = hAPP(U_3842,fun(U_3842,bool),ord_greaterThan(U_3842),U_3841)
    | ~ hBOOL(hAPP(U_3842,bool,hAPP(U_3842,fun(U_3842,bool),ord_less(U_3842),U_3841),U_3840))
    | ~ linorder(U_3842) ),
    inference(clausify,[status(thm)],[f_944_2]) ).

fof(f_945_1,plain,
    ! [X_a] :
      ( ! [L,U] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),L),U)),hAPP(X_a,fun(X_a,bool),ord_greaterThan(X_a),U)) = hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),L)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),U)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_855_ivl__disj__un_I13_J]) ).

fof(f_945_2,plain,
    ! [U_3845] :
      ( ! [U_3844,U_3843] :
          ( hAPP(fun(U_3845,bool),fun(U_3845,bool),hAPP(fun(U_3845,bool),fun(fun(U_3845,bool),fun(U_3845,bool)),semilattice_sup_sup(fun(U_3845,bool)),hAPP(U_3845,fun(U_3845,bool),hAPP(U_3845,fun(U_3845,fun(U_3845,bool)),ord_atLeastAtMost(U_3845),U_3844),U_3843)),hAPP(U_3845,fun(U_3845,bool),ord_greaterThan(U_3845),U_3843)) = hAPP(U_3845,fun(U_3845,bool),ord_atLeast(U_3845),U_3844)
          | ~ hBOOL(hAPP(U_3845,bool,hAPP(U_3845,fun(U_3845,bool),ord_less_eq(U_3845),U_3844),U_3843)) )
      | ~ linorder(U_3845) ),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

cnf(f_945_3,plain,
    ( hAPP(fun(U_3845,bool),fun(U_3845,bool),hAPP(fun(U_3845,bool),fun(fun(U_3845,bool),fun(U_3845,bool)),semilattice_sup_sup(fun(U_3845,bool)),hAPP(U_3845,fun(U_3845,bool),hAPP(U_3845,fun(U_3845,fun(U_3845,bool)),ord_atLeastAtMost(U_3845),U_3844),U_3843)),hAPP(U_3845,fun(U_3845,bool),ord_greaterThan(U_3845),U_3843)) = hAPP(U_3845,fun(U_3845,bool),ord_atLeast(U_3845),U_3844)
    | ~ hBOOL(hAPP(U_3845,bool,hAPP(U_3845,fun(U_3845,bool),ord_less_eq(U_3845),U_3844),U_3843))
    | ~ linorder(U_3845) ),
    inference(clausify,[status(thm)],[f_945_2]) ).

fof(f_946_1,plain,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1))
      | hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1))
      | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_856_sup2E]) ).

fof(f_946_2,plain,
    ! [U_3851,U_3850,U_3849,U_3848,U_3847,U_3846] :
      ( hBOOL(hAPP(U_3851,bool,hAPP(U_3850,fun(U_3851,bool),U_3848,U_3847),U_3846))
      | hBOOL(hAPP(U_3851,bool,hAPP(U_3850,fun(U_3851,bool),U_3849,U_3847),U_3846))
      | ~ hBOOL(hAPP(U_3851,bool,hAPP(U_3850,fun(U_3851,bool),hAPP(fun(U_3850,fun(U_3851,bool)),fun(U_3850,fun(U_3851,bool)),hAPP(fun(U_3850,fun(U_3851,bool)),fun(fun(U_3850,fun(U_3851,bool)),fun(U_3850,fun(U_3851,bool))),semilattice_sup_sup(fun(U_3850,fun(U_3851,bool))),U_3849),U_3848),U_3847),U_3846)) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

cnf(f_946_3,plain,
    ( hBOOL(hAPP(U_3851,bool,hAPP(U_3850,fun(U_3851,bool),U_3848,U_3847),U_3846))
    | hBOOL(hAPP(U_3851,bool,hAPP(U_3850,fun(U_3851,bool),U_3849,U_3847),U_3846))
    | ~ hBOOL(hAPP(U_3851,bool,hAPP(U_3850,fun(U_3851,bool),hAPP(fun(U_3850,fun(U_3851,bool)),fun(U_3850,fun(U_3851,bool)),hAPP(fun(U_3850,fun(U_3851,bool)),fun(fun(U_3850,fun(U_3851,bool)),fun(U_3850,fun(U_3851,bool))),semilattice_sup_sup(fun(U_3850,fun(U_3851,bool))),U_3849),U_3848),U_3847),U_3846)) ),
    inference(clausify,[status(thm)],[f_946_2]) ).

fof(f_947_1,plain,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1))
      | ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1))
        & ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_857_sup2CI]) ).

fof(f_947_2,plain,
    ! [U_3857,U_3856,U_3855,U_3854,U_3853,U_3852] :
      ( hBOOL(hAPP(U_3857,bool,hAPP(U_3856,fun(U_3857,bool),hAPP(fun(U_3856,fun(U_3857,bool)),fun(U_3856,fun(U_3857,bool)),hAPP(fun(U_3856,fun(U_3857,bool)),fun(fun(U_3856,fun(U_3857,bool)),fun(U_3856,fun(U_3857,bool))),semilattice_sup_sup(fun(U_3856,fun(U_3857,bool))),U_3855),U_3854),U_3853),U_3852))
      | ( ~ hBOOL(hAPP(U_3857,bool,hAPP(U_3856,fun(U_3857,bool),U_3855,U_3853),U_3852))
        & ~ hBOOL(hAPP(U_3857,bool,hAPP(U_3856,fun(U_3857,bool),U_3854,U_3853),U_3852)) ) ),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

cnf(f_947_3,plain,
    ( ~ hBOOL(hAPP(U_3857,bool,hAPP(U_3856,fun(U_3857,bool),U_3854,U_3853),U_3852))
    | hBOOL(hAPP(U_3857,bool,hAPP(U_3856,fun(U_3857,bool),hAPP(fun(U_3856,fun(U_3857,bool)),fun(U_3856,fun(U_3857,bool)),hAPP(fun(U_3856,fun(U_3857,bool)),fun(fun(U_3856,fun(U_3857,bool)),fun(U_3856,fun(U_3857,bool))),semilattice_sup_sup(fun(U_3856,fun(U_3857,bool))),U_3855),U_3854),U_3853),U_3852)) ),
    inference(clausify,[status(thm)],[f_947_2]) ).

cnf(f_947_4,plain,
    ( ~ hBOOL(hAPP(U_3857,bool,hAPP(U_3856,fun(U_3857,bool),U_3855,U_3853),U_3852))
    | hBOOL(hAPP(U_3857,bool,hAPP(U_3856,fun(U_3857,bool),hAPP(fun(U_3856,fun(U_3857,bool)),fun(U_3856,fun(U_3857,bool)),hAPP(fun(U_3856,fun(U_3857,bool)),fun(fun(U_3856,fun(U_3857,bool)),fun(U_3856,fun(U_3857,bool))),semilattice_sup_sup(fun(U_3856,fun(U_3857,bool))),U_3855),U_3854),U_3853),U_3852)) ),
    inference(clausify,[status(thm)],[f_947_2]) ).

fof(f_948_1,plain,
    ! [X_b,X_a,B,A_1,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1))
      | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_858_sup2I1]) ).

fof(f_948_2,plain,
    ! [U_3863,U_3862,U_3861,U_3860,U_3859,U_3858] :
      ( hBOOL(hAPP(U_3863,bool,hAPP(U_3862,fun(U_3863,bool),hAPP(fun(U_3862,fun(U_3863,bool)),fun(U_3862,fun(U_3863,bool)),hAPP(fun(U_3862,fun(U_3863,bool)),fun(fun(U_3862,fun(U_3863,bool)),fun(U_3862,fun(U_3863,bool))),semilattice_sup_sup(fun(U_3862,fun(U_3863,bool))),U_3860),U_3861),U_3859),U_3858))
      | ~ hBOOL(hAPP(U_3863,bool,hAPP(U_3862,fun(U_3863,bool),U_3860,U_3859),U_3858)) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

cnf(f_948_3,plain,
    ( hBOOL(hAPP(U_3863,bool,hAPP(U_3862,fun(U_3863,bool),hAPP(fun(U_3862,fun(U_3863,bool)),fun(U_3862,fun(U_3863,bool)),hAPP(fun(U_3862,fun(U_3863,bool)),fun(fun(U_3862,fun(U_3863,bool)),fun(U_3862,fun(U_3863,bool))),semilattice_sup_sup(fun(U_3862,fun(U_3863,bool))),U_3860),U_3861),U_3859),U_3858))
    | ~ hBOOL(hAPP(U_3863,bool,hAPP(U_3862,fun(U_3863,bool),U_3860,U_3859),U_3858)) ),
    inference(clausify,[status(thm)],[f_948_2]) ).

fof(f_949_1,plain,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_sup_sup(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1))
      | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_859_sup2I2]) ).

fof(f_949_2,plain,
    ! [U_3869,U_3868,U_3867,U_3866,U_3865,U_3864] :
      ( hBOOL(hAPP(U_3869,bool,hAPP(U_3868,fun(U_3869,bool),hAPP(fun(U_3868,fun(U_3869,bool)),fun(U_3868,fun(U_3869,bool)),hAPP(fun(U_3868,fun(U_3869,bool)),fun(fun(U_3868,fun(U_3869,bool)),fun(U_3868,fun(U_3869,bool))),semilattice_sup_sup(fun(U_3868,fun(U_3869,bool))),U_3867),U_3866),U_3865),U_3864))
      | ~ hBOOL(hAPP(U_3869,bool,hAPP(U_3868,fun(U_3869,bool),U_3866,U_3865),U_3864)) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

cnf(f_949_3,plain,
    ( hBOOL(hAPP(U_3869,bool,hAPP(U_3868,fun(U_3869,bool),hAPP(fun(U_3868,fun(U_3869,bool)),fun(U_3868,fun(U_3869,bool)),hAPP(fun(U_3868,fun(U_3869,bool)),fun(fun(U_3868,fun(U_3869,bool)),fun(U_3868,fun(U_3869,bool))),semilattice_sup_sup(fun(U_3868,fun(U_3869,bool))),U_3867),U_3866),U_3865),U_3864))
    | ~ hBOOL(hAPP(U_3869,bool,hAPP(U_3868,fun(U_3869,bool),U_3866,U_3865),U_3864)) ),
    inference(clausify,[status(thm)],[f_949_2]) ).

fof(f_950_1,plain,
    ! [X_a] :
      ( ! [I,K] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),K)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),K),I)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),K),I))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),K))) ) )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_860_atLeast__iff]) ).

fof(f_950_2,plain,
    ! [U_3872] :
      ( ! [U_3871,U_3870] :
          ( ( hBOOL(hAPP(fun(U_3872,bool),bool,hAPP(U_3872,fun(fun(U_3872,bool),bool),member(U_3872),U_3871),hAPP(U_3872,fun(U_3872,bool),ord_atLeast(U_3872),U_3870)))
            | ~ hBOOL(hAPP(U_3872,bool,hAPP(U_3872,fun(U_3872,bool),ord_less_eq(U_3872),U_3870),U_3871)) )
          & ( hBOOL(hAPP(U_3872,bool,hAPP(U_3872,fun(U_3872,bool),ord_less_eq(U_3872),U_3870),U_3871))
            | ~ hBOOL(hAPP(fun(U_3872,bool),bool,hAPP(U_3872,fun(fun(U_3872,bool),bool),member(U_3872),U_3871),hAPP(U_3872,fun(U_3872,bool),ord_atLeast(U_3872),U_3870))) ) )
      | ~ ord(U_3872) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

fof(f_950_3,plain,
    ! [U_3872] :
      ( ( ! [U_3876,U_3874] :
            ( hBOOL(hAPP(fun(U_3872,bool),bool,hAPP(U_3872,fun(fun(U_3872,bool),bool),member(U_3872),U_3876),hAPP(U_3872,fun(U_3872,bool),ord_atLeast(U_3872),U_3874)))
            | ~ hBOOL(hAPP(U_3872,bool,hAPP(U_3872,fun(U_3872,bool),ord_less_eq(U_3872),U_3874),U_3876)) )
        & ! [U_3875,U_3873] :
            ( hBOOL(hAPP(U_3872,bool,hAPP(U_3872,fun(U_3872,bool),ord_less_eq(U_3872),U_3873),U_3875))
            | ~ hBOOL(hAPP(fun(U_3872,bool),bool,hAPP(U_3872,fun(fun(U_3872,bool),bool),member(U_3872),U_3875),hAPP(U_3872,fun(U_3872,bool),ord_atLeast(U_3872),U_3873))) ) )
      | ~ ord(U_3872) ),
    inference(miniscope,[status(thm)],[f_950_2]) ).

cnf(f_950_4,plain,
    ( hBOOL(hAPP(U_3872,bool,hAPP(U_3872,fun(U_3872,bool),ord_less_eq(U_3872),U_3873),U_3875))
    | ~ hBOOL(hAPP(fun(U_3872,bool),bool,hAPP(U_3872,fun(fun(U_3872,bool),bool),member(U_3872),U_3875),hAPP(U_3872,fun(U_3872,bool),ord_atLeast(U_3872),U_3873)))
    | ~ ord(U_3872) ),
    inference(clausify,[status(thm)],[f_950_3]) ).

cnf(f_950_5,plain,
    ( hBOOL(hAPP(fun(U_3872,bool),bool,hAPP(U_3872,fun(fun(U_3872,bool),bool),member(U_3872),U_3876),hAPP(U_3872,fun(U_3872,bool),ord_atLeast(U_3872),U_3874)))
    | ~ hBOOL(hAPP(U_3872,bool,hAPP(U_3872,fun(U_3872,bool),ord_less_eq(U_3872),U_3874),U_3876))
    | ~ ord(U_3872) ),
    inference(clausify,[status(thm)],[f_950_3]) ).

fof(f_951_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),X_2) = hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),Y_1)
            | ti(X_a,X_2) != ti(X_a,Y_1) )
          & ( ti(X_a,X_2) = ti(X_a,Y_1)
            | hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),X_2) != hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),Y_1) ) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_861_atLeast__eq__iff]) ).

fof(f_951_2,plain,
    ! [U_3879] :
      ( ! [U_3878,U_3877] :
          ( ( hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3878) = hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3877)
            | ti(U_3879,U_3878) != ti(U_3879,U_3877) )
          & ( ti(U_3879,U_3878) = ti(U_3879,U_3877)
            | hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3878) != hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3877) ) )
      | ~ linorder(U_3879) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

fof(f_951_3,plain,
    ! [U_3879] :
      ( ( ! [U_3883,U_3881] :
            ( hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3883) = hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3881)
            | ti(U_3879,U_3883) != ti(U_3879,U_3881) )
        & ! [U_3882,U_3880] :
            ( ti(U_3879,U_3882) = ti(U_3879,U_3880)
            | hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3882) != hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3880) ) )
      | ~ linorder(U_3879) ),
    inference(miniscope,[status(thm)],[f_951_2]) ).

cnf(f_951_4,plain,
    ( ti(U_3879,U_3882) = ti(U_3879,U_3880)
    | hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3882) != hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3880)
    | ~ linorder(U_3879) ),
    inference(clausify,[status(thm)],[f_951_3]) ).

cnf(f_951_5,plain,
    ( hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3883) = hAPP(U_3879,fun(U_3879,bool),ord_atLeast(U_3879),U_3881)
    | ti(U_3879,U_3883) != ti(U_3879,U_3881)
    | ~ linorder(U_3879) ),
    inference(clausify,[status(thm)],[f_951_3]) ).

fof(f_952_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),X_2)),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),Y_1)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2)) )
          & ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_2))
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),X_2)),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),Y_1))) ) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_862_atLeast__subset__iff]) ).

fof(f_952_2,plain,
    ! [U_3886] :
      ( ! [U_3885,U_3884] :
          ( ( hBOOL(hAPP(fun(U_3886,bool),bool,hAPP(fun(U_3886,bool),fun(fun(U_3886,bool),bool),ord_less_eq(fun(U_3886,bool)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3885)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3884)))
            | ~ hBOOL(hAPP(U_3886,bool,hAPP(U_3886,fun(U_3886,bool),ord_less_eq(U_3886),U_3884),U_3885)) )
          & ( hBOOL(hAPP(U_3886,bool,hAPP(U_3886,fun(U_3886,bool),ord_less_eq(U_3886),U_3884),U_3885))
            | ~ hBOOL(hAPP(fun(U_3886,bool),bool,hAPP(fun(U_3886,bool),fun(fun(U_3886,bool),bool),ord_less_eq(fun(U_3886,bool)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3885)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3884))) ) )
      | ~ order(U_3886) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

fof(f_952_3,plain,
    ! [U_3886] :
      ( ( ! [U_3890,U_3888] :
            ( hBOOL(hAPP(fun(U_3886,bool),bool,hAPP(fun(U_3886,bool),fun(fun(U_3886,bool),bool),ord_less_eq(fun(U_3886,bool)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3890)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3888)))
            | ~ hBOOL(hAPP(U_3886,bool,hAPP(U_3886,fun(U_3886,bool),ord_less_eq(U_3886),U_3888),U_3890)) )
        & ! [U_3889,U_3887] :
            ( hBOOL(hAPP(U_3886,bool,hAPP(U_3886,fun(U_3886,bool),ord_less_eq(U_3886),U_3887),U_3889))
            | ~ hBOOL(hAPP(fun(U_3886,bool),bool,hAPP(fun(U_3886,bool),fun(fun(U_3886,bool),bool),ord_less_eq(fun(U_3886,bool)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3889)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3887))) ) )
      | ~ order(U_3886) ),
    inference(miniscope,[status(thm)],[f_952_2]) ).

cnf(f_952_4,plain,
    ( hBOOL(hAPP(U_3886,bool,hAPP(U_3886,fun(U_3886,bool),ord_less_eq(U_3886),U_3887),U_3889))
    | ~ hBOOL(hAPP(fun(U_3886,bool),bool,hAPP(fun(U_3886,bool),fun(fun(U_3886,bool),bool),ord_less_eq(fun(U_3886,bool)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3889)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3887)))
    | ~ order(U_3886) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

cnf(f_952_5,plain,
    ( hBOOL(hAPP(fun(U_3886,bool),bool,hAPP(fun(U_3886,bool),fun(fun(U_3886,bool),bool),ord_less_eq(fun(U_3886,bool)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3890)),hAPP(U_3886,fun(U_3886,bool),ord_atLeast(U_3886),U_3888)))
    | ~ hBOOL(hAPP(U_3886,bool,hAPP(U_3886,fun(U_3886,bool),ord_less_eq(U_3886),U_3888),U_3890))
    | ~ order(U_3886) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

fof(f_953_1,plain,
    hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
    inference(fof_nnf,[status(thm)],[fact_863_atLeast__0]) ).

cnf(f_953_2,plain,
    hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
    inference(clausify,[status(thm)],[f_953_1]) ).

fof(f_954_1,plain,
    ! [K] : hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,K)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),K),
    inference(fof_nnf,[status(thm)],[fact_864_atLeast__Suc__greaterThan]) ).

fof(f_954_2,plain,
    ! [U_3891] : hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,U_3891)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),U_3891),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

cnf(f_954_3,plain,
    hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,U_3891)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),U_3891),
    inference(clausify,[status(thm)],[f_954_2]) ).

fof(f_955_1,plain,
    ! [X_a] :
      ( ! [L,U] :
          ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),L),U)),hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),U)) = hAPP(X_a,fun(X_a,bool),ord_atLeast(X_a),L)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),L),U)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_865_ivl__disj__un_I14_J]) ).

fof(f_955_2,plain,
    ! [U_3894] :
      ( ! [U_3893,U_3892] :
          ( hAPP(fun(U_3894,bool),fun(U_3894,bool),hAPP(fun(U_3894,bool),fun(fun(U_3894,bool),fun(U_3894,bool)),semilattice_sup_sup(fun(U_3894,bool)),hAPP(U_3894,fun(U_3894,bool),hAPP(U_3894,fun(U_3894,fun(U_3894,bool)),ord_atLeastLessThan(U_3894),U_3893),U_3892)),hAPP(U_3894,fun(U_3894,bool),ord_atLeast(U_3894),U_3892)) = hAPP(U_3894,fun(U_3894,bool),ord_atLeast(U_3894),U_3893)
          | ~ hBOOL(hAPP(U_3894,bool,hAPP(U_3894,fun(U_3894,bool),ord_less_eq(U_3894),U_3893),U_3892)) )
      | ~ linorder(U_3894) ),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

cnf(f_955_3,plain,
    ( hAPP(fun(U_3894,bool),fun(U_3894,bool),hAPP(fun(U_3894,bool),fun(fun(U_3894,bool),fun(U_3894,bool)),semilattice_sup_sup(fun(U_3894,bool)),hAPP(U_3894,fun(U_3894,bool),hAPP(U_3894,fun(U_3894,fun(U_3894,bool)),ord_atLeastLessThan(U_3894),U_3893),U_3892)),hAPP(U_3894,fun(U_3894,bool),ord_atLeast(U_3894),U_3892)) = hAPP(U_3894,fun(U_3894,bool),ord_atLeast(U_3894),U_3893)
    | ~ hBOOL(hAPP(U_3894,bool,hAPP(U_3894,fun(U_3894,bool),ord_less_eq(U_3894),U_3893),U_3892))
    | ~ linorder(U_3894) ),
    inference(clausify,[status(thm)],[f_955_2]) ).

fof(f_956_1,plain,
    ! [X_a,X_b] :
      ( ! [G,B,A_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),one_one(X_b)),A_1)),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),one_one(X_b)),B)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),one_one(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),G),one_one(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_mult(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_866_fold__image__Un__Int]) ).

fof(f_956_2,plain,
    ! [U_3899,U_3898] :
      ( ! [U_3897,U_3896,U_3895] :
          ( hAPP(U_3898,U_3898,hAPP(U_3898,fun(U_3898,U_3898),times_times(U_3898),hAPP(fun(U_3899,bool),U_3898,hAPP(U_3898,fun(fun(U_3899,bool),U_3898),hAPP(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898)),hAPP(fun(U_3898,fun(U_3898,U_3898)),fun(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898))),finite_fold_image(U_3898,U_3899),times_times(U_3898)),U_3897),one_one(U_3898)),U_3895)),hAPP(fun(U_3899,bool),U_3898,hAPP(U_3898,fun(fun(U_3899,bool),U_3898),hAPP(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898)),hAPP(fun(U_3898,fun(U_3898,U_3898)),fun(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898))),finite_fold_image(U_3898,U_3899),times_times(U_3898)),U_3897),one_one(U_3898)),U_3896)) = hAPP(U_3898,U_3898,hAPP(U_3898,fun(U_3898,U_3898),times_times(U_3898),hAPP(fun(U_3899,bool),U_3898,hAPP(U_3898,fun(fun(U_3899,bool),U_3898),hAPP(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898)),hAPP(fun(U_3898,fun(U_3898,U_3898)),fun(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898))),finite_fold_image(U_3898,U_3899),times_times(U_3898)),U_3897),one_one(U_3898)),hAPP(fun(U_3899,bool),fun(U_3899,bool),hAPP(fun(U_3899,bool),fun(fun(U_3899,bool),fun(U_3899,bool)),semilattice_sup_sup(fun(U_3899,bool)),U_3895),U_3896))),hAPP(fun(U_3899,bool),U_3898,hAPP(U_3898,fun(fun(U_3899,bool),U_3898),hAPP(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898)),hAPP(fun(U_3898,fun(U_3898,U_3898)),fun(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898))),finite_fold_image(U_3898,U_3899),times_times(U_3898)),U_3897),one_one(U_3898)),hAPP(fun(U_3899,bool),fun(U_3899,bool),hAPP(fun(U_3899,bool),fun(fun(U_3899,bool),fun(U_3899,bool)),semilattice_inf_inf(fun(U_3899,bool)),U_3895),U_3896)))
          | ~ hBOOL(hAPP(fun(U_3899,bool),bool,finite_finite_1(U_3899),U_3896))
          | ~ hBOOL(hAPP(fun(U_3899,bool),bool,finite_finite_1(U_3899),U_3895)) )
      | ~ comm_monoid_mult(U_3898) ),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

cnf(f_956_3,plain,
    ( hAPP(U_3898,U_3898,hAPP(U_3898,fun(U_3898,U_3898),times_times(U_3898),hAPP(fun(U_3899,bool),U_3898,hAPP(U_3898,fun(fun(U_3899,bool),U_3898),hAPP(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898)),hAPP(fun(U_3898,fun(U_3898,U_3898)),fun(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898))),finite_fold_image(U_3898,U_3899),times_times(U_3898)),U_3897),one_one(U_3898)),U_3895)),hAPP(fun(U_3899,bool),U_3898,hAPP(U_3898,fun(fun(U_3899,bool),U_3898),hAPP(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898)),hAPP(fun(U_3898,fun(U_3898,U_3898)),fun(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898))),finite_fold_image(U_3898,U_3899),times_times(U_3898)),U_3897),one_one(U_3898)),U_3896)) = hAPP(U_3898,U_3898,hAPP(U_3898,fun(U_3898,U_3898),times_times(U_3898),hAPP(fun(U_3899,bool),U_3898,hAPP(U_3898,fun(fun(U_3899,bool),U_3898),hAPP(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898)),hAPP(fun(U_3898,fun(U_3898,U_3898)),fun(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898))),finite_fold_image(U_3898,U_3899),times_times(U_3898)),U_3897),one_one(U_3898)),hAPP(fun(U_3899,bool),fun(U_3899,bool),hAPP(fun(U_3899,bool),fun(fun(U_3899,bool),fun(U_3899,bool)),semilattice_sup_sup(fun(U_3899,bool)),U_3895),U_3896))),hAPP(fun(U_3899,bool),U_3898,hAPP(U_3898,fun(fun(U_3899,bool),U_3898),hAPP(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898)),hAPP(fun(U_3898,fun(U_3898,U_3898)),fun(fun(U_3899,U_3898),fun(U_3898,fun(fun(U_3899,bool),U_3898))),finite_fold_image(U_3898,U_3899),times_times(U_3898)),U_3897),one_one(U_3898)),hAPP(fun(U_3899,bool),fun(U_3899,bool),hAPP(fun(U_3899,bool),fun(fun(U_3899,bool),fun(U_3899,bool)),semilattice_inf_inf(fun(U_3899,bool)),U_3895),U_3896)))
    | ~ hBOOL(hAPP(fun(U_3899,bool),bool,finite_finite_1(U_3899),U_3896))
    | ~ hBOOL(hAPP(fun(U_3899,bool),bool,finite_finite_1(U_3899),U_3895))
    | ~ comm_monoid_mult(U_3898) ),
    inference(clausify,[status(thm)],[f_956_2]) ).

fof(f_957_1,plain,
    ! [X_a] :
      ( ! [F,P_1,M,Na] :
          ( hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),P_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),P_1))))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),one_one(nat)))) )
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_867_setsum__ub__add__nat]) ).

fof(f_957_2,plain,
    ! [U_3904] :
      ( ! [U_3903,U_3902,U_3901,U_3900] :
          ( hAPP(fun(nat,bool),U_3904,hAPP(fun(nat,U_3904),fun(fun(nat,bool),U_3904),big_co1399186613setsum(nat,U_3904),U_3903),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3901),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3900),U_3902))) = hAPP(U_3904,U_3904,hAPP(U_3904,fun(U_3904,U_3904),plus_plus(U_3904),hAPP(fun(nat,bool),U_3904,hAPP(fun(nat,U_3904),fun(fun(nat,bool),U_3904),big_co1399186613setsum(nat,U_3904),U_3903),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3901),U_3900))),hAPP(fun(nat,bool),U_3904,hAPP(fun(nat,U_3904),fun(fun(nat,bool),U_3904),big_co1399186613setsum(nat,U_3904),U_3903),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3900),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3900),U_3902))))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3901),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3900),one_one(nat)))) )
      | ~ comm_monoid_add(U_3904) ),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

cnf(f_957_3,plain,
    ( hAPP(fun(nat,bool),U_3904,hAPP(fun(nat,U_3904),fun(fun(nat,bool),U_3904),big_co1399186613setsum(nat,U_3904),U_3903),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3901),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3900),U_3902))) = hAPP(U_3904,U_3904,hAPP(U_3904,fun(U_3904,U_3904),plus_plus(U_3904),hAPP(fun(nat,bool),U_3904,hAPP(fun(nat,U_3904),fun(fun(nat,bool),U_3904),big_co1399186613setsum(nat,U_3904),U_3903),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3901),U_3900))),hAPP(fun(nat,bool),U_3904,hAPP(fun(nat,U_3904),fun(fun(nat,bool),U_3904),big_co1399186613setsum(nat,U_3904),U_3903),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3900),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3900),U_3902))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_3901),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3900),one_one(nat))))
    | ~ comm_monoid_add(U_3904) ),
    inference(clausify,[status(thm)],[f_957_2]) ).

fof(f_958_1,plain,
    ! [X_a,A_1,B,X_2] :
      ( ( hBOOL(hAPP(X_a,bool,B,X_2))
        & hBOOL(hAPP(X_a,bool,A_1,X_2)) )
      | ~ hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_868_inf1E]) ).

fof(f_958_2,plain,
    ! [U_3908,U_3907,U_3906,U_3905] :
      ( ( hBOOL(hAPP(U_3908,bool,U_3906,U_3905))
        & hBOOL(hAPP(U_3908,bool,U_3907,U_3905)) )
      | ~ hBOOL(hAPP(U_3908,bool,hAPP(fun(U_3908,bool),fun(U_3908,bool),hAPP(fun(U_3908,bool),fun(fun(U_3908,bool),fun(U_3908,bool)),semilattice_inf_inf(fun(U_3908,bool)),U_3907),U_3906),U_3905)) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

cnf(f_958_3,plain,
    ( hBOOL(hAPP(U_3908,bool,U_3907,U_3905))
    | ~ hBOOL(hAPP(U_3908,bool,hAPP(fun(U_3908,bool),fun(U_3908,bool),hAPP(fun(U_3908,bool),fun(fun(U_3908,bool),fun(U_3908,bool)),semilattice_inf_inf(fun(U_3908,bool)),U_3907),U_3906),U_3905)) ),
    inference(clausify,[status(thm)],[f_958_2]) ).

cnf(f_958_4,plain,
    ( hBOOL(hAPP(U_3908,bool,U_3906,U_3905))
    | ~ hBOOL(hAPP(U_3908,bool,hAPP(fun(U_3908,bool),fun(U_3908,bool),hAPP(fun(U_3908,bool),fun(fun(U_3908,bool),fun(U_3908,bool)),semilattice_inf_inf(fun(U_3908,bool)),U_3907),U_3906),U_3905)) ),
    inference(clausify,[status(thm)],[f_958_2]) ).

fof(f_959_1,plain,
    ! [X_a,Ca,A_1,B] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
        & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) ),
    inference(fof_nnf,[status(thm)],[fact_869_IntE]) ).

fof(f_959_2,plain,
    ! [U_3912,U_3911,U_3910,U_3909] :
      ( ( hBOOL(hAPP(fun(U_3912,bool),bool,hAPP(U_3912,fun(fun(U_3912,bool),bool),member(U_3912),U_3911),U_3909))
        & hBOOL(hAPP(fun(U_3912,bool),bool,hAPP(U_3912,fun(fun(U_3912,bool),bool),member(U_3912),U_3911),U_3910)) )
      | ~ hBOOL(hAPP(fun(U_3912,bool),bool,hAPP(U_3912,fun(fun(U_3912,bool),bool),member(U_3912),U_3911),hAPP(fun(U_3912,bool),fun(U_3912,bool),hAPP(fun(U_3912,bool),fun(fun(U_3912,bool),fun(U_3912,bool)),semilattice_inf_inf(fun(U_3912,bool)),U_3910),U_3909))) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

cnf(f_959_3,plain,
    ( hBOOL(hAPP(fun(U_3912,bool),bool,hAPP(U_3912,fun(fun(U_3912,bool),bool),member(U_3912),U_3911),U_3910))
    | ~ hBOOL(hAPP(fun(U_3912,bool),bool,hAPP(U_3912,fun(fun(U_3912,bool),bool),member(U_3912),U_3911),hAPP(fun(U_3912,bool),fun(U_3912,bool),hAPP(fun(U_3912,bool),fun(fun(U_3912,bool),fun(U_3912,bool)),semilattice_inf_inf(fun(U_3912,bool)),U_3910),U_3909))) ),
    inference(clausify,[status(thm)],[f_959_2]) ).

cnf(f_959_4,plain,
    ( hBOOL(hAPP(fun(U_3912,bool),bool,hAPP(U_3912,fun(fun(U_3912,bool),bool),member(U_3912),U_3911),U_3909))
    | ~ hBOOL(hAPP(fun(U_3912,bool),bool,hAPP(U_3912,fun(fun(U_3912,bool),bool),member(U_3912),U_3911),hAPP(fun(U_3912,bool),fun(U_3912,bool),hAPP(fun(U_3912,bool),fun(fun(U_3912,bool),fun(U_3912,bool)),semilattice_inf_inf(fun(U_3912,bool)),U_3910),U_3909))) ),
    inference(clausify,[status(thm)],[f_959_2]) ).

fof(f_960_1,plain,
    ! [X_a,B,Ca,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_870_IntI]) ).

fof(f_960_2,plain,
    ! [U_3916,U_3915,U_3914,U_3913] :
      ( hBOOL(hAPP(fun(U_3916,bool),bool,hAPP(U_3916,fun(fun(U_3916,bool),bool),member(U_3916),U_3914),hAPP(fun(U_3916,bool),fun(U_3916,bool),hAPP(fun(U_3916,bool),fun(fun(U_3916,bool),fun(U_3916,bool)),semilattice_inf_inf(fun(U_3916,bool)),U_3913),U_3915)))
      | ~ hBOOL(hAPP(fun(U_3916,bool),bool,hAPP(U_3916,fun(fun(U_3916,bool),bool),member(U_3916),U_3914),U_3915))
      | ~ hBOOL(hAPP(fun(U_3916,bool),bool,hAPP(U_3916,fun(fun(U_3916,bool),bool),member(U_3916),U_3914),U_3913)) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

cnf(f_960_3,plain,
    ( hBOOL(hAPP(fun(U_3916,bool),bool,hAPP(U_3916,fun(fun(U_3916,bool),bool),member(U_3916),U_3914),hAPP(fun(U_3916,bool),fun(U_3916,bool),hAPP(fun(U_3916,bool),fun(fun(U_3916,bool),fun(U_3916,bool)),semilattice_inf_inf(fun(U_3916,bool)),U_3913),U_3915)))
    | ~ hBOOL(hAPP(fun(U_3916,bool),bool,hAPP(U_3916,fun(fun(U_3916,bool),bool),member(U_3916),U_3914),U_3915))
    | ~ hBOOL(hAPP(fun(U_3916,bool),bool,hAPP(U_3916,fun(fun(U_3916,bool),bool),member(U_3916),U_3914),U_3913)) ),
    inference(clausify,[status(thm)],[f_960_2]) ).

fof(f_961_1,plain,
    ! [X_a,B,A_1,X_2] :
      ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2))
      | ~ hBOOL(hAPP(X_a,bool,B,X_2))
      | ~ hBOOL(hAPP(X_a,bool,A_1,X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_871_inf1I]) ).

fof(f_961_2,plain,
    ! [U_3920,U_3919,U_3918,U_3917] :
      ( hBOOL(hAPP(U_3920,bool,hAPP(fun(U_3920,bool),fun(U_3920,bool),hAPP(fun(U_3920,bool),fun(fun(U_3920,bool),fun(U_3920,bool)),semilattice_inf_inf(fun(U_3920,bool)),U_3918),U_3919),U_3917))
      | ~ hBOOL(hAPP(U_3920,bool,U_3919,U_3917))
      | ~ hBOOL(hAPP(U_3920,bool,U_3918,U_3917)) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

cnf(f_961_3,plain,
    ( hBOOL(hAPP(U_3920,bool,hAPP(fun(U_3920,bool),fun(U_3920,bool),hAPP(fun(U_3920,bool),fun(fun(U_3920,bool),fun(U_3920,bool)),semilattice_inf_inf(fun(U_3920,bool)),U_3918),U_3919),U_3917))
    | ~ hBOOL(hAPP(U_3920,bool,U_3919,U_3917))
    | ~ hBOOL(hAPP(U_3920,bool,U_3918,U_3917)) ),
    inference(clausify,[status(thm)],[f_961_2]) ).

fof(f_962_1,plain,
    ! [X_a,G_1,Fa] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),Fa),G_1)))
      | ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),G_1))
        & ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_872_finite__Int]) ).

fof(f_962_2,plain,
    ! [U_3923,U_3922,U_3921] :
      ( hBOOL(hAPP(fun(U_3923,bool),bool,finite_finite_1(U_3923),hAPP(fun(U_3923,bool),fun(U_3923,bool),hAPP(fun(U_3923,bool),fun(fun(U_3923,bool),fun(U_3923,bool)),semilattice_inf_inf(fun(U_3923,bool)),U_3921),U_3922)))
      | ( ~ hBOOL(hAPP(fun(U_3923,bool),bool,finite_finite_1(U_3923),U_3922))
        & ~ hBOOL(hAPP(fun(U_3923,bool),bool,finite_finite_1(U_3923),U_3921)) ) ),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

cnf(f_962_3,plain,
    ( ~ hBOOL(hAPP(fun(U_3923,bool),bool,finite_finite_1(U_3923),U_3921))
    | hBOOL(hAPP(fun(U_3923,bool),bool,finite_finite_1(U_3923),hAPP(fun(U_3923,bool),fun(U_3923,bool),hAPP(fun(U_3923,bool),fun(fun(U_3923,bool),fun(U_3923,bool)),semilattice_inf_inf(fun(U_3923,bool)),U_3921),U_3922))) ),
    inference(clausify,[status(thm)],[f_962_2]) ).

cnf(f_962_4,plain,
    ( ~ hBOOL(hAPP(fun(U_3923,bool),bool,finite_finite_1(U_3923),U_3922))
    | hBOOL(hAPP(fun(U_3923,bool),bool,finite_finite_1(U_3923),hAPP(fun(U_3923,bool),fun(U_3923,bool),hAPP(fun(U_3923,bool),fun(fun(U_3923,bool),fun(U_3923,bool)),semilattice_inf_inf(fun(U_3923,bool)),U_3921),U_3922))) ),
    inference(clausify,[status(thm)],[f_962_2]) ).

fof(f_963_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z))))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_873_distrib__inf__le]) ).

fof(f_963_2,plain,
    ! [U_3927] :
      ( ! [U_3926,U_3925,U_3924] : hBOOL(hAPP(U_3927,bool,hAPP(U_3927,fun(U_3927,bool),ord_less_eq(U_3927),hAPP(U_3927,U_3927,hAPP(U_3927,fun(U_3927,U_3927),semilattice_sup_sup(U_3927),hAPP(U_3927,U_3927,hAPP(U_3927,fun(U_3927,U_3927),semilattice_inf_inf(U_3927),U_3926),U_3925)),hAPP(U_3927,U_3927,hAPP(U_3927,fun(U_3927,U_3927),semilattice_inf_inf(U_3927),U_3926),U_3924))),hAPP(U_3927,U_3927,hAPP(U_3927,fun(U_3927,U_3927),semilattice_inf_inf(U_3927),U_3926),hAPP(U_3927,U_3927,hAPP(U_3927,fun(U_3927,U_3927),semilattice_sup_sup(U_3927),U_3925),U_3924))))
      | ~ lattice(U_3927) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

cnf(f_963_3,plain,
    ( hBOOL(hAPP(U_3927,bool,hAPP(U_3927,fun(U_3927,bool),ord_less_eq(U_3927),hAPP(U_3927,U_3927,hAPP(U_3927,fun(U_3927,U_3927),semilattice_sup_sup(U_3927),hAPP(U_3927,U_3927,hAPP(U_3927,fun(U_3927,U_3927),semilattice_inf_inf(U_3927),U_3926),U_3925)),hAPP(U_3927,U_3927,hAPP(U_3927,fun(U_3927,U_3927),semilattice_inf_inf(U_3927),U_3926),U_3924))),hAPP(U_3927,U_3927,hAPP(U_3927,fun(U_3927,U_3927),semilattice_inf_inf(U_3927),U_3926),hAPP(U_3927,U_3927,hAPP(U_3927,fun(U_3927,U_3927),semilattice_sup_sup(U_3927),U_3925),U_3924))))
    | ~ lattice(U_3927) ),
    inference(clausify,[status(thm)],[f_963_2]) ).

fof(f_964_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z))))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_874_distrib__sup__le]) ).

fof(f_964_2,plain,
    ! [U_3931] :
      ( ! [U_3930,U_3929,U_3928] : hBOOL(hAPP(U_3931,bool,hAPP(U_3931,fun(U_3931,bool),ord_less_eq(U_3931),hAPP(U_3931,U_3931,hAPP(U_3931,fun(U_3931,U_3931),semilattice_sup_sup(U_3931),U_3930),hAPP(U_3931,U_3931,hAPP(U_3931,fun(U_3931,U_3931),semilattice_inf_inf(U_3931),U_3929),U_3928))),hAPP(U_3931,U_3931,hAPP(U_3931,fun(U_3931,U_3931),semilattice_inf_inf(U_3931),hAPP(U_3931,U_3931,hAPP(U_3931,fun(U_3931,U_3931),semilattice_sup_sup(U_3931),U_3930),U_3929)),hAPP(U_3931,U_3931,hAPP(U_3931,fun(U_3931,U_3931),semilattice_sup_sup(U_3931),U_3930),U_3928))))
      | ~ lattice(U_3931) ),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

cnf(f_964_3,plain,
    ( hBOOL(hAPP(U_3931,bool,hAPP(U_3931,fun(U_3931,bool),ord_less_eq(U_3931),hAPP(U_3931,U_3931,hAPP(U_3931,fun(U_3931,U_3931),semilattice_sup_sup(U_3931),U_3930),hAPP(U_3931,U_3931,hAPP(U_3931,fun(U_3931,U_3931),semilattice_inf_inf(U_3931),U_3929),U_3928))),hAPP(U_3931,U_3931,hAPP(U_3931,fun(U_3931,U_3931),semilattice_inf_inf(U_3931),hAPP(U_3931,U_3931,hAPP(U_3931,fun(U_3931,U_3931),semilattice_sup_sup(U_3931),U_3930),U_3929)),hAPP(U_3931,U_3931,hAPP(U_3931,fun(U_3931,U_3931),semilattice_sup_sup(U_3931),U_3930),U_3928))))
    | ~ lattice(U_3931) ),
    inference(clausify,[status(thm)],[f_964_2]) ).

fof(f_965_1,plain,
    ! [X_a,A_1,B,C] :
      ( ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C),A_1)) )
      & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C),A_1))
        | hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),C) != hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)) ) ),
    inference(fof_nnf,[status(thm)],[fact_875_Un__Int__assoc__eq]) ).

fof(f_965_2,plain,
    ! [U_3935,U_3934,U_3933,U_3932] :
      ( ( hAPP(fun(U_3935,bool),fun(U_3935,bool),hAPP(fun(U_3935,bool),fun(fun(U_3935,bool),fun(U_3935,bool)),semilattice_sup_sup(fun(U_3935,bool)),hAPP(fun(U_3935,bool),fun(U_3935,bool),hAPP(fun(U_3935,bool),fun(fun(U_3935,bool),fun(U_3935,bool)),semilattice_inf_inf(fun(U_3935,bool)),U_3934),U_3933)),U_3932) = hAPP(fun(U_3935,bool),fun(U_3935,bool),hAPP(fun(U_3935,bool),fun(fun(U_3935,bool),fun(U_3935,bool)),semilattice_inf_inf(fun(U_3935,bool)),U_3934),hAPP(fun(U_3935,bool),fun(U_3935,bool),hAPP(fun(U_3935,bool),fun(fun(U_3935,bool),fun(U_3935,bool)),semilattice_sup_sup(fun(U_3935,bool)),U_3933),U_3932))
        | ~ hBOOL(hAPP(fun(U_3935,bool),bool,hAPP(fun(U_3935,bool),fun(fun(U_3935,bool),bool),ord_less_eq(fun(U_3935,bool)),U_3932),U_3934)) )
      & ( hBOOL(hAPP(fun(U_3935,bool),bool,hAPP(fun(U_3935,bool),fun(fun(U_3935,bool),bool),ord_less_eq(fun(U_3935,bool)),U_3932),U_3934))
        | hAPP(fun(U_3935,bool),fun(U_3935,bool),hAPP(fun(U_3935,bool),fun(fun(U_3935,bool),fun(U_3935,bool)),semilattice_sup_sup(fun(U_3935,bool)),hAPP(fun(U_3935,bool),fun(U_3935,bool),hAPP(fun(U_3935,bool),fun(fun(U_3935,bool),fun(U_3935,bool)),semilattice_inf_inf(fun(U_3935,bool)),U_3934),U_3933)),U_3932) != hAPP(fun(U_3935,bool),fun(U_3935,bool),hAPP(fun(U_3935,bool),fun(fun(U_3935,bool),fun(U_3935,bool)),semilattice_inf_inf(fun(U_3935,bool)),U_3934),hAPP(fun(U_3935,bool),fun(U_3935,bool),hAPP(fun(U_3935,bool),fun(fun(U_3935,bool),fun(U_3935,bool)),semilattice_sup_sup(fun(U_3935,bool)),U_3933),U_3932)) ) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

fof(f_965_3,plain,
    ( ! [U_3943,U_3941,U_3939,U_3937] :
        ( hAPP(fun(U_3943,bool),fun(U_3943,bool),hAPP(fun(U_3943,bool),fun(fun(U_3943,bool),fun(U_3943,bool)),semilattice_sup_sup(fun(U_3943,bool)),hAPP(fun(U_3943,bool),fun(U_3943,bool),hAPP(fun(U_3943,bool),fun(fun(U_3943,bool),fun(U_3943,bool)),semilattice_inf_inf(fun(U_3943,bool)),U_3941),U_3939)),U_3937) = hAPP(fun(U_3943,bool),fun(U_3943,bool),hAPP(fun(U_3943,bool),fun(fun(U_3943,bool),fun(U_3943,bool)),semilattice_inf_inf(fun(U_3943,bool)),U_3941),hAPP(fun(U_3943,bool),fun(U_3943,bool),hAPP(fun(U_3943,bool),fun(fun(U_3943,bool),fun(U_3943,bool)),semilattice_sup_sup(fun(U_3943,bool)),U_3939),U_3937))
        | ~ hBOOL(hAPP(fun(U_3943,bool),bool,hAPP(fun(U_3943,bool),fun(fun(U_3943,bool),bool),ord_less_eq(fun(U_3943,bool)),U_3937),U_3941)) )
    & ! [U_3942,U_3940,U_3938,U_3936] :
        ( hBOOL(hAPP(fun(U_3942,bool),bool,hAPP(fun(U_3942,bool),fun(fun(U_3942,bool),bool),ord_less_eq(fun(U_3942,bool)),U_3936),U_3940))
        | hAPP(fun(U_3942,bool),fun(U_3942,bool),hAPP(fun(U_3942,bool),fun(fun(U_3942,bool),fun(U_3942,bool)),semilattice_sup_sup(fun(U_3942,bool)),hAPP(fun(U_3942,bool),fun(U_3942,bool),hAPP(fun(U_3942,bool),fun(fun(U_3942,bool),fun(U_3942,bool)),semilattice_inf_inf(fun(U_3942,bool)),U_3940),U_3938)),U_3936) != hAPP(fun(U_3942,bool),fun(U_3942,bool),hAPP(fun(U_3942,bool),fun(fun(U_3942,bool),fun(U_3942,bool)),semilattice_inf_inf(fun(U_3942,bool)),U_3940),hAPP(fun(U_3942,bool),fun(U_3942,bool),hAPP(fun(U_3942,bool),fun(fun(U_3942,bool),fun(U_3942,bool)),semilattice_sup_sup(fun(U_3942,bool)),U_3938),U_3936)) ) ),
    inference(miniscope,[status(thm)],[f_965_2]) ).

cnf(f_965_4,plain,
    ( hBOOL(hAPP(fun(U_3942,bool),bool,hAPP(fun(U_3942,bool),fun(fun(U_3942,bool),bool),ord_less_eq(fun(U_3942,bool)),U_3936),U_3940))
    | hAPP(fun(U_3942,bool),fun(U_3942,bool),hAPP(fun(U_3942,bool),fun(fun(U_3942,bool),fun(U_3942,bool)),semilattice_sup_sup(fun(U_3942,bool)),hAPP(fun(U_3942,bool),fun(U_3942,bool),hAPP(fun(U_3942,bool),fun(fun(U_3942,bool),fun(U_3942,bool)),semilattice_inf_inf(fun(U_3942,bool)),U_3940),U_3938)),U_3936) != hAPP(fun(U_3942,bool),fun(U_3942,bool),hAPP(fun(U_3942,bool),fun(fun(U_3942,bool),fun(U_3942,bool)),semilattice_inf_inf(fun(U_3942,bool)),U_3940),hAPP(fun(U_3942,bool),fun(U_3942,bool),hAPP(fun(U_3942,bool),fun(fun(U_3942,bool),fun(U_3942,bool)),semilattice_sup_sup(fun(U_3942,bool)),U_3938),U_3936)) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

cnf(f_965_5,plain,
    ( hAPP(fun(U_3943,bool),fun(U_3943,bool),hAPP(fun(U_3943,bool),fun(fun(U_3943,bool),fun(U_3943,bool)),semilattice_sup_sup(fun(U_3943,bool)),hAPP(fun(U_3943,bool),fun(U_3943,bool),hAPP(fun(U_3943,bool),fun(fun(U_3943,bool),fun(U_3943,bool)),semilattice_inf_inf(fun(U_3943,bool)),U_3941),U_3939)),U_3937) = hAPP(fun(U_3943,bool),fun(U_3943,bool),hAPP(fun(U_3943,bool),fun(fun(U_3943,bool),fun(U_3943,bool)),semilattice_inf_inf(fun(U_3943,bool)),U_3941),hAPP(fun(U_3943,bool),fun(U_3943,bool),hAPP(fun(U_3943,bool),fun(fun(U_3943,bool),fun(U_3943,bool)),semilattice_sup_sup(fun(U_3943,bool)),U_3939),U_3937))
    | ~ hBOOL(hAPP(fun(U_3943,bool),bool,hAPP(fun(U_3943,bool),fun(fun(U_3943,bool),bool),ord_less_eq(fun(U_3943,bool)),U_3937),U_3941)) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

fof(f_966_1,plain,
    ! [X_a] :
      ( ! [Y,Z,X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Z),X))
      | ~ distrib_lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_876_sup__inf__distrib2]) ).

fof(f_966_2,plain,
    ! [U_3947] :
      ( ! [U_3946,U_3945,U_3944] : hAPP(U_3947,U_3947,hAPP(U_3947,fun(U_3947,U_3947),semilattice_sup_sup(U_3947),hAPP(U_3947,U_3947,hAPP(U_3947,fun(U_3947,U_3947),semilattice_inf_inf(U_3947),U_3946),U_3945)),U_3944) = hAPP(U_3947,U_3947,hAPP(U_3947,fun(U_3947,U_3947),semilattice_inf_inf(U_3947),hAPP(U_3947,U_3947,hAPP(U_3947,fun(U_3947,U_3947),semilattice_sup_sup(U_3947),U_3946),U_3944)),hAPP(U_3947,U_3947,hAPP(U_3947,fun(U_3947,U_3947),semilattice_sup_sup(U_3947),U_3945),U_3944))
      | ~ distrib_lattice(U_3947) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

cnf(f_966_3,plain,
    ( hAPP(U_3947,U_3947,hAPP(U_3947,fun(U_3947,U_3947),semilattice_sup_sup(U_3947),hAPP(U_3947,U_3947,hAPP(U_3947,fun(U_3947,U_3947),semilattice_inf_inf(U_3947),U_3946),U_3945)),U_3944) = hAPP(U_3947,U_3947,hAPP(U_3947,fun(U_3947,U_3947),semilattice_inf_inf(U_3947),hAPP(U_3947,U_3947,hAPP(U_3947,fun(U_3947,U_3947),semilattice_sup_sup(U_3947),U_3946),U_3944)),hAPP(U_3947,U_3947,hAPP(U_3947,fun(U_3947,U_3947),semilattice_sup_sup(U_3947),U_3945),U_3944))
    | ~ distrib_lattice(U_3947) ),
    inference(clausify,[status(thm)],[f_966_2]) ).

fof(f_967_1,plain,
    ! [X_a] :
      ( ! [Y,Z,X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Z),X))
      | ~ distrib_lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_877_inf__sup__distrib2]) ).

fof(f_967_2,plain,
    ! [U_3951] :
      ( ! [U_3950,U_3949,U_3948] : hAPP(U_3951,U_3951,hAPP(U_3951,fun(U_3951,U_3951),semilattice_inf_inf(U_3951),hAPP(U_3951,U_3951,hAPP(U_3951,fun(U_3951,U_3951),semilattice_sup_sup(U_3951),U_3950),U_3949)),U_3948) = hAPP(U_3951,U_3951,hAPP(U_3951,fun(U_3951,U_3951),semilattice_sup_sup(U_3951),hAPP(U_3951,U_3951,hAPP(U_3951,fun(U_3951,U_3951),semilattice_inf_inf(U_3951),U_3950),U_3948)),hAPP(U_3951,U_3951,hAPP(U_3951,fun(U_3951,U_3951),semilattice_inf_inf(U_3951),U_3949),U_3948))
      | ~ distrib_lattice(U_3951) ),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

cnf(f_967_3,plain,
    ( hAPP(U_3951,U_3951,hAPP(U_3951,fun(U_3951,U_3951),semilattice_inf_inf(U_3951),hAPP(U_3951,U_3951,hAPP(U_3951,fun(U_3951,U_3951),semilattice_sup_sup(U_3951),U_3950),U_3949)),U_3948) = hAPP(U_3951,U_3951,hAPP(U_3951,fun(U_3951,U_3951),semilattice_sup_sup(U_3951),hAPP(U_3951,U_3951,hAPP(U_3951,fun(U_3951,U_3951),semilattice_inf_inf(U_3951),U_3950),U_3948)),hAPP(U_3951,U_3951,hAPP(U_3951,fun(U_3951,U_3951),semilattice_inf_inf(U_3951),U_3949),U_3948))
    | ~ distrib_lattice(U_3951) ),
    inference(clausify,[status(thm)],[f_967_2]) ).

fof(f_968_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z))
      | ~ distrib_lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_878_sup__inf__distrib1]) ).

fof(f_968_2,plain,
    ! [U_3955] :
      ( ! [U_3954,U_3953,U_3952] : hAPP(U_3955,U_3955,hAPP(U_3955,fun(U_3955,U_3955),semilattice_sup_sup(U_3955),U_3954),hAPP(U_3955,U_3955,hAPP(U_3955,fun(U_3955,U_3955),semilattice_inf_inf(U_3955),U_3953),U_3952)) = hAPP(U_3955,U_3955,hAPP(U_3955,fun(U_3955,U_3955),semilattice_inf_inf(U_3955),hAPP(U_3955,U_3955,hAPP(U_3955,fun(U_3955,U_3955),semilattice_sup_sup(U_3955),U_3954),U_3953)),hAPP(U_3955,U_3955,hAPP(U_3955,fun(U_3955,U_3955),semilattice_sup_sup(U_3955),U_3954),U_3952))
      | ~ distrib_lattice(U_3955) ),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

cnf(f_968_3,plain,
    ( hAPP(U_3955,U_3955,hAPP(U_3955,fun(U_3955,U_3955),semilattice_sup_sup(U_3955),U_3954),hAPP(U_3955,U_3955,hAPP(U_3955,fun(U_3955,U_3955),semilattice_inf_inf(U_3955),U_3953),U_3952)) = hAPP(U_3955,U_3955,hAPP(U_3955,fun(U_3955,U_3955),semilattice_inf_inf(U_3955),hAPP(U_3955,U_3955,hAPP(U_3955,fun(U_3955,U_3955),semilattice_sup_sup(U_3955),U_3954),U_3953)),hAPP(U_3955,U_3955,hAPP(U_3955,fun(U_3955,U_3955),semilattice_sup_sup(U_3955),U_3954),U_3952))
    | ~ distrib_lattice(U_3955) ),
    inference(clausify,[status(thm)],[f_968_2]) ).

fof(f_969_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z))
      | ~ distrib_lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_879_inf__sup__distrib1]) ).

fof(f_969_2,plain,
    ! [U_3959] :
      ( ! [U_3958,U_3957,U_3956] : hAPP(U_3959,U_3959,hAPP(U_3959,fun(U_3959,U_3959),semilattice_inf_inf(U_3959),U_3958),hAPP(U_3959,U_3959,hAPP(U_3959,fun(U_3959,U_3959),semilattice_sup_sup(U_3959),U_3957),U_3956)) = hAPP(U_3959,U_3959,hAPP(U_3959,fun(U_3959,U_3959),semilattice_sup_sup(U_3959),hAPP(U_3959,U_3959,hAPP(U_3959,fun(U_3959,U_3959),semilattice_inf_inf(U_3959),U_3958),U_3957)),hAPP(U_3959,U_3959,hAPP(U_3959,fun(U_3959,U_3959),semilattice_inf_inf(U_3959),U_3958),U_3956))
      | ~ distrib_lattice(U_3959) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

cnf(f_969_3,plain,
    ( hAPP(U_3959,U_3959,hAPP(U_3959,fun(U_3959,U_3959),semilattice_inf_inf(U_3959),U_3958),hAPP(U_3959,U_3959,hAPP(U_3959,fun(U_3959,U_3959),semilattice_sup_sup(U_3959),U_3957),U_3956)) = hAPP(U_3959,U_3959,hAPP(U_3959,fun(U_3959,U_3959),semilattice_sup_sup(U_3959),hAPP(U_3959,U_3959,hAPP(U_3959,fun(U_3959,U_3959),semilattice_inf_inf(U_3959),U_3958),U_3957)),hAPP(U_3959,U_3959,hAPP(U_3959,fun(U_3959,U_3959),semilattice_inf_inf(U_3959),U_3958),U_3956))
    | ~ distrib_lattice(U_3959) ),
    inference(clausify,[status(thm)],[f_969_2]) ).

fof(f_970_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)) = ti(X_a,X)
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_880_sup__inf__absorb]) ).

fof(f_970_2,plain,
    ! [U_3962] :
      ( ! [U_3961,U_3960] : hAPP(U_3962,U_3962,hAPP(U_3962,fun(U_3962,U_3962),semilattice_sup_sup(U_3962),U_3961),hAPP(U_3962,U_3962,hAPP(U_3962,fun(U_3962,U_3962),semilattice_inf_inf(U_3962),U_3961),U_3960)) = ti(U_3962,U_3961)
      | ~ lattice(U_3962) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

cnf(f_970_3,plain,
    ( hAPP(U_3962,U_3962,hAPP(U_3962,fun(U_3962,U_3962),semilattice_sup_sup(U_3962),U_3961),hAPP(U_3962,U_3962,hAPP(U_3962,fun(U_3962,U_3962),semilattice_inf_inf(U_3962),U_3961),U_3960)) = ti(U_3962,U_3961)
    | ~ lattice(U_3962) ),
    inference(clausify,[status(thm)],[f_970_2]) ).

fof(f_971_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)) = ti(X_a,X)
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_881_inf__sup__absorb]) ).

fof(f_971_2,plain,
    ! [U_3965] :
      ( ! [U_3964,U_3963] : hAPP(U_3965,U_3965,hAPP(U_3965,fun(U_3965,U_3965),semilattice_inf_inf(U_3965),U_3964),hAPP(U_3965,U_3965,hAPP(U_3965,fun(U_3965,U_3965),semilattice_sup_sup(U_3965),U_3964),U_3963)) = ti(U_3965,U_3964)
      | ~ lattice(U_3965) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

cnf(f_971_3,plain,
    ( hAPP(U_3965,U_3965,hAPP(U_3965,fun(U_3965,U_3965),semilattice_inf_inf(U_3965),U_3964),hAPP(U_3965,U_3965,hAPP(U_3965,fun(U_3965,U_3965),semilattice_sup_sup(U_3965),U_3964),U_3963)) = ti(U_3965,U_3964)
    | ~ lattice(U_3965) ),
    inference(clausify,[status(thm)],[f_971_2]) ).

fof(f_972_1,plain,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C)),
    inference(fof_nnf,[status(thm)],[fact_882_Int__Un__distrib]) ).

fof(f_972_2,plain,
    ! [U_3969,U_3968,U_3967,U_3966] : hAPP(fun(U_3969,bool),fun(U_3969,bool),hAPP(fun(U_3969,bool),fun(fun(U_3969,bool),fun(U_3969,bool)),semilattice_inf_inf(fun(U_3969,bool)),U_3968),hAPP(fun(U_3969,bool),fun(U_3969,bool),hAPP(fun(U_3969,bool),fun(fun(U_3969,bool),fun(U_3969,bool)),semilattice_sup_sup(fun(U_3969,bool)),U_3967),U_3966)) = hAPP(fun(U_3969,bool),fun(U_3969,bool),hAPP(fun(U_3969,bool),fun(fun(U_3969,bool),fun(U_3969,bool)),semilattice_sup_sup(fun(U_3969,bool)),hAPP(fun(U_3969,bool),fun(U_3969,bool),hAPP(fun(U_3969,bool),fun(fun(U_3969,bool),fun(U_3969,bool)),semilattice_inf_inf(fun(U_3969,bool)),U_3968),U_3967)),hAPP(fun(U_3969,bool),fun(U_3969,bool),hAPP(fun(U_3969,bool),fun(fun(U_3969,bool),fun(U_3969,bool)),semilattice_inf_inf(fun(U_3969,bool)),U_3968),U_3966)),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

cnf(f_972_3,plain,
    hAPP(fun(U_3969,bool),fun(U_3969,bool),hAPP(fun(U_3969,bool),fun(fun(U_3969,bool),fun(U_3969,bool)),semilattice_inf_inf(fun(U_3969,bool)),U_3968),hAPP(fun(U_3969,bool),fun(U_3969,bool),hAPP(fun(U_3969,bool),fun(fun(U_3969,bool),fun(U_3969,bool)),semilattice_sup_sup(fun(U_3969,bool)),U_3967),U_3966)) = hAPP(fun(U_3969,bool),fun(U_3969,bool),hAPP(fun(U_3969,bool),fun(fun(U_3969,bool),fun(U_3969,bool)),semilattice_sup_sup(fun(U_3969,bool)),hAPP(fun(U_3969,bool),fun(U_3969,bool),hAPP(fun(U_3969,bool),fun(fun(U_3969,bool),fun(U_3969,bool)),semilattice_inf_inf(fun(U_3969,bool)),U_3968),U_3967)),hAPP(fun(U_3969,bool),fun(U_3969,bool),hAPP(fun(U_3969,bool),fun(fun(U_3969,bool),fun(U_3969,bool)),semilattice_inf_inf(fun(U_3969,bool)),U_3968),U_3966)),
    inference(clausify,[status(thm)],[f_972_2]) ).

fof(f_973_1,plain,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),C)),
    inference(fof_nnf,[status(thm)],[fact_883_Un__Int__distrib]) ).

fof(f_973_2,plain,
    ! [U_3973,U_3972,U_3971,U_3970] : hAPP(fun(U_3973,bool),fun(U_3973,bool),hAPP(fun(U_3973,bool),fun(fun(U_3973,bool),fun(U_3973,bool)),semilattice_sup_sup(fun(U_3973,bool)),U_3972),hAPP(fun(U_3973,bool),fun(U_3973,bool),hAPP(fun(U_3973,bool),fun(fun(U_3973,bool),fun(U_3973,bool)),semilattice_inf_inf(fun(U_3973,bool)),U_3971),U_3970)) = hAPP(fun(U_3973,bool),fun(U_3973,bool),hAPP(fun(U_3973,bool),fun(fun(U_3973,bool),fun(U_3973,bool)),semilattice_inf_inf(fun(U_3973,bool)),hAPP(fun(U_3973,bool),fun(U_3973,bool),hAPP(fun(U_3973,bool),fun(fun(U_3973,bool),fun(U_3973,bool)),semilattice_sup_sup(fun(U_3973,bool)),U_3972),U_3971)),hAPP(fun(U_3973,bool),fun(U_3973,bool),hAPP(fun(U_3973,bool),fun(fun(U_3973,bool),fun(U_3973,bool)),semilattice_sup_sup(fun(U_3973,bool)),U_3972),U_3970)),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

cnf(f_973_3,plain,
    hAPP(fun(U_3973,bool),fun(U_3973,bool),hAPP(fun(U_3973,bool),fun(fun(U_3973,bool),fun(U_3973,bool)),semilattice_sup_sup(fun(U_3973,bool)),U_3972),hAPP(fun(U_3973,bool),fun(U_3973,bool),hAPP(fun(U_3973,bool),fun(fun(U_3973,bool),fun(U_3973,bool)),semilattice_inf_inf(fun(U_3973,bool)),U_3971),U_3970)) = hAPP(fun(U_3973,bool),fun(U_3973,bool),hAPP(fun(U_3973,bool),fun(fun(U_3973,bool),fun(U_3973,bool)),semilattice_inf_inf(fun(U_3973,bool)),hAPP(fun(U_3973,bool),fun(U_3973,bool),hAPP(fun(U_3973,bool),fun(fun(U_3973,bool),fun(U_3973,bool)),semilattice_sup_sup(fun(U_3973,bool)),U_3972),U_3971)),hAPP(fun(U_3973,bool),fun(U_3973,bool),hAPP(fun(U_3973,bool),fun(fun(U_3973,bool),fun(U_3973,bool)),semilattice_sup_sup(fun(U_3973,bool)),U_3972),U_3970)),
    inference(clausify,[status(thm)],[f_973_2]) ).

fof(f_974_1,plain,
    ! [X_a,B,C,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),A_1)),
    inference(fof_nnf,[status(thm)],[fact_884_Int__Un__distrib2]) ).

fof(f_974_2,plain,
    ! [U_3977,U_3976,U_3975,U_3974] : hAPP(fun(U_3977,bool),fun(U_3977,bool),hAPP(fun(U_3977,bool),fun(fun(U_3977,bool),fun(U_3977,bool)),semilattice_inf_inf(fun(U_3977,bool)),hAPP(fun(U_3977,bool),fun(U_3977,bool),hAPP(fun(U_3977,bool),fun(fun(U_3977,bool),fun(U_3977,bool)),semilattice_sup_sup(fun(U_3977,bool)),U_3976),U_3975)),U_3974) = hAPP(fun(U_3977,bool),fun(U_3977,bool),hAPP(fun(U_3977,bool),fun(fun(U_3977,bool),fun(U_3977,bool)),semilattice_sup_sup(fun(U_3977,bool)),hAPP(fun(U_3977,bool),fun(U_3977,bool),hAPP(fun(U_3977,bool),fun(fun(U_3977,bool),fun(U_3977,bool)),semilattice_inf_inf(fun(U_3977,bool)),U_3976),U_3974)),hAPP(fun(U_3977,bool),fun(U_3977,bool),hAPP(fun(U_3977,bool),fun(fun(U_3977,bool),fun(U_3977,bool)),semilattice_inf_inf(fun(U_3977,bool)),U_3975),U_3974)),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

cnf(f_974_3,plain,
    hAPP(fun(U_3977,bool),fun(U_3977,bool),hAPP(fun(U_3977,bool),fun(fun(U_3977,bool),fun(U_3977,bool)),semilattice_inf_inf(fun(U_3977,bool)),hAPP(fun(U_3977,bool),fun(U_3977,bool),hAPP(fun(U_3977,bool),fun(fun(U_3977,bool),fun(U_3977,bool)),semilattice_sup_sup(fun(U_3977,bool)),U_3976),U_3975)),U_3974) = hAPP(fun(U_3977,bool),fun(U_3977,bool),hAPP(fun(U_3977,bool),fun(fun(U_3977,bool),fun(U_3977,bool)),semilattice_sup_sup(fun(U_3977,bool)),hAPP(fun(U_3977,bool),fun(U_3977,bool),hAPP(fun(U_3977,bool),fun(fun(U_3977,bool),fun(U_3977,bool)),semilattice_inf_inf(fun(U_3977,bool)),U_3976),U_3974)),hAPP(fun(U_3977,bool),fun(U_3977,bool),hAPP(fun(U_3977,bool),fun(fun(U_3977,bool),fun(U_3977,bool)),semilattice_inf_inf(fun(U_3977,bool)),U_3975),U_3974)),
    inference(clausify,[status(thm)],[f_974_2]) ).

fof(f_975_1,plain,
    ! [X_a,B,C,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C),A_1)),
    inference(fof_nnf,[status(thm)],[fact_885_Un__Int__distrib2]) ).

fof(f_975_2,plain,
    ! [U_3981,U_3980,U_3979,U_3978] : hAPP(fun(U_3981,bool),fun(U_3981,bool),hAPP(fun(U_3981,bool),fun(fun(U_3981,bool),fun(U_3981,bool)),semilattice_sup_sup(fun(U_3981,bool)),hAPP(fun(U_3981,bool),fun(U_3981,bool),hAPP(fun(U_3981,bool),fun(fun(U_3981,bool),fun(U_3981,bool)),semilattice_inf_inf(fun(U_3981,bool)),U_3980),U_3979)),U_3978) = hAPP(fun(U_3981,bool),fun(U_3981,bool),hAPP(fun(U_3981,bool),fun(fun(U_3981,bool),fun(U_3981,bool)),semilattice_inf_inf(fun(U_3981,bool)),hAPP(fun(U_3981,bool),fun(U_3981,bool),hAPP(fun(U_3981,bool),fun(fun(U_3981,bool),fun(U_3981,bool)),semilattice_sup_sup(fun(U_3981,bool)),U_3980),U_3978)),hAPP(fun(U_3981,bool),fun(U_3981,bool),hAPP(fun(U_3981,bool),fun(fun(U_3981,bool),fun(U_3981,bool)),semilattice_sup_sup(fun(U_3981,bool)),U_3979),U_3978)),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

cnf(f_975_3,plain,
    hAPP(fun(U_3981,bool),fun(U_3981,bool),hAPP(fun(U_3981,bool),fun(fun(U_3981,bool),fun(U_3981,bool)),semilattice_sup_sup(fun(U_3981,bool)),hAPP(fun(U_3981,bool),fun(U_3981,bool),hAPP(fun(U_3981,bool),fun(fun(U_3981,bool),fun(U_3981,bool)),semilattice_inf_inf(fun(U_3981,bool)),U_3980),U_3979)),U_3978) = hAPP(fun(U_3981,bool),fun(U_3981,bool),hAPP(fun(U_3981,bool),fun(fun(U_3981,bool),fun(U_3981,bool)),semilattice_inf_inf(fun(U_3981,bool)),hAPP(fun(U_3981,bool),fun(U_3981,bool),hAPP(fun(U_3981,bool),fun(fun(U_3981,bool),fun(U_3981,bool)),semilattice_sup_sup(fun(U_3981,bool)),U_3980),U_3978)),hAPP(fun(U_3981,bool),fun(U_3981,bool),hAPP(fun(U_3981,bool),fun(fun(U_3981,bool),fun(U_3981,bool)),semilattice_sup_sup(fun(U_3981,bool)),U_3979),U_3978)),
    inference(clausify,[status(thm)],[f_975_2]) ).

fof(f_976_1,plain,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C),A_1)),
    inference(fof_nnf,[status(thm)],[fact_886_Un__Int__crazy]) ).

fof(f_976_2,plain,
    ! [U_3985,U_3984,U_3983,U_3982] : hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_sup_sup(fun(U_3985,bool)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_sup_sup(fun(U_3985,bool)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_inf_inf(fun(U_3985,bool)),U_3984),U_3983)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_inf_inf(fun(U_3985,bool)),U_3983),U_3982))),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_inf_inf(fun(U_3985,bool)),U_3982),U_3984)) = hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_inf_inf(fun(U_3985,bool)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_inf_inf(fun(U_3985,bool)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_sup_sup(fun(U_3985,bool)),U_3984),U_3983)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_sup_sup(fun(U_3985,bool)),U_3983),U_3982))),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_sup_sup(fun(U_3985,bool)),U_3982),U_3984)),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

cnf(f_976_3,plain,
    hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_sup_sup(fun(U_3985,bool)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_sup_sup(fun(U_3985,bool)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_inf_inf(fun(U_3985,bool)),U_3984),U_3983)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_inf_inf(fun(U_3985,bool)),U_3983),U_3982))),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_inf_inf(fun(U_3985,bool)),U_3982),U_3984)) = hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_inf_inf(fun(U_3985,bool)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_inf_inf(fun(U_3985,bool)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_sup_sup(fun(U_3985,bool)),U_3984),U_3983)),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_sup_sup(fun(U_3985,bool)),U_3983),U_3982))),hAPP(fun(U_3985,bool),fun(U_3985,bool),hAPP(fun(U_3985,bool),fun(fun(U_3985,bool),fun(U_3985,bool)),semilattice_sup_sup(fun(U_3985,bool)),U_3982),U_3984)),
    inference(clausify,[status(thm)],[f_976_2]) ).

fof(f_977_1,plain,
    ! [X_b,X_a,Pa,F,G,S] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_b,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combs(X_b,X_a,fun(X_a,X_a)),hAPP(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),X_b),if(X_a)),Pa)),F)),G)),S) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),S),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),S),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),Pa))))),
    inference(fof_nnf,[status(thm)],[fact_887_if__image__distrib]) ).

fof(f_977_2,plain,
    ! [U_3991,U_3990,U_3989,U_3988,U_3987,U_3986] : hAPP(fun(U_3991,bool),fun(U_3990,bool),hAPP(fun(U_3991,U_3990),fun(fun(U_3991,bool),fun(U_3990,bool)),image(U_3991,U_3990),hAPP(fun(U_3991,U_3990),fun(U_3991,U_3990),hAPP(fun(U_3991,fun(U_3990,U_3990)),fun(fun(U_3991,U_3990),fun(U_3991,U_3990)),combs(U_3991,U_3990,U_3990),hAPP(fun(U_3991,U_3990),fun(U_3991,fun(U_3990,U_3990)),hAPP(fun(U_3991,fun(U_3990,fun(U_3990,U_3990))),fun(fun(U_3991,U_3990),fun(U_3991,fun(U_3990,U_3990))),combs(U_3991,U_3990,fun(U_3990,U_3990)),hAPP(fun(U_3991,bool),fun(U_3991,fun(U_3990,fun(U_3990,U_3990))),hAPP(fun(bool,fun(U_3990,fun(U_3990,U_3990))),fun(fun(U_3991,bool),fun(U_3991,fun(U_3990,fun(U_3990,U_3990)))),combb(bool,fun(U_3990,fun(U_3990,U_3990)),U_3991),if(U_3990)),U_3989)),U_3988)),U_3987)),U_3986) = hAPP(fun(U_3990,bool),fun(U_3990,bool),hAPP(fun(U_3990,bool),fun(fun(U_3990,bool),fun(U_3990,bool)),semilattice_sup_sup(fun(U_3990,bool)),hAPP(fun(U_3991,bool),fun(U_3990,bool),hAPP(fun(U_3991,U_3990),fun(fun(U_3991,bool),fun(U_3990,bool)),image(U_3991,U_3990),U_3988),hAPP(fun(U_3991,bool),fun(U_3991,bool),hAPP(fun(U_3991,bool),fun(fun(U_3991,bool),fun(U_3991,bool)),semilattice_inf_inf(fun(U_3991,bool)),U_3986),hAPP(fun(U_3991,bool),fun(U_3991,bool),collect(U_3991),U_3989)))),hAPP(fun(U_3991,bool),fun(U_3990,bool),hAPP(fun(U_3991,U_3990),fun(fun(U_3991,bool),fun(U_3990,bool)),image(U_3991,U_3990),U_3987),hAPP(fun(U_3991,bool),fun(U_3991,bool),hAPP(fun(U_3991,bool),fun(fun(U_3991,bool),fun(U_3991,bool)),semilattice_inf_inf(fun(U_3991,bool)),U_3986),hAPP(fun(U_3991,bool),fun(U_3991,bool),collect(U_3991),hAPP(fun(U_3991,bool),fun(U_3991,bool),hAPP(fun(bool,bool),fun(fun(U_3991,bool),fun(U_3991,bool)),combb(bool,bool,U_3991),fNot),U_3989))))),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

cnf(f_977_3,plain,
    hAPP(fun(U_3991,bool),fun(U_3990,bool),hAPP(fun(U_3991,U_3990),fun(fun(U_3991,bool),fun(U_3990,bool)),image(U_3991,U_3990),hAPP(fun(U_3991,U_3990),fun(U_3991,U_3990),hAPP(fun(U_3991,fun(U_3990,U_3990)),fun(fun(U_3991,U_3990),fun(U_3991,U_3990)),combs(U_3991,U_3990,U_3990),hAPP(fun(U_3991,U_3990),fun(U_3991,fun(U_3990,U_3990)),hAPP(fun(U_3991,fun(U_3990,fun(U_3990,U_3990))),fun(fun(U_3991,U_3990),fun(U_3991,fun(U_3990,U_3990))),combs(U_3991,U_3990,fun(U_3990,U_3990)),hAPP(fun(U_3991,bool),fun(U_3991,fun(U_3990,fun(U_3990,U_3990))),hAPP(fun(bool,fun(U_3990,fun(U_3990,U_3990))),fun(fun(U_3991,bool),fun(U_3991,fun(U_3990,fun(U_3990,U_3990)))),combb(bool,fun(U_3990,fun(U_3990,U_3990)),U_3991),if(U_3990)),U_3989)),U_3988)),U_3987)),U_3986) = hAPP(fun(U_3990,bool),fun(U_3990,bool),hAPP(fun(U_3990,bool),fun(fun(U_3990,bool),fun(U_3990,bool)),semilattice_sup_sup(fun(U_3990,bool)),hAPP(fun(U_3991,bool),fun(U_3990,bool),hAPP(fun(U_3991,U_3990),fun(fun(U_3991,bool),fun(U_3990,bool)),image(U_3991,U_3990),U_3988),hAPP(fun(U_3991,bool),fun(U_3991,bool),hAPP(fun(U_3991,bool),fun(fun(U_3991,bool),fun(U_3991,bool)),semilattice_inf_inf(fun(U_3991,bool)),U_3986),hAPP(fun(U_3991,bool),fun(U_3991,bool),collect(U_3991),U_3989)))),hAPP(fun(U_3991,bool),fun(U_3990,bool),hAPP(fun(U_3991,U_3990),fun(fun(U_3991,bool),fun(U_3990,bool)),image(U_3991,U_3990),U_3987),hAPP(fun(U_3991,bool),fun(U_3991,bool),hAPP(fun(U_3991,bool),fun(fun(U_3991,bool),fun(U_3991,bool)),semilattice_inf_inf(fun(U_3991,bool)),U_3986),hAPP(fun(U_3991,bool),fun(U_3991,bool),collect(U_3991),hAPP(fun(U_3991,bool),fun(U_3991,bool),hAPP(fun(bool,bool),fun(fun(U_3991,bool),fun(U_3991,bool)),combb(bool,bool,U_3991),fNot),U_3989))))),
    inference(clausify,[status(thm)],[f_977_2]) ).

fof(f_978_1,plain,
    ! [X_a] :
      ( ! [F,M,K,Na] : hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na))
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_888_setsum__shift__bounds__cl__nat__ivl]) ).

fof(f_978_2,plain,
    ! [U_3996] :
      ( ! [U_3995,U_3994,U_3993,U_3992] : hAPP(fun(nat,bool),U_3996,hAPP(fun(nat,U_3996),fun(fun(nat,bool),U_3996),big_co1399186613setsum(nat,U_3996),U_3995),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3994),U_3993)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3992),U_3993))) = hAPP(fun(nat,bool),U_3996,hAPP(fun(nat,U_3996),fun(fun(nat,bool),U_3996),big_co1399186613setsum(nat,U_3996),hAPP(fun(nat,nat),fun(nat,U_3996),hAPP(fun(nat,U_3996),fun(fun(nat,nat),fun(nat,U_3996)),combb(nat,U_3996,nat),U_3995),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),U_3993))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3994),U_3992))
      | ~ comm_monoid_add(U_3996) ),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

cnf(f_978_3,plain,
    ( hAPP(fun(nat,bool),U_3996,hAPP(fun(nat,U_3996),fun(fun(nat,bool),U_3996),big_co1399186613setsum(nat,U_3996),U_3995),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3994),U_3993)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_3992),U_3993))) = hAPP(fun(nat,bool),U_3996,hAPP(fun(nat,U_3996),fun(fun(nat,bool),U_3996),big_co1399186613setsum(nat,U_3996),hAPP(fun(nat,nat),fun(nat,U_3996),hAPP(fun(nat,U_3996),fun(fun(nat,nat),fun(nat,U_3996)),combb(nat,U_3996,nat),U_3995),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),U_3993))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3994),U_3992))
    | ~ comm_monoid_add(U_3996) ),
    inference(clausify,[status(thm)],[f_978_2]) ).

fof(f_979_1,plain,
    ! [X_a] :
      ( ! [F,M,Na] : hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na))
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_889_setsum__shift__bounds__cl__Suc__ivl]) ).

fof(f_979_2,plain,
    ! [U_4000] :
      ( ! [U_3999,U_3998,U_3997] : hAPP(fun(nat,bool),U_4000,hAPP(fun(nat,U_4000),fun(fun(nat,bool),U_4000),big_co1399186613setsum(nat,U_4000),U_3999),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,U_3998)),hAPP(nat,nat,suc,U_3997))) = hAPP(fun(nat,bool),U_4000,hAPP(fun(nat,U_4000),fun(fun(nat,bool),U_4000),big_co1399186613setsum(nat,U_4000),hAPP(fun(nat,nat),fun(nat,U_4000),hAPP(fun(nat,U_4000),fun(fun(nat,nat),fun(nat,U_4000)),combb(nat,U_4000,nat),U_3999),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3998),U_3997))
      | ~ comm_monoid_add(U_4000) ),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

cnf(f_979_3,plain,
    ( hAPP(fun(nat,bool),U_4000,hAPP(fun(nat,U_4000),fun(fun(nat,bool),U_4000),big_co1399186613setsum(nat,U_4000),U_3999),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,U_3998)),hAPP(nat,nat,suc,U_3997))) = hAPP(fun(nat,bool),U_4000,hAPP(fun(nat,U_4000),fun(fun(nat,bool),U_4000),big_co1399186613setsum(nat,U_4000),hAPP(fun(nat,nat),fun(nat,U_4000),hAPP(fun(nat,U_4000),fun(fun(nat,nat),fun(nat,U_4000)),combb(nat,U_4000,nat),U_3999),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_3998),U_3997))
    | ~ comm_monoid_add(U_4000) ),
    inference(clausify,[status(thm)],[f_979_2]) ).

fof(f_980_1,plain,
    ! [X_a] :
      ( ! [F,M,K,Na] : hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Na))
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_890_setsum__shift__bounds__nat__ivl]) ).

fof(f_980_2,plain,
    ! [U_4005] :
      ( ! [U_4004,U_4003,U_4002,U_4001] : hAPP(fun(nat,bool),U_4005,hAPP(fun(nat,U_4005),fun(fun(nat,bool),U_4005),big_co1399186613setsum(nat,U_4005),U_4004),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_4003),U_4002)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_4001),U_4002))) = hAPP(fun(nat,bool),U_4005,hAPP(fun(nat,U_4005),fun(fun(nat,bool),U_4005),big_co1399186613setsum(nat,U_4005),hAPP(fun(nat,nat),fun(nat,U_4005),hAPP(fun(nat,U_4005),fun(fun(nat,nat),fun(nat,U_4005)),combb(nat,U_4005,nat),U_4004),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),U_4002))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4003),U_4001))
      | ~ comm_monoid_add(U_4005) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

cnf(f_980_3,plain,
    ( hAPP(fun(nat,bool),U_4005,hAPP(fun(nat,U_4005),fun(fun(nat,bool),U_4005),big_co1399186613setsum(nat,U_4005),U_4004),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_4003),U_4002)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_4001),U_4002))) = hAPP(fun(nat,bool),U_4005,hAPP(fun(nat,U_4005),fun(fun(nat,bool),U_4005),big_co1399186613setsum(nat,U_4005),hAPP(fun(nat,nat),fun(nat,U_4005),hAPP(fun(nat,U_4005),fun(fun(nat,nat),fun(nat,U_4005)),combb(nat,U_4005,nat),U_4004),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),U_4002))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4003),U_4001))
    | ~ comm_monoid_add(U_4005) ),
    inference(clausify,[status(thm)],[f_980_2]) ).

fof(f_981_1,plain,
    ! [X_c,X_a,X_b] :
      ( ! [G,F,S] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),S) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,X_b),hAPP(fun(fun(X_a,bool),X_b),fun(fun(X_c,fun(X_a,bool)),fun(X_c,X_b)),combb(fun(X_a,bool),X_b,X_c),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),collect(X_a)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_c,bool)),fun(X_c,fun(X_a,bool)),combc(X_a,X_c,bool),hAPP(fun(X_a,X_c),fun(X_a,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_a,X_c),fun(X_a,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_a),fequal(X_c)),F)))))),hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),F),S))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_891_setsum__image__gen]) ).

fof(f_981_2,plain,
    ! [U_4011,U_4010,U_4009] :
      ( ! [U_4008,U_4007,U_4006] :
          ( hAPP(fun(U_4010,bool),U_4009,hAPP(fun(U_4010,U_4009),fun(fun(U_4010,bool),U_4009),big_co1399186613setsum(U_4010,U_4009),U_4008),U_4006) = hAPP(fun(U_4011,bool),U_4009,hAPP(fun(U_4011,U_4009),fun(fun(U_4011,bool),U_4009),big_co1399186613setsum(U_4011,U_4009),hAPP(fun(U_4011,fun(U_4010,bool)),fun(U_4011,U_4009),hAPP(fun(fun(U_4010,bool),U_4009),fun(fun(U_4011,fun(U_4010,bool)),fun(U_4011,U_4009)),combb(fun(U_4010,bool),U_4009,U_4011),hAPP(fun(U_4010,U_4009),fun(fun(U_4010,bool),U_4009),big_co1399186613setsum(U_4010,U_4009),U_4008)),hAPP(fun(U_4011,fun(U_4010,bool)),fun(U_4011,fun(U_4010,bool)),hAPP(fun(fun(U_4010,bool),fun(U_4010,bool)),fun(fun(U_4011,fun(U_4010,bool)),fun(U_4011,fun(U_4010,bool))),combb(fun(U_4010,bool),fun(U_4010,bool),U_4011),collect(U_4010)),hAPP(fun(U_4011,fun(U_4010,bool)),fun(U_4011,fun(U_4010,bool)),hAPP(fun(fun(U_4010,bool),fun(U_4010,bool)),fun(fun(U_4011,fun(U_4010,bool)),fun(U_4011,fun(U_4010,bool))),combb(fun(U_4010,bool),fun(U_4010,bool),U_4011),hAPP(fun(U_4010,fun(bool,bool)),fun(fun(U_4010,bool),fun(U_4010,bool)),combs(U_4010,bool,bool),hAPP(fun(U_4010,bool),fun(U_4010,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4010,bool),fun(U_4010,fun(bool,bool))),combb(bool,fun(bool,bool),U_4010),fconj),hAPP(fun(U_4010,bool),fun(U_4010,bool),hAPP(fun(U_4010,fun(fun(U_4010,bool),bool)),fun(fun(U_4010,bool),fun(U_4010,bool)),combc(U_4010,fun(U_4010,bool),bool),member(U_4010)),U_4006)))),hAPP(fun(U_4010,fun(U_4011,bool)),fun(U_4011,fun(U_4010,bool)),combc(U_4010,U_4011,bool),hAPP(fun(U_4010,U_4011),fun(U_4010,fun(U_4011,bool)),hAPP(fun(U_4011,fun(U_4011,bool)),fun(fun(U_4010,U_4011),fun(U_4010,fun(U_4011,bool))),combb(U_4011,fun(U_4011,bool),U_4010),fequal(U_4011)),U_4007)))))),hAPP(fun(U_4010,bool),fun(U_4011,bool),hAPP(fun(U_4010,U_4011),fun(fun(U_4010,bool),fun(U_4011,bool)),image(U_4010,U_4011),U_4007),U_4006))
          | ~ hBOOL(hAPP(fun(U_4010,bool),bool,finite_finite_1(U_4010),U_4006)) )
      | ~ comm_monoid_add(U_4009) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

cnf(f_981_3,plain,
    ( hAPP(fun(U_4010,bool),U_4009,hAPP(fun(U_4010,U_4009),fun(fun(U_4010,bool),U_4009),big_co1399186613setsum(U_4010,U_4009),U_4008),U_4006) = hAPP(fun(U_4011,bool),U_4009,hAPP(fun(U_4011,U_4009),fun(fun(U_4011,bool),U_4009),big_co1399186613setsum(U_4011,U_4009),hAPP(fun(U_4011,fun(U_4010,bool)),fun(U_4011,U_4009),hAPP(fun(fun(U_4010,bool),U_4009),fun(fun(U_4011,fun(U_4010,bool)),fun(U_4011,U_4009)),combb(fun(U_4010,bool),U_4009,U_4011),hAPP(fun(U_4010,U_4009),fun(fun(U_4010,bool),U_4009),big_co1399186613setsum(U_4010,U_4009),U_4008)),hAPP(fun(U_4011,fun(U_4010,bool)),fun(U_4011,fun(U_4010,bool)),hAPP(fun(fun(U_4010,bool),fun(U_4010,bool)),fun(fun(U_4011,fun(U_4010,bool)),fun(U_4011,fun(U_4010,bool))),combb(fun(U_4010,bool),fun(U_4010,bool),U_4011),collect(U_4010)),hAPP(fun(U_4011,fun(U_4010,bool)),fun(U_4011,fun(U_4010,bool)),hAPP(fun(fun(U_4010,bool),fun(U_4010,bool)),fun(fun(U_4011,fun(U_4010,bool)),fun(U_4011,fun(U_4010,bool))),combb(fun(U_4010,bool),fun(U_4010,bool),U_4011),hAPP(fun(U_4010,fun(bool,bool)),fun(fun(U_4010,bool),fun(U_4010,bool)),combs(U_4010,bool,bool),hAPP(fun(U_4010,bool),fun(U_4010,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4010,bool),fun(U_4010,fun(bool,bool))),combb(bool,fun(bool,bool),U_4010),fconj),hAPP(fun(U_4010,bool),fun(U_4010,bool),hAPP(fun(U_4010,fun(fun(U_4010,bool),bool)),fun(fun(U_4010,bool),fun(U_4010,bool)),combc(U_4010,fun(U_4010,bool),bool),member(U_4010)),U_4006)))),hAPP(fun(U_4010,fun(U_4011,bool)),fun(U_4011,fun(U_4010,bool)),combc(U_4010,U_4011,bool),hAPP(fun(U_4010,U_4011),fun(U_4010,fun(U_4011,bool)),hAPP(fun(U_4011,fun(U_4011,bool)),fun(fun(U_4010,U_4011),fun(U_4010,fun(U_4011,bool))),combb(U_4011,fun(U_4011,bool),U_4010),fequal(U_4011)),U_4007)))))),hAPP(fun(U_4010,bool),fun(U_4011,bool),hAPP(fun(U_4010,U_4011),fun(fun(U_4010,bool),fun(U_4011,bool)),image(U_4010,U_4011),U_4007),U_4006))
    | ~ hBOOL(hAPP(fun(U_4010,bool),bool,finite_finite_1(U_4010),U_4006))
    | ~ comm_monoid_add(U_4009) ),
    inference(clausify,[status(thm)],[f_981_2]) ).

fof(f_982_1,plain,
    ! [X_b,X_a,X_c] :
      ( ! [F,R_2,T_3,S] :
          ( hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,X_c),hAPP(fun(X_a,fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,X_c)),combs(X_a,fun(X_b,bool),X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c)),hAPP(fun(fun(X_b,X_c),fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c))),combb(fun(X_b,X_c),fun(fun(X_b,bool),X_c),X_a),big_co1399186613setsum(X_b,X_c)),F)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),T_3)))),R_2)))),S) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,X_c)),combs(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),collect(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_2))))),T_3)
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_3))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) )
      | ~ comm_monoid_add(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_892_setsum__setsum__restrict]) ).

fof(f_982_2,plain,
    ! [U_4018,U_4017,U_4016] :
      ( ! [U_4015,U_4014,U_4013,U_4012] :
          ( hAPP(fun(U_4017,bool),U_4016,hAPP(fun(U_4017,U_4016),fun(fun(U_4017,bool),U_4016),big_co1399186613setsum(U_4017,U_4016),hAPP(fun(U_4017,fun(U_4018,bool)),fun(U_4017,U_4016),hAPP(fun(U_4017,fun(fun(U_4018,bool),U_4016)),fun(fun(U_4017,fun(U_4018,bool)),fun(U_4017,U_4016)),combs(U_4017,fun(U_4018,bool),U_4016),hAPP(fun(U_4017,fun(U_4018,U_4016)),fun(U_4017,fun(fun(U_4018,bool),U_4016)),hAPP(fun(fun(U_4018,U_4016),fun(fun(U_4018,bool),U_4016)),fun(fun(U_4017,fun(U_4018,U_4016)),fun(U_4017,fun(fun(U_4018,bool),U_4016))),combb(fun(U_4018,U_4016),fun(fun(U_4018,bool),U_4016),U_4017),big_co1399186613setsum(U_4018,U_4016)),U_4015)),hAPP(fun(U_4017,fun(U_4018,bool)),fun(U_4017,fun(U_4018,bool)),hAPP(fun(fun(U_4018,bool),fun(U_4018,bool)),fun(fun(U_4017,fun(U_4018,bool)),fun(U_4017,fun(U_4018,bool))),combb(fun(U_4018,bool),fun(U_4018,bool),U_4017),collect(U_4018)),hAPP(fun(U_4017,fun(U_4018,bool)),fun(U_4017,fun(U_4018,bool)),hAPP(fun(fun(U_4018,bool),fun(U_4018,bool)),fun(fun(U_4017,fun(U_4018,bool)),fun(U_4017,fun(U_4018,bool))),combb(fun(U_4018,bool),fun(U_4018,bool),U_4017),hAPP(fun(U_4018,fun(bool,bool)),fun(fun(U_4018,bool),fun(U_4018,bool)),combs(U_4018,bool,bool),hAPP(fun(U_4018,bool),fun(U_4018,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4018,bool),fun(U_4018,fun(bool,bool))),combb(bool,fun(bool,bool),U_4018),fconj),hAPP(fun(U_4018,bool),fun(U_4018,bool),hAPP(fun(U_4018,fun(fun(U_4018,bool),bool)),fun(fun(U_4018,bool),fun(U_4018,bool)),combc(U_4018,fun(U_4018,bool),bool),member(U_4018)),U_4013)))),U_4014)))),U_4012) = hAPP(fun(U_4018,bool),U_4016,hAPP(fun(U_4018,U_4016),fun(fun(U_4018,bool),U_4016),big_co1399186613setsum(U_4018,U_4016),hAPP(fun(U_4018,fun(U_4017,bool)),fun(U_4018,U_4016),hAPP(fun(U_4018,fun(fun(U_4017,bool),U_4016)),fun(fun(U_4018,fun(U_4017,bool)),fun(U_4018,U_4016)),combs(U_4018,fun(U_4017,bool),U_4016),hAPP(fun(U_4018,fun(U_4017,U_4016)),fun(U_4018,fun(fun(U_4017,bool),U_4016)),hAPP(fun(fun(U_4017,U_4016),fun(fun(U_4017,bool),U_4016)),fun(fun(U_4018,fun(U_4017,U_4016)),fun(U_4018,fun(fun(U_4017,bool),U_4016))),combb(fun(U_4017,U_4016),fun(fun(U_4017,bool),U_4016),U_4018),big_co1399186613setsum(U_4017,U_4016)),hAPP(fun(U_4017,fun(U_4018,U_4016)),fun(U_4018,fun(U_4017,U_4016)),combc(U_4017,U_4018,U_4016),U_4015))),hAPP(fun(U_4018,fun(U_4017,bool)),fun(U_4018,fun(U_4017,bool)),hAPP(fun(fun(U_4017,bool),fun(U_4017,bool)),fun(fun(U_4018,fun(U_4017,bool)),fun(U_4018,fun(U_4017,bool))),combb(fun(U_4017,bool),fun(U_4017,bool),U_4018),collect(U_4017)),hAPP(fun(U_4018,fun(U_4017,bool)),fun(U_4018,fun(U_4017,bool)),hAPP(fun(fun(U_4017,bool),fun(U_4017,bool)),fun(fun(U_4018,fun(U_4017,bool)),fun(U_4018,fun(U_4017,bool))),combb(fun(U_4017,bool),fun(U_4017,bool),U_4018),hAPP(fun(U_4017,fun(bool,bool)),fun(fun(U_4017,bool),fun(U_4017,bool)),combs(U_4017,bool,bool),hAPP(fun(U_4017,bool),fun(U_4017,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4017,bool),fun(U_4017,fun(bool,bool))),combb(bool,fun(bool,bool),U_4017),fconj),hAPP(fun(U_4017,bool),fun(U_4017,bool),hAPP(fun(U_4017,fun(fun(U_4017,bool),bool)),fun(fun(U_4017,bool),fun(U_4017,bool)),combc(U_4017,fun(U_4017,bool),bool),member(U_4017)),U_4012)))),hAPP(fun(U_4017,fun(U_4018,bool)),fun(U_4018,fun(U_4017,bool)),combc(U_4017,U_4018,bool),U_4014))))),U_4013)
          | ~ hBOOL(hAPP(fun(U_4018,bool),bool,finite_finite_1(U_4018),U_4013))
          | ~ hBOOL(hAPP(fun(U_4017,bool),bool,finite_finite_1(U_4017),U_4012)) )
      | ~ comm_monoid_add(U_4016) ),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

cnf(f_982_3,plain,
    ( hAPP(fun(U_4017,bool),U_4016,hAPP(fun(U_4017,U_4016),fun(fun(U_4017,bool),U_4016),big_co1399186613setsum(U_4017,U_4016),hAPP(fun(U_4017,fun(U_4018,bool)),fun(U_4017,U_4016),hAPP(fun(U_4017,fun(fun(U_4018,bool),U_4016)),fun(fun(U_4017,fun(U_4018,bool)),fun(U_4017,U_4016)),combs(U_4017,fun(U_4018,bool),U_4016),hAPP(fun(U_4017,fun(U_4018,U_4016)),fun(U_4017,fun(fun(U_4018,bool),U_4016)),hAPP(fun(fun(U_4018,U_4016),fun(fun(U_4018,bool),U_4016)),fun(fun(U_4017,fun(U_4018,U_4016)),fun(U_4017,fun(fun(U_4018,bool),U_4016))),combb(fun(U_4018,U_4016),fun(fun(U_4018,bool),U_4016),U_4017),big_co1399186613setsum(U_4018,U_4016)),U_4015)),hAPP(fun(U_4017,fun(U_4018,bool)),fun(U_4017,fun(U_4018,bool)),hAPP(fun(fun(U_4018,bool),fun(U_4018,bool)),fun(fun(U_4017,fun(U_4018,bool)),fun(U_4017,fun(U_4018,bool))),combb(fun(U_4018,bool),fun(U_4018,bool),U_4017),collect(U_4018)),hAPP(fun(U_4017,fun(U_4018,bool)),fun(U_4017,fun(U_4018,bool)),hAPP(fun(fun(U_4018,bool),fun(U_4018,bool)),fun(fun(U_4017,fun(U_4018,bool)),fun(U_4017,fun(U_4018,bool))),combb(fun(U_4018,bool),fun(U_4018,bool),U_4017),hAPP(fun(U_4018,fun(bool,bool)),fun(fun(U_4018,bool),fun(U_4018,bool)),combs(U_4018,bool,bool),hAPP(fun(U_4018,bool),fun(U_4018,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4018,bool),fun(U_4018,fun(bool,bool))),combb(bool,fun(bool,bool),U_4018),fconj),hAPP(fun(U_4018,bool),fun(U_4018,bool),hAPP(fun(U_4018,fun(fun(U_4018,bool),bool)),fun(fun(U_4018,bool),fun(U_4018,bool)),combc(U_4018,fun(U_4018,bool),bool),member(U_4018)),U_4013)))),U_4014)))),U_4012) = hAPP(fun(U_4018,bool),U_4016,hAPP(fun(U_4018,U_4016),fun(fun(U_4018,bool),U_4016),big_co1399186613setsum(U_4018,U_4016),hAPP(fun(U_4018,fun(U_4017,bool)),fun(U_4018,U_4016),hAPP(fun(U_4018,fun(fun(U_4017,bool),U_4016)),fun(fun(U_4018,fun(U_4017,bool)),fun(U_4018,U_4016)),combs(U_4018,fun(U_4017,bool),U_4016),hAPP(fun(U_4018,fun(U_4017,U_4016)),fun(U_4018,fun(fun(U_4017,bool),U_4016)),hAPP(fun(fun(U_4017,U_4016),fun(fun(U_4017,bool),U_4016)),fun(fun(U_4018,fun(U_4017,U_4016)),fun(U_4018,fun(fun(U_4017,bool),U_4016))),combb(fun(U_4017,U_4016),fun(fun(U_4017,bool),U_4016),U_4018),big_co1399186613setsum(U_4017,U_4016)),hAPP(fun(U_4017,fun(U_4018,U_4016)),fun(U_4018,fun(U_4017,U_4016)),combc(U_4017,U_4018,U_4016),U_4015))),hAPP(fun(U_4018,fun(U_4017,bool)),fun(U_4018,fun(U_4017,bool)),hAPP(fun(fun(U_4017,bool),fun(U_4017,bool)),fun(fun(U_4018,fun(U_4017,bool)),fun(U_4018,fun(U_4017,bool))),combb(fun(U_4017,bool),fun(U_4017,bool),U_4018),collect(U_4017)),hAPP(fun(U_4018,fun(U_4017,bool)),fun(U_4018,fun(U_4017,bool)),hAPP(fun(fun(U_4017,bool),fun(U_4017,bool)),fun(fun(U_4018,fun(U_4017,bool)),fun(U_4018,fun(U_4017,bool))),combb(fun(U_4017,bool),fun(U_4017,bool),U_4018),hAPP(fun(U_4017,fun(bool,bool)),fun(fun(U_4017,bool),fun(U_4017,bool)),combs(U_4017,bool,bool),hAPP(fun(U_4017,bool),fun(U_4017,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4017,bool),fun(U_4017,fun(bool,bool))),combb(bool,fun(bool,bool),U_4017),fconj),hAPP(fun(U_4017,bool),fun(U_4017,bool),hAPP(fun(U_4017,fun(fun(U_4017,bool),bool)),fun(fun(U_4017,bool),fun(U_4017,bool)),combc(U_4017,fun(U_4017,bool),bool),member(U_4017)),U_4012)))),hAPP(fun(U_4017,fun(U_4018,bool)),fun(U_4018,fun(U_4017,bool)),combc(U_4017,U_4018,bool),U_4014))))),U_4013)
    | ~ hBOOL(hAPP(fun(U_4018,bool),bool,finite_finite_1(U_4018),U_4013))
    | ~ hBOOL(hAPP(fun(U_4017,bool),bool,finite_finite_1(U_4017),U_4012))
    | ~ comm_monoid_add(U_4016) ),
    inference(clausify,[status(thm)],[f_982_2]) ).

fof(f_983_1,plain,
    ! [X_a,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),top_top(fun(X_a,bool))) = ti(fun(X_a,bool),A_1),
    inference(fof_nnf,[status(thm)],[fact_893_Int__UNIV__right]) ).

fof(f_983_2,plain,
    ! [U_4020,U_4019] : hAPP(fun(U_4020,bool),fun(U_4020,bool),hAPP(fun(U_4020,bool),fun(fun(U_4020,bool),fun(U_4020,bool)),semilattice_inf_inf(fun(U_4020,bool)),U_4019),top_top(fun(U_4020,bool))) = ti(fun(U_4020,bool),U_4019),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

cnf(f_983_3,plain,
    hAPP(fun(U_4020,bool),fun(U_4020,bool),hAPP(fun(U_4020,bool),fun(fun(U_4020,bool),fun(U_4020,bool)),semilattice_inf_inf(fun(U_4020,bool)),U_4019),top_top(fun(U_4020,bool))) = ti(fun(U_4020,bool),U_4019),
    inference(clausify,[status(thm)],[f_983_2]) ).

fof(f_984_1,plain,
    ! [X_a,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),top_top(fun(X_a,bool))),B) = ti(fun(X_a,bool),B),
    inference(fof_nnf,[status(thm)],[fact_894_Int__UNIV__left]) ).

fof(f_984_2,plain,
    ! [U_4022,U_4021] : hAPP(fun(U_4022,bool),fun(U_4022,bool),hAPP(fun(U_4022,bool),fun(fun(U_4022,bool),fun(U_4022,bool)),semilattice_inf_inf(fun(U_4022,bool)),top_top(fun(U_4022,bool))),U_4021) = ti(fun(U_4022,bool),U_4021),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

cnf(f_984_3,plain,
    hAPP(fun(U_4022,bool),fun(U_4022,bool),hAPP(fun(U_4022,bool),fun(fun(U_4022,bool),fun(U_4022,bool)),semilattice_inf_inf(fun(U_4022,bool)),top_top(fun(U_4022,bool))),U_4021) = ti(fun(U_4022,bool),U_4021),
    inference(clausify,[status(thm)],[f_984_2]) ).

fof(f_985_1,plain,
    ! [X_a,Pa,Q_1] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),Pa)),Q_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)),
    inference(fof_nnf,[status(thm)],[fact_895_Collect__conj__eq]) ).

fof(f_985_2,plain,
    ! [U_4025,U_4024,U_4023] : hAPP(fun(U_4025,bool),fun(U_4025,bool),collect(U_4025),hAPP(fun(U_4025,bool),fun(U_4025,bool),hAPP(fun(U_4025,fun(bool,bool)),fun(fun(U_4025,bool),fun(U_4025,bool)),combs(U_4025,bool,bool),hAPP(fun(U_4025,bool),fun(U_4025,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4025,bool),fun(U_4025,fun(bool,bool))),combb(bool,fun(bool,bool),U_4025),fconj),U_4024)),U_4023)) = hAPP(fun(U_4025,bool),fun(U_4025,bool),hAPP(fun(U_4025,bool),fun(fun(U_4025,bool),fun(U_4025,bool)),semilattice_inf_inf(fun(U_4025,bool)),hAPP(fun(U_4025,bool),fun(U_4025,bool),collect(U_4025),U_4024)),hAPP(fun(U_4025,bool),fun(U_4025,bool),collect(U_4025),U_4023)),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

cnf(f_985_3,plain,
    hAPP(fun(U_4025,bool),fun(U_4025,bool),collect(U_4025),hAPP(fun(U_4025,bool),fun(U_4025,bool),hAPP(fun(U_4025,fun(bool,bool)),fun(fun(U_4025,bool),fun(U_4025,bool)),combs(U_4025,bool,bool),hAPP(fun(U_4025,bool),fun(U_4025,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4025,bool),fun(U_4025,fun(bool,bool))),combb(bool,fun(bool,bool),U_4025),fconj),U_4024)),U_4023)) = hAPP(fun(U_4025,bool),fun(U_4025,bool),hAPP(fun(U_4025,bool),fun(fun(U_4025,bool),fun(U_4025,bool)),semilattice_inf_inf(fun(U_4025,bool)),hAPP(fun(U_4025,bool),fun(U_4025,bool),collect(U_4025),U_4024)),hAPP(fun(U_4025,bool),fun(U_4025,bool),collect(U_4025),U_4023)),
    inference(clausify,[status(thm)],[f_985_2]) ).

fof(f_986_1,plain,
    ! [X_a,X_2,A_1,Pa] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa))))
        | ~ hBOOL(hAPP(X_a,bool,Pa,X_2))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) )
      & ( ( hBOOL(hAPP(X_a,bool,Pa,X_2))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) )
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_896_Int__Collect]) ).

fof(f_986_2,plain,
    ! [U_4029,U_4028,U_4027,U_4026] :
      ( ( hBOOL(hAPP(fun(U_4029,bool),bool,hAPP(U_4029,fun(fun(U_4029,bool),bool),member(U_4029),U_4028),hAPP(fun(U_4029,bool),fun(U_4029,bool),hAPP(fun(U_4029,bool),fun(fun(U_4029,bool),fun(U_4029,bool)),semilattice_inf_inf(fun(U_4029,bool)),U_4027),hAPP(fun(U_4029,bool),fun(U_4029,bool),collect(U_4029),U_4026))))
        | ~ hBOOL(hAPP(U_4029,bool,U_4026,U_4028))
        | ~ hBOOL(hAPP(fun(U_4029,bool),bool,hAPP(U_4029,fun(fun(U_4029,bool),bool),member(U_4029),U_4028),U_4027)) )
      & ( ( hBOOL(hAPP(U_4029,bool,U_4026,U_4028))
          & hBOOL(hAPP(fun(U_4029,bool),bool,hAPP(U_4029,fun(fun(U_4029,bool),bool),member(U_4029),U_4028),U_4027)) )
        | ~ hBOOL(hAPP(fun(U_4029,bool),bool,hAPP(U_4029,fun(fun(U_4029,bool),bool),member(U_4029),U_4028),hAPP(fun(U_4029,bool),fun(U_4029,bool),hAPP(fun(U_4029,bool),fun(fun(U_4029,bool),fun(U_4029,bool)),semilattice_inf_inf(fun(U_4029,bool)),U_4027),hAPP(fun(U_4029,bool),fun(U_4029,bool),collect(U_4029),U_4026)))) ) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

fof(f_986_3,plain,
    ( ! [U_4037,U_4035,U_4033,U_4031] :
        ( hBOOL(hAPP(fun(U_4037,bool),bool,hAPP(U_4037,fun(fun(U_4037,bool),bool),member(U_4037),U_4035),hAPP(fun(U_4037,bool),fun(U_4037,bool),hAPP(fun(U_4037,bool),fun(fun(U_4037,bool),fun(U_4037,bool)),semilattice_inf_inf(fun(U_4037,bool)),U_4033),hAPP(fun(U_4037,bool),fun(U_4037,bool),collect(U_4037),U_4031))))
        | ~ hBOOL(hAPP(U_4037,bool,U_4031,U_4035))
        | ~ hBOOL(hAPP(fun(U_4037,bool),bool,hAPP(U_4037,fun(fun(U_4037,bool),bool),member(U_4037),U_4035),U_4033)) )
    & ! [U_4036,U_4034,U_4032,U_4030] :
        ( ( hBOOL(hAPP(U_4036,bool,U_4030,U_4034))
          & hBOOL(hAPP(fun(U_4036,bool),bool,hAPP(U_4036,fun(fun(U_4036,bool),bool),member(U_4036),U_4034),U_4032)) )
        | ~ hBOOL(hAPP(fun(U_4036,bool),bool,hAPP(U_4036,fun(fun(U_4036,bool),bool),member(U_4036),U_4034),hAPP(fun(U_4036,bool),fun(U_4036,bool),hAPP(fun(U_4036,bool),fun(fun(U_4036,bool),fun(U_4036,bool)),semilattice_inf_inf(fun(U_4036,bool)),U_4032),hAPP(fun(U_4036,bool),fun(U_4036,bool),collect(U_4036),U_4030)))) ) ),
    inference(miniscope,[status(thm)],[f_986_2]) ).

cnf(f_986_4,plain,
    ( hBOOL(hAPP(fun(U_4036,bool),bool,hAPP(U_4036,fun(fun(U_4036,bool),bool),member(U_4036),U_4034),U_4032))
    | ~ hBOOL(hAPP(fun(U_4036,bool),bool,hAPP(U_4036,fun(fun(U_4036,bool),bool),member(U_4036),U_4034),hAPP(fun(U_4036,bool),fun(U_4036,bool),hAPP(fun(U_4036,bool),fun(fun(U_4036,bool),fun(U_4036,bool)),semilattice_inf_inf(fun(U_4036,bool)),U_4032),hAPP(fun(U_4036,bool),fun(U_4036,bool),collect(U_4036),U_4030)))) ),
    inference(clausify,[status(thm)],[f_986_3]) ).

cnf(f_986_5,plain,
    ( hBOOL(hAPP(U_4036,bool,U_4030,U_4034))
    | ~ hBOOL(hAPP(fun(U_4036,bool),bool,hAPP(U_4036,fun(fun(U_4036,bool),bool),member(U_4036),U_4034),hAPP(fun(U_4036,bool),fun(U_4036,bool),hAPP(fun(U_4036,bool),fun(fun(U_4036,bool),fun(U_4036,bool)),semilattice_inf_inf(fun(U_4036,bool)),U_4032),hAPP(fun(U_4036,bool),fun(U_4036,bool),collect(U_4036),U_4030)))) ),
    inference(clausify,[status(thm)],[f_986_3]) ).

cnf(f_986_6,plain,
    ( hBOOL(hAPP(fun(U_4037,bool),bool,hAPP(U_4037,fun(fun(U_4037,bool),bool),member(U_4037),U_4035),hAPP(fun(U_4037,bool),fun(U_4037,bool),hAPP(fun(U_4037,bool),fun(fun(U_4037,bool),fun(U_4037,bool)),semilattice_inf_inf(fun(U_4037,bool)),U_4033),hAPP(fun(U_4037,bool),fun(U_4037,bool),collect(U_4037),U_4031))))
    | ~ hBOOL(hAPP(U_4037,bool,U_4031,U_4035))
    | ~ hBOOL(hAPP(fun(U_4037,bool),bool,hAPP(U_4037,fun(fun(U_4037,bool),bool),member(U_4037),U_4035),U_4033)) ),
    inference(clausify,[status(thm)],[f_986_3]) ).

fof(f_987_1,plain,
    ! [X_a,R_2,S,X_1] :
      ( ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)),X_1))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),R_2),S))) )
      & ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),R_2),S)))
        | ~ hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)),X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_897_inf__Int__eq]) ).

fof(f_987_2,plain,
    ! [U_4041,U_4040,U_4039,U_4038] :
      ( ( hBOOL(hAPP(U_4041,bool,hAPP(fun(U_4041,bool),fun(U_4041,bool),hAPP(fun(U_4041,bool),fun(fun(U_4041,bool),fun(U_4041,bool)),semilattice_inf_inf(fun(U_4041,bool)),hAPP(fun(U_4041,bool),fun(U_4041,bool),hAPP(fun(U_4041,fun(fun(U_4041,bool),bool)),fun(fun(U_4041,bool),fun(U_4041,bool)),combc(U_4041,fun(U_4041,bool),bool),member(U_4041)),U_4040)),hAPP(fun(U_4041,bool),fun(U_4041,bool),hAPP(fun(U_4041,fun(fun(U_4041,bool),bool)),fun(fun(U_4041,bool),fun(U_4041,bool)),combc(U_4041,fun(U_4041,bool),bool),member(U_4041)),U_4039)),U_4038))
        | ~ hBOOL(hAPP(fun(U_4041,bool),bool,hAPP(U_4041,fun(fun(U_4041,bool),bool),member(U_4041),U_4038),hAPP(fun(U_4041,bool),fun(U_4041,bool),hAPP(fun(U_4041,bool),fun(fun(U_4041,bool),fun(U_4041,bool)),semilattice_inf_inf(fun(U_4041,bool)),U_4040),U_4039))) )
      & ( hBOOL(hAPP(fun(U_4041,bool),bool,hAPP(U_4041,fun(fun(U_4041,bool),bool),member(U_4041),U_4038),hAPP(fun(U_4041,bool),fun(U_4041,bool),hAPP(fun(U_4041,bool),fun(fun(U_4041,bool),fun(U_4041,bool)),semilattice_inf_inf(fun(U_4041,bool)),U_4040),U_4039)))
        | ~ hBOOL(hAPP(U_4041,bool,hAPP(fun(U_4041,bool),fun(U_4041,bool),hAPP(fun(U_4041,bool),fun(fun(U_4041,bool),fun(U_4041,bool)),semilattice_inf_inf(fun(U_4041,bool)),hAPP(fun(U_4041,bool),fun(U_4041,bool),hAPP(fun(U_4041,fun(fun(U_4041,bool),bool)),fun(fun(U_4041,bool),fun(U_4041,bool)),combc(U_4041,fun(U_4041,bool),bool),member(U_4041)),U_4040)),hAPP(fun(U_4041,bool),fun(U_4041,bool),hAPP(fun(U_4041,fun(fun(U_4041,bool),bool)),fun(fun(U_4041,bool),fun(U_4041,bool)),combc(U_4041,fun(U_4041,bool),bool),member(U_4041)),U_4039)),U_4038)) ) ),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

fof(f_987_3,plain,
    ( ! [U_4049,U_4047,U_4045,U_4043] :
        ( hBOOL(hAPP(U_4049,bool,hAPP(fun(U_4049,bool),fun(U_4049,bool),hAPP(fun(U_4049,bool),fun(fun(U_4049,bool),fun(U_4049,bool)),semilattice_inf_inf(fun(U_4049,bool)),hAPP(fun(U_4049,bool),fun(U_4049,bool),hAPP(fun(U_4049,fun(fun(U_4049,bool),bool)),fun(fun(U_4049,bool),fun(U_4049,bool)),combc(U_4049,fun(U_4049,bool),bool),member(U_4049)),U_4047)),hAPP(fun(U_4049,bool),fun(U_4049,bool),hAPP(fun(U_4049,fun(fun(U_4049,bool),bool)),fun(fun(U_4049,bool),fun(U_4049,bool)),combc(U_4049,fun(U_4049,bool),bool),member(U_4049)),U_4045)),U_4043))
        | ~ hBOOL(hAPP(fun(U_4049,bool),bool,hAPP(U_4049,fun(fun(U_4049,bool),bool),member(U_4049),U_4043),hAPP(fun(U_4049,bool),fun(U_4049,bool),hAPP(fun(U_4049,bool),fun(fun(U_4049,bool),fun(U_4049,bool)),semilattice_inf_inf(fun(U_4049,bool)),U_4047),U_4045))) )
    & ! [U_4048,U_4046,U_4044,U_4042] :
        ( hBOOL(hAPP(fun(U_4048,bool),bool,hAPP(U_4048,fun(fun(U_4048,bool),bool),member(U_4048),U_4042),hAPP(fun(U_4048,bool),fun(U_4048,bool),hAPP(fun(U_4048,bool),fun(fun(U_4048,bool),fun(U_4048,bool)),semilattice_inf_inf(fun(U_4048,bool)),U_4046),U_4044)))
        | ~ hBOOL(hAPP(U_4048,bool,hAPP(fun(U_4048,bool),fun(U_4048,bool),hAPP(fun(U_4048,bool),fun(fun(U_4048,bool),fun(U_4048,bool)),semilattice_inf_inf(fun(U_4048,bool)),hAPP(fun(U_4048,bool),fun(U_4048,bool),hAPP(fun(U_4048,fun(fun(U_4048,bool),bool)),fun(fun(U_4048,bool),fun(U_4048,bool)),combc(U_4048,fun(U_4048,bool),bool),member(U_4048)),U_4046)),hAPP(fun(U_4048,bool),fun(U_4048,bool),hAPP(fun(U_4048,fun(fun(U_4048,bool),bool)),fun(fun(U_4048,bool),fun(U_4048,bool)),combc(U_4048,fun(U_4048,bool),bool),member(U_4048)),U_4044)),U_4042)) ) ),
    inference(miniscope,[status(thm)],[f_987_2]) ).

cnf(f_987_4,plain,
    ( hBOOL(hAPP(fun(U_4048,bool),bool,hAPP(U_4048,fun(fun(U_4048,bool),bool),member(U_4048),U_4042),hAPP(fun(U_4048,bool),fun(U_4048,bool),hAPP(fun(U_4048,bool),fun(fun(U_4048,bool),fun(U_4048,bool)),semilattice_inf_inf(fun(U_4048,bool)),U_4046),U_4044)))
    | ~ hBOOL(hAPP(U_4048,bool,hAPP(fun(U_4048,bool),fun(U_4048,bool),hAPP(fun(U_4048,bool),fun(fun(U_4048,bool),fun(U_4048,bool)),semilattice_inf_inf(fun(U_4048,bool)),hAPP(fun(U_4048,bool),fun(U_4048,bool),hAPP(fun(U_4048,fun(fun(U_4048,bool),bool)),fun(fun(U_4048,bool),fun(U_4048,bool)),combc(U_4048,fun(U_4048,bool),bool),member(U_4048)),U_4046)),hAPP(fun(U_4048,bool),fun(U_4048,bool),hAPP(fun(U_4048,fun(fun(U_4048,bool),bool)),fun(fun(U_4048,bool),fun(U_4048,bool)),combc(U_4048,fun(U_4048,bool),bool),member(U_4048)),U_4044)),U_4042)) ),
    inference(clausify,[status(thm)],[f_987_3]) ).

cnf(f_987_5,plain,
    ( hBOOL(hAPP(U_4049,bool,hAPP(fun(U_4049,bool),fun(U_4049,bool),hAPP(fun(U_4049,bool),fun(fun(U_4049,bool),fun(U_4049,bool)),semilattice_inf_inf(fun(U_4049,bool)),hAPP(fun(U_4049,bool),fun(U_4049,bool),hAPP(fun(U_4049,fun(fun(U_4049,bool),bool)),fun(fun(U_4049,bool),fun(U_4049,bool)),combc(U_4049,fun(U_4049,bool),bool),member(U_4049)),U_4047)),hAPP(fun(U_4049,bool),fun(U_4049,bool),hAPP(fun(U_4049,fun(fun(U_4049,bool),bool)),fun(fun(U_4049,bool),fun(U_4049,bool)),combc(U_4049,fun(U_4049,bool),bool),member(U_4049)),U_4045)),U_4043))
    | ~ hBOOL(hAPP(fun(U_4049,bool),bool,hAPP(U_4049,fun(fun(U_4049,bool),bool),member(U_4049),U_4043),hAPP(fun(U_4049,bool),fun(U_4049,bool),hAPP(fun(U_4049,bool),fun(fun(U_4049,bool),fun(U_4049,bool)),semilattice_inf_inf(fun(U_4049,bool)),U_4047),U_4045))) ),
    inference(clausify,[status(thm)],[f_987_3]) ).

fof(f_988_1,plain,
    ! [X_a,A_1,B,X_2] :
      ( hBOOL(hAPP(X_a,bool,B,X_2))
      | ~ hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_898_inf1D2]) ).

fof(f_988_2,plain,
    ! [U_4053,U_4052,U_4051,U_4050] :
      ( hBOOL(hAPP(U_4053,bool,U_4051,U_4050))
      | ~ hBOOL(hAPP(U_4053,bool,hAPP(fun(U_4053,bool),fun(U_4053,bool),hAPP(fun(U_4053,bool),fun(fun(U_4053,bool),fun(U_4053,bool)),semilattice_inf_inf(fun(U_4053,bool)),U_4052),U_4051),U_4050)) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

cnf(f_988_3,plain,
    ( hBOOL(hAPP(U_4053,bool,U_4051,U_4050))
    | ~ hBOOL(hAPP(U_4053,bool,hAPP(fun(U_4053,bool),fun(U_4053,bool),hAPP(fun(U_4053,bool),fun(fun(U_4053,bool),fun(U_4053,bool)),semilattice_inf_inf(fun(U_4053,bool)),U_4052),U_4051),U_4050)) ),
    inference(clausify,[status(thm)],[f_988_2]) ).

fof(f_989_1,plain,
    ! [X_a,A_1,B,X_2] :
      ( hBOOL(hAPP(X_a,bool,A_1,X_2))
      | ~ hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_899_inf1D1]) ).

fof(f_989_2,plain,
    ! [U_4057,U_4056,U_4055,U_4054] :
      ( hBOOL(hAPP(U_4057,bool,U_4056,U_4054))
      | ~ hBOOL(hAPP(U_4057,bool,hAPP(fun(U_4057,bool),fun(U_4057,bool),hAPP(fun(U_4057,bool),fun(fun(U_4057,bool),fun(U_4057,bool)),semilattice_inf_inf(fun(U_4057,bool)),U_4056),U_4055),U_4054)) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

cnf(f_989_3,plain,
    ( hBOOL(hAPP(U_4057,bool,U_4056,U_4054))
    | ~ hBOOL(hAPP(U_4057,bool,hAPP(fun(U_4057,bool),fun(U_4057,bool),hAPP(fun(U_4057,bool),fun(fun(U_4057,bool),fun(U_4057,bool)),semilattice_inf_inf(fun(U_4057,bool)),U_4056),U_4055),U_4054)) ),
    inference(clausify,[status(thm)],[f_989_2]) ).

fof(f_990_1,plain,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) ),
    inference(fof_nnf,[status(thm)],[fact_900_IntD2]) ).

fof(f_990_2,plain,
    ! [U_4061,U_4060,U_4059,U_4058] :
      ( hBOOL(hAPP(fun(U_4061,bool),bool,hAPP(U_4061,fun(fun(U_4061,bool),bool),member(U_4061),U_4060),U_4058))
      | ~ hBOOL(hAPP(fun(U_4061,bool),bool,hAPP(U_4061,fun(fun(U_4061,bool),bool),member(U_4061),U_4060),hAPP(fun(U_4061,bool),fun(U_4061,bool),hAPP(fun(U_4061,bool),fun(fun(U_4061,bool),fun(U_4061,bool)),semilattice_inf_inf(fun(U_4061,bool)),U_4059),U_4058))) ),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

cnf(f_990_3,plain,
    ( hBOOL(hAPP(fun(U_4061,bool),bool,hAPP(U_4061,fun(fun(U_4061,bool),bool),member(U_4061),U_4060),U_4058))
    | ~ hBOOL(hAPP(fun(U_4061,bool),bool,hAPP(U_4061,fun(fun(U_4061,bool),bool),member(U_4061),U_4060),hAPP(fun(U_4061,bool),fun(U_4061,bool),hAPP(fun(U_4061,bool),fun(fun(U_4061,bool),fun(U_4061,bool)),semilattice_inf_inf(fun(U_4061,bool)),U_4059),U_4058))) ),
    inference(clausify,[status(thm)],[f_990_2]) ).

fof(f_991_1,plain,
    ! [X_a,Ca,A_1,B] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) ),
    inference(fof_nnf,[status(thm)],[fact_901_IntD1]) ).

fof(f_991_2,plain,
    ! [U_4065,U_4064,U_4063,U_4062] :
      ( hBOOL(hAPP(fun(U_4065,bool),bool,hAPP(U_4065,fun(fun(U_4065,bool),bool),member(U_4065),U_4064),U_4063))
      | ~ hBOOL(hAPP(fun(U_4065,bool),bool,hAPP(U_4065,fun(fun(U_4065,bool),bool),member(U_4065),U_4064),hAPP(fun(U_4065,bool),fun(U_4065,bool),hAPP(fun(U_4065,bool),fun(fun(U_4065,bool),fun(U_4065,bool)),semilattice_inf_inf(fun(U_4065,bool)),U_4063),U_4062))) ),
    inference(variable_rename,[status(thm)],[f_991_1]) ).

fof(f_991_3,plain,
    ! [U_4065,U_4064,U_4063] :
      ( ! [U_4062] : ~ hBOOL(hAPP(fun(U_4065,bool),bool,hAPP(U_4065,fun(fun(U_4065,bool),bool),member(U_4065),U_4064),hAPP(fun(U_4065,bool),fun(U_4065,bool),hAPP(fun(U_4065,bool),fun(fun(U_4065,bool),fun(U_4065,bool)),semilattice_inf_inf(fun(U_4065,bool)),U_4063),U_4062)))
      | hBOOL(hAPP(fun(U_4065,bool),bool,hAPP(U_4065,fun(fun(U_4065,bool),bool),member(U_4065),U_4064),U_4063)) ),
    inference(miniscope,[status(thm)],[f_991_2]) ).

cnf(f_991_4,plain,
    ( ~ hBOOL(hAPP(fun(U_4065,bool),bool,hAPP(U_4065,fun(fun(U_4065,bool),bool),member(U_4065),U_4064),hAPP(fun(U_4065,bool),fun(U_4065,bool),hAPP(fun(U_4065,bool),fun(fun(U_4065,bool),fun(U_4065,bool)),semilattice_inf_inf(fun(U_4065,bool)),U_4063),U_4062)))
    | hBOOL(hAPP(fun(U_4065,bool),bool,hAPP(U_4065,fun(fun(U_4065,bool),bool),member(U_4065),U_4064),U_4063)) ),
    inference(clausify,[status(thm)],[f_991_3]) ).

fof(f_992_1,plain,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)),
    inference(fof_nnf,[status(thm)],[fact_902_Int__assoc]) ).

fof(f_992_2,plain,
    ! [U_4069,U_4068,U_4067,U_4066] : hAPP(fun(U_4069,bool),fun(U_4069,bool),hAPP(fun(U_4069,bool),fun(fun(U_4069,bool),fun(U_4069,bool)),semilattice_inf_inf(fun(U_4069,bool)),hAPP(fun(U_4069,bool),fun(U_4069,bool),hAPP(fun(U_4069,bool),fun(fun(U_4069,bool),fun(U_4069,bool)),semilattice_inf_inf(fun(U_4069,bool)),U_4068),U_4067)),U_4066) = hAPP(fun(U_4069,bool),fun(U_4069,bool),hAPP(fun(U_4069,bool),fun(fun(U_4069,bool),fun(U_4069,bool)),semilattice_inf_inf(fun(U_4069,bool)),U_4068),hAPP(fun(U_4069,bool),fun(U_4069,bool),hAPP(fun(U_4069,bool),fun(fun(U_4069,bool),fun(U_4069,bool)),semilattice_inf_inf(fun(U_4069,bool)),U_4067),U_4066)),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

cnf(f_992_3,plain,
    hAPP(fun(U_4069,bool),fun(U_4069,bool),hAPP(fun(U_4069,bool),fun(fun(U_4069,bool),fun(U_4069,bool)),semilattice_inf_inf(fun(U_4069,bool)),hAPP(fun(U_4069,bool),fun(U_4069,bool),hAPP(fun(U_4069,bool),fun(fun(U_4069,bool),fun(U_4069,bool)),semilattice_inf_inf(fun(U_4069,bool)),U_4068),U_4067)),U_4066) = hAPP(fun(U_4069,bool),fun(U_4069,bool),hAPP(fun(U_4069,bool),fun(fun(U_4069,bool),fun(U_4069,bool)),semilattice_inf_inf(fun(U_4069,bool)),U_4068),hAPP(fun(U_4069,bool),fun(U_4069,bool),hAPP(fun(U_4069,bool),fun(fun(U_4069,bool),fun(U_4069,bool)),semilattice_inf_inf(fun(U_4069,bool)),U_4067),U_4066)),
    inference(clausify,[status(thm)],[f_992_2]) ).

fof(f_993_1,plain,
    ! [X_a,Ca,A_1,B] :
      ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) )
      & ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))
          & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) )
        | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_903_Int__iff]) ).

fof(f_993_2,plain,
    ! [U_4073,U_4072,U_4071,U_4070] :
      ( ( hBOOL(hAPP(fun(U_4073,bool),bool,hAPP(U_4073,fun(fun(U_4073,bool),bool),member(U_4073),U_4072),hAPP(fun(U_4073,bool),fun(U_4073,bool),hAPP(fun(U_4073,bool),fun(fun(U_4073,bool),fun(U_4073,bool)),semilattice_inf_inf(fun(U_4073,bool)),U_4071),U_4070)))
        | ~ hBOOL(hAPP(fun(U_4073,bool),bool,hAPP(U_4073,fun(fun(U_4073,bool),bool),member(U_4073),U_4072),U_4070))
        | ~ hBOOL(hAPP(fun(U_4073,bool),bool,hAPP(U_4073,fun(fun(U_4073,bool),bool),member(U_4073),U_4072),U_4071)) )
      & ( ( hBOOL(hAPP(fun(U_4073,bool),bool,hAPP(U_4073,fun(fun(U_4073,bool),bool),member(U_4073),U_4072),U_4070))
          & hBOOL(hAPP(fun(U_4073,bool),bool,hAPP(U_4073,fun(fun(U_4073,bool),bool),member(U_4073),U_4072),U_4071)) )
        | ~ hBOOL(hAPP(fun(U_4073,bool),bool,hAPP(U_4073,fun(fun(U_4073,bool),bool),member(U_4073),U_4072),hAPP(fun(U_4073,bool),fun(U_4073,bool),hAPP(fun(U_4073,bool),fun(fun(U_4073,bool),fun(U_4073,bool)),semilattice_inf_inf(fun(U_4073,bool)),U_4071),U_4070))) ) ),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

fof(f_993_3,plain,
    ( ! [U_4081,U_4079,U_4077,U_4075] :
        ( hBOOL(hAPP(fun(U_4081,bool),bool,hAPP(U_4081,fun(fun(U_4081,bool),bool),member(U_4081),U_4079),hAPP(fun(U_4081,bool),fun(U_4081,bool),hAPP(fun(U_4081,bool),fun(fun(U_4081,bool),fun(U_4081,bool)),semilattice_inf_inf(fun(U_4081,bool)),U_4077),U_4075)))
        | ~ hBOOL(hAPP(fun(U_4081,bool),bool,hAPP(U_4081,fun(fun(U_4081,bool),bool),member(U_4081),U_4079),U_4075))
        | ~ hBOOL(hAPP(fun(U_4081,bool),bool,hAPP(U_4081,fun(fun(U_4081,bool),bool),member(U_4081),U_4079),U_4077)) )
    & ! [U_4080,U_4078,U_4076,U_4074] :
        ( ( hBOOL(hAPP(fun(U_4080,bool),bool,hAPP(U_4080,fun(fun(U_4080,bool),bool),member(U_4080),U_4078),U_4074))
          & hBOOL(hAPP(fun(U_4080,bool),bool,hAPP(U_4080,fun(fun(U_4080,bool),bool),member(U_4080),U_4078),U_4076)) )
        | ~ hBOOL(hAPP(fun(U_4080,bool),bool,hAPP(U_4080,fun(fun(U_4080,bool),bool),member(U_4080),U_4078),hAPP(fun(U_4080,bool),fun(U_4080,bool),hAPP(fun(U_4080,bool),fun(fun(U_4080,bool),fun(U_4080,bool)),semilattice_inf_inf(fun(U_4080,bool)),U_4076),U_4074))) ) ),
    inference(miniscope,[status(thm)],[f_993_2]) ).

cnf(f_993_4,plain,
    ( hBOOL(hAPP(fun(U_4080,bool),bool,hAPP(U_4080,fun(fun(U_4080,bool),bool),member(U_4080),U_4078),U_4076))
    | ~ hBOOL(hAPP(fun(U_4080,bool),bool,hAPP(U_4080,fun(fun(U_4080,bool),bool),member(U_4080),U_4078),hAPP(fun(U_4080,bool),fun(U_4080,bool),hAPP(fun(U_4080,bool),fun(fun(U_4080,bool),fun(U_4080,bool)),semilattice_inf_inf(fun(U_4080,bool)),U_4076),U_4074))) ),
    inference(clausify,[status(thm)],[f_993_3]) ).

cnf(f_993_5,plain,
    ( hBOOL(hAPP(fun(U_4080,bool),bool,hAPP(U_4080,fun(fun(U_4080,bool),bool),member(U_4080),U_4078),U_4074))
    | ~ hBOOL(hAPP(fun(U_4080,bool),bool,hAPP(U_4080,fun(fun(U_4080,bool),bool),member(U_4080),U_4078),hAPP(fun(U_4080,bool),fun(U_4080,bool),hAPP(fun(U_4080,bool),fun(fun(U_4080,bool),fun(U_4080,bool)),semilattice_inf_inf(fun(U_4080,bool)),U_4076),U_4074))) ),
    inference(clausify,[status(thm)],[f_993_3]) ).

cnf(f_993_6,plain,
    ( hBOOL(hAPP(fun(U_4081,bool),bool,hAPP(U_4081,fun(fun(U_4081,bool),bool),member(U_4081),U_4079),hAPP(fun(U_4081,bool),fun(U_4081,bool),hAPP(fun(U_4081,bool),fun(fun(U_4081,bool),fun(U_4081,bool)),semilattice_inf_inf(fun(U_4081,bool)),U_4077),U_4075)))
    | ~ hBOOL(hAPP(fun(U_4081,bool),bool,hAPP(U_4081,fun(fun(U_4081,bool),bool),member(U_4081),U_4079),U_4075))
    | ~ hBOOL(hAPP(fun(U_4081,bool),bool,hAPP(U_4081,fun(fun(U_4081,bool),bool),member(U_4081),U_4079),U_4077)) ),
    inference(clausify,[status(thm)],[f_993_3]) ).

fof(f_994_1,plain,
    ! [X_a,A_1,B,C] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C)),
    inference(fof_nnf,[status(thm)],[fact_904_Int__left__commute]) ).

fof(f_994_2,plain,
    ! [U_4085,U_4084,U_4083,U_4082] : hAPP(fun(U_4085,bool),fun(U_4085,bool),hAPP(fun(U_4085,bool),fun(fun(U_4085,bool),fun(U_4085,bool)),semilattice_inf_inf(fun(U_4085,bool)),U_4084),hAPP(fun(U_4085,bool),fun(U_4085,bool),hAPP(fun(U_4085,bool),fun(fun(U_4085,bool),fun(U_4085,bool)),semilattice_inf_inf(fun(U_4085,bool)),U_4083),U_4082)) = hAPP(fun(U_4085,bool),fun(U_4085,bool),hAPP(fun(U_4085,bool),fun(fun(U_4085,bool),fun(U_4085,bool)),semilattice_inf_inf(fun(U_4085,bool)),U_4083),hAPP(fun(U_4085,bool),fun(U_4085,bool),hAPP(fun(U_4085,bool),fun(fun(U_4085,bool),fun(U_4085,bool)),semilattice_inf_inf(fun(U_4085,bool)),U_4084),U_4082)),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

cnf(f_994_3,plain,
    hAPP(fun(U_4085,bool),fun(U_4085,bool),hAPP(fun(U_4085,bool),fun(fun(U_4085,bool),fun(U_4085,bool)),semilattice_inf_inf(fun(U_4085,bool)),U_4084),hAPP(fun(U_4085,bool),fun(U_4085,bool),hAPP(fun(U_4085,bool),fun(fun(U_4085,bool),fun(U_4085,bool)),semilattice_inf_inf(fun(U_4085,bool)),U_4083),U_4082)) = hAPP(fun(U_4085,bool),fun(U_4085,bool),hAPP(fun(U_4085,bool),fun(fun(U_4085,bool),fun(U_4085,bool)),semilattice_inf_inf(fun(U_4085,bool)),U_4083),hAPP(fun(U_4085,bool),fun(U_4085,bool),hAPP(fun(U_4085,bool),fun(fun(U_4085,bool),fun(U_4085,bool)),semilattice_inf_inf(fun(U_4085,bool)),U_4084),U_4082)),
    inference(clausify,[status(thm)],[f_994_2]) ).

fof(f_995_1,plain,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),
    inference(fof_nnf,[status(thm)],[fact_905_Int__left__absorb]) ).

fof(f_995_2,plain,
    ! [U_4088,U_4087,U_4086] : hAPP(fun(U_4088,bool),fun(U_4088,bool),hAPP(fun(U_4088,bool),fun(fun(U_4088,bool),fun(U_4088,bool)),semilattice_inf_inf(fun(U_4088,bool)),U_4087),hAPP(fun(U_4088,bool),fun(U_4088,bool),hAPP(fun(U_4088,bool),fun(fun(U_4088,bool),fun(U_4088,bool)),semilattice_inf_inf(fun(U_4088,bool)),U_4087),U_4086)) = hAPP(fun(U_4088,bool),fun(U_4088,bool),hAPP(fun(U_4088,bool),fun(fun(U_4088,bool),fun(U_4088,bool)),semilattice_inf_inf(fun(U_4088,bool)),U_4087),U_4086),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

cnf(f_995_3,plain,
    hAPP(fun(U_4088,bool),fun(U_4088,bool),hAPP(fun(U_4088,bool),fun(fun(U_4088,bool),fun(U_4088,bool)),semilattice_inf_inf(fun(U_4088,bool)),U_4087),hAPP(fun(U_4088,bool),fun(U_4088,bool),hAPP(fun(U_4088,bool),fun(fun(U_4088,bool),fun(U_4088,bool)),semilattice_inf_inf(fun(U_4088,bool)),U_4087),U_4086)) = hAPP(fun(U_4088,bool),fun(U_4088,bool),hAPP(fun(U_4088,bool),fun(fun(U_4088,bool),fun(U_4088,bool)),semilattice_inf_inf(fun(U_4088,bool)),U_4087),U_4086),
    inference(clausify,[status(thm)],[f_995_2]) ).

fof(f_996_1,plain,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),A_1),
    inference(fof_nnf,[status(thm)],[fact_906_Int__commute]) ).

fof(f_996_2,plain,
    ! [U_4091,U_4090,U_4089] : hAPP(fun(U_4091,bool),fun(U_4091,bool),hAPP(fun(U_4091,bool),fun(fun(U_4091,bool),fun(U_4091,bool)),semilattice_inf_inf(fun(U_4091,bool)),U_4090),U_4089) = hAPP(fun(U_4091,bool),fun(U_4091,bool),hAPP(fun(U_4091,bool),fun(fun(U_4091,bool),fun(U_4091,bool)),semilattice_inf_inf(fun(U_4091,bool)),U_4089),U_4090),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

cnf(f_996_3,plain,
    hAPP(fun(U_4091,bool),fun(U_4091,bool),hAPP(fun(U_4091,bool),fun(fun(U_4091,bool),fun(U_4091,bool)),semilattice_inf_inf(fun(U_4091,bool)),U_4090),U_4089) = hAPP(fun(U_4091,bool),fun(U_4091,bool),hAPP(fun(U_4091,bool),fun(fun(U_4091,bool),fun(U_4091,bool)),semilattice_inf_inf(fun(U_4091,bool)),U_4089),U_4090),
    inference(clausify,[status(thm)],[f_996_2]) ).

fof(f_997_1,plain,
    ! [X_a,A_1,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))),
    inference(fof_nnf,[status(thm)],[fact_907_Int__def]) ).

fof(f_997_2,plain,
    ! [U_4094,U_4093,U_4092] : hAPP(fun(U_4094,bool),fun(U_4094,bool),hAPP(fun(U_4094,bool),fun(fun(U_4094,bool),fun(U_4094,bool)),semilattice_inf_inf(fun(U_4094,bool)),U_4093),U_4092) = hAPP(fun(U_4094,bool),fun(U_4094,bool),collect(U_4094),hAPP(fun(U_4094,bool),fun(U_4094,bool),hAPP(fun(U_4094,fun(bool,bool)),fun(fun(U_4094,bool),fun(U_4094,bool)),combs(U_4094,bool,bool),hAPP(fun(U_4094,bool),fun(U_4094,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4094,bool),fun(U_4094,fun(bool,bool))),combb(bool,fun(bool,bool),U_4094),fconj),hAPP(fun(U_4094,bool),fun(U_4094,bool),hAPP(fun(U_4094,fun(fun(U_4094,bool),bool)),fun(fun(U_4094,bool),fun(U_4094,bool)),combc(U_4094,fun(U_4094,bool),bool),member(U_4094)),U_4093))),hAPP(fun(U_4094,bool),fun(U_4094,bool),hAPP(fun(U_4094,fun(fun(U_4094,bool),bool)),fun(fun(U_4094,bool),fun(U_4094,bool)),combc(U_4094,fun(U_4094,bool),bool),member(U_4094)),U_4092))),
    inference(variable_rename,[status(thm)],[f_997_1]) ).

cnf(f_997_3,plain,
    hAPP(fun(U_4094,bool),fun(U_4094,bool),hAPP(fun(U_4094,bool),fun(fun(U_4094,bool),fun(U_4094,bool)),semilattice_inf_inf(fun(U_4094,bool)),U_4093),U_4092) = hAPP(fun(U_4094,bool),fun(U_4094,bool),collect(U_4094),hAPP(fun(U_4094,bool),fun(U_4094,bool),hAPP(fun(U_4094,fun(bool,bool)),fun(fun(U_4094,bool),fun(U_4094,bool)),combs(U_4094,bool,bool),hAPP(fun(U_4094,bool),fun(U_4094,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4094,bool),fun(U_4094,fun(bool,bool))),combb(bool,fun(bool,bool),U_4094),fconj),hAPP(fun(U_4094,bool),fun(U_4094,bool),hAPP(fun(U_4094,fun(fun(U_4094,bool),bool)),fun(fun(U_4094,bool),fun(U_4094,bool)),combc(U_4094,fun(U_4094,bool),bool),member(U_4094)),U_4093))),hAPP(fun(U_4094,bool),fun(U_4094,bool),hAPP(fun(U_4094,fun(fun(U_4094,bool),bool)),fun(fun(U_4094,bool),fun(U_4094,bool)),combc(U_4094,fun(U_4094,bool),bool),member(U_4094)),U_4092))),
    inference(clausify,[status(thm)],[f_997_2]) ).

fof(f_998_1,plain,
    ! [X_a,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),A_1) = ti(fun(X_a,bool),A_1),
    inference(fof_nnf,[status(thm)],[fact_908_Int__absorb]) ).

fof(f_998_2,plain,
    ! [U_4096,U_4095] : hAPP(fun(U_4096,bool),fun(U_4096,bool),hAPP(fun(U_4096,bool),fun(fun(U_4096,bool),fun(U_4096,bool)),semilattice_inf_inf(fun(U_4096,bool)),U_4095),U_4095) = ti(fun(U_4096,bool),U_4095),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

cnf(f_998_3,plain,
    hAPP(fun(U_4096,bool),fun(U_4096,bool),hAPP(fun(U_4096,bool),fun(fun(U_4096,bool),fun(U_4096,bool)),semilattice_inf_inf(fun(U_4096,bool)),U_4095),U_4095) = ti(fun(U_4096,bool),U_4095),
    inference(clausify,[status(thm)],[f_998_2]) ).

fof(f_999_1,plain,
    ! [X_a,B,D_1,A_1,C] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),D_1)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),D_1))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C)) ),
    inference(fof_nnf,[status(thm)],[fact_909_Int__mono]) ).

fof(f_999_2,plain,
    ! [U_4101,U_4100,U_4099,U_4098,U_4097] :
      ( hBOOL(hAPP(fun(U_4101,bool),bool,hAPP(fun(U_4101,bool),fun(fun(U_4101,bool),bool),ord_less_eq(fun(U_4101,bool)),hAPP(fun(U_4101,bool),fun(U_4101,bool),hAPP(fun(U_4101,bool),fun(fun(U_4101,bool),fun(U_4101,bool)),semilattice_inf_inf(fun(U_4101,bool)),U_4098),U_4100)),hAPP(fun(U_4101,bool),fun(U_4101,bool),hAPP(fun(U_4101,bool),fun(fun(U_4101,bool),fun(U_4101,bool)),semilattice_inf_inf(fun(U_4101,bool)),U_4097),U_4099)))
      | ~ hBOOL(hAPP(fun(U_4101,bool),bool,hAPP(fun(U_4101,bool),fun(fun(U_4101,bool),bool),ord_less_eq(fun(U_4101,bool)),U_4100),U_4099))
      | ~ hBOOL(hAPP(fun(U_4101,bool),bool,hAPP(fun(U_4101,bool),fun(fun(U_4101,bool),bool),ord_less_eq(fun(U_4101,bool)),U_4098),U_4097)) ),
    inference(variable_rename,[status(thm)],[f_999_1]) ).

cnf(f_999_3,plain,
    ( hBOOL(hAPP(fun(U_4101,bool),bool,hAPP(fun(U_4101,bool),fun(fun(U_4101,bool),bool),ord_less_eq(fun(U_4101,bool)),hAPP(fun(U_4101,bool),fun(U_4101,bool),hAPP(fun(U_4101,bool),fun(fun(U_4101,bool),fun(U_4101,bool)),semilattice_inf_inf(fun(U_4101,bool)),U_4098),U_4100)),hAPP(fun(U_4101,bool),fun(U_4101,bool),hAPP(fun(U_4101,bool),fun(fun(U_4101,bool),fun(U_4101,bool)),semilattice_inf_inf(fun(U_4101,bool)),U_4097),U_4099)))
    | ~ hBOOL(hAPP(fun(U_4101,bool),bool,hAPP(fun(U_4101,bool),fun(fun(U_4101,bool),bool),ord_less_eq(fun(U_4101,bool)),U_4100),U_4099))
    | ~ hBOOL(hAPP(fun(U_4101,bool),bool,hAPP(fun(U_4101,bool),fun(fun(U_4101,bool),bool),ord_less_eq(fun(U_4101,bool)),U_4098),U_4097)) ),
    inference(clausify,[status(thm)],[f_999_2]) ).

fof(f_1000_1,plain,
    ! [X_a,B,C,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_910_Int__greatest]) ).

fof(f_1000_2,plain,
    ! [U_4105,U_4104,U_4103,U_4102] :
      ( hBOOL(hAPP(fun(U_4105,bool),bool,hAPP(fun(U_4105,bool),fun(fun(U_4105,bool),bool),ord_less_eq(fun(U_4105,bool)),U_4103),hAPP(fun(U_4105,bool),fun(U_4105,bool),hAPP(fun(U_4105,bool),fun(fun(U_4105,bool),fun(U_4105,bool)),semilattice_inf_inf(fun(U_4105,bool)),U_4102),U_4104)))
      | ~ hBOOL(hAPP(fun(U_4105,bool),bool,hAPP(fun(U_4105,bool),fun(fun(U_4105,bool),bool),ord_less_eq(fun(U_4105,bool)),U_4103),U_4104))
      | ~ hBOOL(hAPP(fun(U_4105,bool),bool,hAPP(fun(U_4105,bool),fun(fun(U_4105,bool),bool),ord_less_eq(fun(U_4105,bool)),U_4103),U_4102)) ),
    inference(variable_rename,[status(thm)],[f_1000_1]) ).

cnf(f_1000_3,plain,
    ( hBOOL(hAPP(fun(U_4105,bool),bool,hAPP(fun(U_4105,bool),fun(fun(U_4105,bool),bool),ord_less_eq(fun(U_4105,bool)),U_4103),hAPP(fun(U_4105,bool),fun(U_4105,bool),hAPP(fun(U_4105,bool),fun(fun(U_4105,bool),fun(U_4105,bool)),semilattice_inf_inf(fun(U_4105,bool)),U_4102),U_4104)))
    | ~ hBOOL(hAPP(fun(U_4105,bool),bool,hAPP(fun(U_4105,bool),fun(fun(U_4105,bool),bool),ord_less_eq(fun(U_4105,bool)),U_4103),U_4104))
    | ~ hBOOL(hAPP(fun(U_4105,bool),bool,hAPP(fun(U_4105,bool),fun(fun(U_4105,bool),bool),ord_less_eq(fun(U_4105,bool)),U_4103),U_4102)) ),
    inference(clausify,[status(thm)],[f_1000_2]) ).

fof(f_1001_1,plain,
    ! [X_a,B,A_1] :
      ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),B)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_911_Int__absorb1]) ).

fof(f_1001_2,plain,
    ! [U_4108,U_4107,U_4106] :
      ( hAPP(fun(U_4108,bool),fun(U_4108,bool),hAPP(fun(U_4108,bool),fun(fun(U_4108,bool),fun(U_4108,bool)),semilattice_inf_inf(fun(U_4108,bool)),U_4106),U_4107) = ti(fun(U_4108,bool),U_4107)
      | ~ hBOOL(hAPP(fun(U_4108,bool),bool,hAPP(fun(U_4108,bool),fun(fun(U_4108,bool),bool),ord_less_eq(fun(U_4108,bool)),U_4107),U_4106)) ),
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

cnf(f_1001_3,plain,
    ( hAPP(fun(U_4108,bool),fun(U_4108,bool),hAPP(fun(U_4108,bool),fun(fun(U_4108,bool),fun(U_4108,bool)),semilattice_inf_inf(fun(U_4108,bool)),U_4106),U_4107) = ti(fun(U_4108,bool),U_4107)
    | ~ hBOOL(hAPP(fun(U_4108,bool),bool,hAPP(fun(U_4108,bool),fun(fun(U_4108,bool),bool),ord_less_eq(fun(U_4108,bool)),U_4107),U_4106)) ),
    inference(clausify,[status(thm)],[f_1001_2]) ).

fof(f_1002_1,plain,
    ! [X_a,A_1,B] :
      ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),A_1)
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_912_Int__absorb2]) ).

fof(f_1002_2,plain,
    ! [U_4111,U_4110,U_4109] :
      ( hAPP(fun(U_4111,bool),fun(U_4111,bool),hAPP(fun(U_4111,bool),fun(fun(U_4111,bool),fun(U_4111,bool)),semilattice_inf_inf(fun(U_4111,bool)),U_4110),U_4109) = ti(fun(U_4111,bool),U_4110)
      | ~ hBOOL(hAPP(fun(U_4111,bool),bool,hAPP(fun(U_4111,bool),fun(fun(U_4111,bool),bool),ord_less_eq(fun(U_4111,bool)),U_4110),U_4109)) ),
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

cnf(f_1002_3,plain,
    ( hAPP(fun(U_4111,bool),fun(U_4111,bool),hAPP(fun(U_4111,bool),fun(fun(U_4111,bool),fun(U_4111,bool)),semilattice_inf_inf(fun(U_4111,bool)),U_4110),U_4109) = ti(fun(U_4111,bool),U_4110)
    | ~ hBOOL(hAPP(fun(U_4111,bool),bool,hAPP(fun(U_4111,bool),fun(fun(U_4111,bool),bool),ord_less_eq(fun(U_4111,bool)),U_4110),U_4109)) ),
    inference(clausify,[status(thm)],[f_1002_2]) ).

fof(f_1003_1,plain,
    ! [X_a,A_1,B] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),B)),
    inference(fof_nnf,[status(thm)],[fact_913_Int__lower2]) ).

fof(f_1003_2,plain,
    ! [U_4114,U_4113,U_4112] : hBOOL(hAPP(fun(U_4114,bool),bool,hAPP(fun(U_4114,bool),fun(fun(U_4114,bool),bool),ord_less_eq(fun(U_4114,bool)),hAPP(fun(U_4114,bool),fun(U_4114,bool),hAPP(fun(U_4114,bool),fun(fun(U_4114,bool),fun(U_4114,bool)),semilattice_inf_inf(fun(U_4114,bool)),U_4113),U_4112)),U_4112)),
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

cnf(f_1003_3,plain,
    hBOOL(hAPP(fun(U_4114,bool),bool,hAPP(fun(U_4114,bool),fun(fun(U_4114,bool),bool),ord_less_eq(fun(U_4114,bool)),hAPP(fun(U_4114,bool),fun(U_4114,bool),hAPP(fun(U_4114,bool),fun(fun(U_4114,bool),fun(U_4114,bool)),semilattice_inf_inf(fun(U_4114,bool)),U_4113),U_4112)),U_4112)),
    inference(clausify,[status(thm)],[f_1003_2]) ).

fof(f_1004_1,plain,
    ! [X_a,A_1,B] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),A_1)),
    inference(fof_nnf,[status(thm)],[fact_914_Int__lower1]) ).

fof(f_1004_2,plain,
    ! [U_4117,U_4116,U_4115] : hBOOL(hAPP(fun(U_4117,bool),bool,hAPP(fun(U_4117,bool),fun(fun(U_4117,bool),bool),ord_less_eq(fun(U_4117,bool)),hAPP(fun(U_4117,bool),fun(U_4117,bool),hAPP(fun(U_4117,bool),fun(fun(U_4117,bool),fun(U_4117,bool)),semilattice_inf_inf(fun(U_4117,bool)),U_4116),U_4115)),U_4116)),
    inference(variable_rename,[status(thm)],[f_1004_1]) ).

cnf(f_1004_3,plain,
    hBOOL(hAPP(fun(U_4117,bool),bool,hAPP(fun(U_4117,bool),fun(fun(U_4117,bool),bool),ord_less_eq(fun(U_4117,bool)),hAPP(fun(U_4117,bool),fun(U_4117,bool),hAPP(fun(U_4117,bool),fun(fun(U_4117,bool),fun(U_4117,bool)),semilattice_inf_inf(fun(U_4117,bool)),U_4116),U_4115)),U_4116)),
    inference(clausify,[status(thm)],[f_1004_2]) ).

fof(f_1005_1,plain,
    ! [X_a,X_b,B,F,A_1] :
      ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_915_inj__on__Int]) ).

fof(f_1005_2,plain,
    ! [U_4122,U_4121,U_4120,U_4119,U_4118] :
      ( hBOOL(hAPP(fun(U_4122,bool),bool,hAPP(fun(U_4122,U_4121),fun(fun(U_4122,bool),bool),inj_on(U_4122,U_4121),U_4119),hAPP(fun(U_4122,bool),fun(U_4122,bool),hAPP(fun(U_4122,bool),fun(fun(U_4122,bool),fun(U_4122,bool)),semilattice_inf_inf(fun(U_4122,bool)),U_4118),U_4120)))
      | ~ hBOOL(hAPP(fun(U_4122,bool),bool,hAPP(fun(U_4122,U_4121),fun(fun(U_4122,bool),bool),inj_on(U_4122,U_4121),U_4119),U_4120))
      | ~ hBOOL(hAPP(fun(U_4122,bool),bool,hAPP(fun(U_4122,U_4121),fun(fun(U_4122,bool),bool),inj_on(U_4122,U_4121),U_4119),U_4118)) ),
    inference(variable_rename,[status(thm)],[f_1005_1]) ).

cnf(f_1005_3,plain,
    ( hBOOL(hAPP(fun(U_4122,bool),bool,hAPP(fun(U_4122,U_4121),fun(fun(U_4122,bool),bool),inj_on(U_4122,U_4121),U_4119),hAPP(fun(U_4122,bool),fun(U_4122,bool),hAPP(fun(U_4122,bool),fun(fun(U_4122,bool),fun(U_4122,bool)),semilattice_inf_inf(fun(U_4122,bool)),U_4118),U_4120)))
    | ~ hBOOL(hAPP(fun(U_4122,bool),bool,hAPP(fun(U_4122,U_4121),fun(fun(U_4122,bool),bool),inj_on(U_4122,U_4121),U_4119),U_4120))
    | ~ hBOOL(hAPP(fun(U_4122,bool),bool,hAPP(fun(U_4122,U_4121),fun(fun(U_4122,bool),bool),inj_on(U_4122,U_4121),U_4119),U_4118)) ),
    inference(clausify,[status(thm)],[f_1005_2]) ).

fof(f_1006_1,plain,
    ! [X_a,X_b] :
      ( ! [F,Pa,A_1] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),Pa))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),Pa)),F)),zero_zero(X_b))),A_1)
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_916_setsum__restrict__set_H_H]) ).

fof(f_1006_2,plain,
    ! [U_4127,U_4126] :
      ( ! [U_4125,U_4124,U_4123] :
          ( hAPP(fun(U_4127,bool),U_4126,hAPP(fun(U_4127,U_4126),fun(fun(U_4127,bool),U_4126),big_co1399186613setsum(U_4127,U_4126),U_4125),hAPP(fun(U_4127,bool),fun(U_4127,bool),collect(U_4127),hAPP(fun(U_4127,bool),fun(U_4127,bool),hAPP(fun(U_4127,fun(bool,bool)),fun(fun(U_4127,bool),fun(U_4127,bool)),combs(U_4127,bool,bool),hAPP(fun(U_4127,bool),fun(U_4127,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4127,bool),fun(U_4127,fun(bool,bool))),combb(bool,fun(bool,bool),U_4127),fconj),hAPP(fun(U_4127,bool),fun(U_4127,bool),hAPP(fun(U_4127,fun(fun(U_4127,bool),bool)),fun(fun(U_4127,bool),fun(U_4127,bool)),combc(U_4127,fun(U_4127,bool),bool),member(U_4127)),U_4123))),U_4124))) = hAPP(fun(U_4127,bool),U_4126,hAPP(fun(U_4127,U_4126),fun(fun(U_4127,bool),U_4126),big_co1399186613setsum(U_4127,U_4126),hAPP(U_4126,fun(U_4127,U_4126),hAPP(fun(U_4127,fun(U_4126,U_4126)),fun(U_4126,fun(U_4127,U_4126)),combc(U_4127,U_4126,U_4126),hAPP(fun(U_4127,U_4126),fun(U_4127,fun(U_4126,U_4126)),hAPP(fun(U_4127,fun(U_4126,fun(U_4126,U_4126))),fun(fun(U_4127,U_4126),fun(U_4127,fun(U_4126,U_4126))),combs(U_4127,U_4126,fun(U_4126,U_4126)),hAPP(fun(U_4127,bool),fun(U_4127,fun(U_4126,fun(U_4126,U_4126))),hAPP(fun(bool,fun(U_4126,fun(U_4126,U_4126))),fun(fun(U_4127,bool),fun(U_4127,fun(U_4126,fun(U_4126,U_4126)))),combb(bool,fun(U_4126,fun(U_4126,U_4126)),U_4127),if(U_4126)),U_4124)),U_4125)),zero_zero(U_4126))),U_4123)
          | ~ hBOOL(hAPP(fun(U_4127,bool),bool,finite_finite_1(U_4127),U_4123)) )
      | ~ comm_monoid_add(U_4126) ),
    inference(variable_rename,[status(thm)],[f_1006_1]) ).

cnf(f_1006_3,plain,
    ( hAPP(fun(U_4127,bool),U_4126,hAPP(fun(U_4127,U_4126),fun(fun(U_4127,bool),U_4126),big_co1399186613setsum(U_4127,U_4126),U_4125),hAPP(fun(U_4127,bool),fun(U_4127,bool),collect(U_4127),hAPP(fun(U_4127,bool),fun(U_4127,bool),hAPP(fun(U_4127,fun(bool,bool)),fun(fun(U_4127,bool),fun(U_4127,bool)),combs(U_4127,bool,bool),hAPP(fun(U_4127,bool),fun(U_4127,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4127,bool),fun(U_4127,fun(bool,bool))),combb(bool,fun(bool,bool),U_4127),fconj),hAPP(fun(U_4127,bool),fun(U_4127,bool),hAPP(fun(U_4127,fun(fun(U_4127,bool),bool)),fun(fun(U_4127,bool),fun(U_4127,bool)),combc(U_4127,fun(U_4127,bool),bool),member(U_4127)),U_4123))),U_4124))) = hAPP(fun(U_4127,bool),U_4126,hAPP(fun(U_4127,U_4126),fun(fun(U_4127,bool),U_4126),big_co1399186613setsum(U_4127,U_4126),hAPP(U_4126,fun(U_4127,U_4126),hAPP(fun(U_4127,fun(U_4126,U_4126)),fun(U_4126,fun(U_4127,U_4126)),combc(U_4127,U_4126,U_4126),hAPP(fun(U_4127,U_4126),fun(U_4127,fun(U_4126,U_4126)),hAPP(fun(U_4127,fun(U_4126,fun(U_4126,U_4126))),fun(fun(U_4127,U_4126),fun(U_4127,fun(U_4126,U_4126))),combs(U_4127,U_4126,fun(U_4126,U_4126)),hAPP(fun(U_4127,bool),fun(U_4127,fun(U_4126,fun(U_4126,U_4126))),hAPP(fun(bool,fun(U_4126,fun(U_4126,U_4126))),fun(fun(U_4127,bool),fun(U_4127,fun(U_4126,fun(U_4126,U_4126)))),combb(bool,fun(U_4126,fun(U_4126,U_4126)),U_4127),if(U_4126)),U_4124)),U_4125)),zero_zero(U_4126))),U_4123)
    | ~ hBOOL(hAPP(fun(U_4127,bool),bool,finite_finite_1(U_4127),U_4123))
    | ~ comm_monoid_add(U_4126) ),
    inference(clausify,[status(thm)],[f_1006_2]) ).

fof(f_1007_1,plain,
    ! [X_a,X_b] :
      ( ! [F,B,A_1] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B)))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))),F)),zero_zero(X_b))),A_1)
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_917_setsum__restrict__set_H]) ).

fof(f_1007_2,plain,
    ! [U_4132,U_4131] :
      ( ! [U_4130,U_4129,U_4128] :
          ( hAPP(fun(U_4132,bool),U_4131,hAPP(fun(U_4132,U_4131),fun(fun(U_4132,bool),U_4131),big_co1399186613setsum(U_4132,U_4131),U_4130),hAPP(fun(U_4132,bool),fun(U_4132,bool),collect(U_4132),hAPP(fun(U_4132,bool),fun(U_4132,bool),hAPP(fun(U_4132,fun(bool,bool)),fun(fun(U_4132,bool),fun(U_4132,bool)),combs(U_4132,bool,bool),hAPP(fun(U_4132,bool),fun(U_4132,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4132,bool),fun(U_4132,fun(bool,bool))),combb(bool,fun(bool,bool),U_4132),fconj),hAPP(fun(U_4132,bool),fun(U_4132,bool),hAPP(fun(U_4132,fun(fun(U_4132,bool),bool)),fun(fun(U_4132,bool),fun(U_4132,bool)),combc(U_4132,fun(U_4132,bool),bool),member(U_4132)),U_4128))),hAPP(fun(U_4132,bool),fun(U_4132,bool),hAPP(fun(U_4132,fun(fun(U_4132,bool),bool)),fun(fun(U_4132,bool),fun(U_4132,bool)),combc(U_4132,fun(U_4132,bool),bool),member(U_4132)),U_4129)))) = hAPP(fun(U_4132,bool),U_4131,hAPP(fun(U_4132,U_4131),fun(fun(U_4132,bool),U_4131),big_co1399186613setsum(U_4132,U_4131),hAPP(U_4131,fun(U_4132,U_4131),hAPP(fun(U_4132,fun(U_4131,U_4131)),fun(U_4131,fun(U_4132,U_4131)),combc(U_4132,U_4131,U_4131),hAPP(fun(U_4132,U_4131),fun(U_4132,fun(U_4131,U_4131)),hAPP(fun(U_4132,fun(U_4131,fun(U_4131,U_4131))),fun(fun(U_4132,U_4131),fun(U_4132,fun(U_4131,U_4131))),combs(U_4132,U_4131,fun(U_4131,U_4131)),hAPP(fun(U_4132,bool),fun(U_4132,fun(U_4131,fun(U_4131,U_4131))),hAPP(fun(bool,fun(U_4131,fun(U_4131,U_4131))),fun(fun(U_4132,bool),fun(U_4132,fun(U_4131,fun(U_4131,U_4131)))),combb(bool,fun(U_4131,fun(U_4131,U_4131)),U_4132),if(U_4131)),hAPP(fun(U_4132,bool),fun(U_4132,bool),hAPP(fun(U_4132,fun(fun(U_4132,bool),bool)),fun(fun(U_4132,bool),fun(U_4132,bool)),combc(U_4132,fun(U_4132,bool),bool),member(U_4132)),U_4129))),U_4130)),zero_zero(U_4131))),U_4128)
          | ~ hBOOL(hAPP(fun(U_4132,bool),bool,finite_finite_1(U_4132),U_4128)) )
      | ~ comm_monoid_add(U_4131) ),
    inference(variable_rename,[status(thm)],[f_1007_1]) ).

cnf(f_1007_3,plain,
    ( hAPP(fun(U_4132,bool),U_4131,hAPP(fun(U_4132,U_4131),fun(fun(U_4132,bool),U_4131),big_co1399186613setsum(U_4132,U_4131),U_4130),hAPP(fun(U_4132,bool),fun(U_4132,bool),collect(U_4132),hAPP(fun(U_4132,bool),fun(U_4132,bool),hAPP(fun(U_4132,fun(bool,bool)),fun(fun(U_4132,bool),fun(U_4132,bool)),combs(U_4132,bool,bool),hAPP(fun(U_4132,bool),fun(U_4132,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_4132,bool),fun(U_4132,fun(bool,bool))),combb(bool,fun(bool,bool),U_4132),fconj),hAPP(fun(U_4132,bool),fun(U_4132,bool),hAPP(fun(U_4132,fun(fun(U_4132,bool),bool)),fun(fun(U_4132,bool),fun(U_4132,bool)),combc(U_4132,fun(U_4132,bool),bool),member(U_4132)),U_4128))),hAPP(fun(U_4132,bool),fun(U_4132,bool),hAPP(fun(U_4132,fun(fun(U_4132,bool),bool)),fun(fun(U_4132,bool),fun(U_4132,bool)),combc(U_4132,fun(U_4132,bool),bool),member(U_4132)),U_4129)))) = hAPP(fun(U_4132,bool),U_4131,hAPP(fun(U_4132,U_4131),fun(fun(U_4132,bool),U_4131),big_co1399186613setsum(U_4132,U_4131),hAPP(U_4131,fun(U_4132,U_4131),hAPP(fun(U_4132,fun(U_4131,U_4131)),fun(U_4131,fun(U_4132,U_4131)),combc(U_4132,U_4131,U_4131),hAPP(fun(U_4132,U_4131),fun(U_4132,fun(U_4131,U_4131)),hAPP(fun(U_4132,fun(U_4131,fun(U_4131,U_4131))),fun(fun(U_4132,U_4131),fun(U_4132,fun(U_4131,U_4131))),combs(U_4132,U_4131,fun(U_4131,U_4131)),hAPP(fun(U_4132,bool),fun(U_4132,fun(U_4131,fun(U_4131,U_4131))),hAPP(fun(bool,fun(U_4131,fun(U_4131,U_4131))),fun(fun(U_4132,bool),fun(U_4132,fun(U_4131,fun(U_4131,U_4131)))),combb(bool,fun(U_4131,fun(U_4131,U_4131)),U_4132),if(U_4131)),hAPP(fun(U_4132,bool),fun(U_4132,bool),hAPP(fun(U_4132,fun(fun(U_4132,bool),bool)),fun(fun(U_4132,bool),fun(U_4132,bool)),combc(U_4132,fun(U_4132,bool),bool),member(U_4132)),U_4129))),U_4130)),zero_zero(U_4131))),U_4128)
    | ~ hBOOL(hAPP(fun(U_4132,bool),bool,finite_finite_1(U_4132),U_4128))
    | ~ comm_monoid_add(U_4131) ),
    inference(clausify,[status(thm)],[f_1007_2]) ).

fof(f_1008_1,plain,
    ! [X_a,X_b,F,A_1,B] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B)))),
    inference(fof_nnf,[status(thm)],[fact_918_image__Int__subset]) ).

fof(f_1008_2,plain,
    ! [U_4137,U_4136,U_4135,U_4134,U_4133] : hBOOL(hAPP(fun(U_4137,bool),bool,hAPP(fun(U_4137,bool),fun(fun(U_4137,bool),bool),ord_less_eq(fun(U_4137,bool)),hAPP(fun(U_4136,bool),fun(U_4137,bool),hAPP(fun(U_4136,U_4137),fun(fun(U_4136,bool),fun(U_4137,bool)),image(U_4136,U_4137),U_4135),hAPP(fun(U_4136,bool),fun(U_4136,bool),hAPP(fun(U_4136,bool),fun(fun(U_4136,bool),fun(U_4136,bool)),semilattice_inf_inf(fun(U_4136,bool)),U_4134),U_4133))),hAPP(fun(U_4137,bool),fun(U_4137,bool),hAPP(fun(U_4137,bool),fun(fun(U_4137,bool),fun(U_4137,bool)),semilattice_inf_inf(fun(U_4137,bool)),hAPP(fun(U_4136,bool),fun(U_4137,bool),hAPP(fun(U_4136,U_4137),fun(fun(U_4136,bool),fun(U_4137,bool)),image(U_4136,U_4137),U_4135),U_4134)),hAPP(fun(U_4136,bool),fun(U_4137,bool),hAPP(fun(U_4136,U_4137),fun(fun(U_4136,bool),fun(U_4137,bool)),image(U_4136,U_4137),U_4135),U_4133)))),
    inference(variable_rename,[status(thm)],[f_1008_1]) ).

cnf(f_1008_3,plain,
    hBOOL(hAPP(fun(U_4137,bool),bool,hAPP(fun(U_4137,bool),fun(fun(U_4137,bool),bool),ord_less_eq(fun(U_4137,bool)),hAPP(fun(U_4136,bool),fun(U_4137,bool),hAPP(fun(U_4136,U_4137),fun(fun(U_4136,bool),fun(U_4137,bool)),image(U_4136,U_4137),U_4135),hAPP(fun(U_4136,bool),fun(U_4136,bool),hAPP(fun(U_4136,bool),fun(fun(U_4136,bool),fun(U_4136,bool)),semilattice_inf_inf(fun(U_4136,bool)),U_4134),U_4133))),hAPP(fun(U_4137,bool),fun(U_4137,bool),hAPP(fun(U_4137,bool),fun(fun(U_4137,bool),fun(U_4137,bool)),semilattice_inf_inf(fun(U_4137,bool)),hAPP(fun(U_4136,bool),fun(U_4137,bool),hAPP(fun(U_4136,U_4137),fun(fun(U_4136,bool),fun(U_4137,bool)),image(U_4136,U_4137),U_4135),U_4134)),hAPP(fun(U_4136,bool),fun(U_4137,bool),hAPP(fun(U_4136,U_4137),fun(fun(U_4136,bool),fun(U_4137,bool)),image(U_4136,U_4137),U_4135),U_4133)))),
    inference(clausify,[status(thm)],[f_1008_2]) ).

fof(f_1009_1,plain,
    ! [X_a] :
      ( ! [F,M,Na] : hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Na))
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_919_setsum__shift__bounds__Suc__ivl]) ).

fof(f_1009_2,plain,
    ! [U_4141] :
      ( ! [U_4140,U_4139,U_4138] : hAPP(fun(nat,bool),U_4141,hAPP(fun(nat,U_4141),fun(fun(nat,bool),U_4141),big_co1399186613setsum(nat,U_4141),U_4140),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,U_4139)),hAPP(nat,nat,suc,U_4138))) = hAPP(fun(nat,bool),U_4141,hAPP(fun(nat,U_4141),fun(fun(nat,bool),U_4141),big_co1399186613setsum(nat,U_4141),hAPP(fun(nat,nat),fun(nat,U_4141),hAPP(fun(nat,U_4141),fun(fun(nat,nat),fun(nat,U_4141)),combb(nat,U_4141,nat),U_4140),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4139),U_4138))
      | ~ comm_monoid_add(U_4141) ),
    inference(variable_rename,[status(thm)],[f_1009_1]) ).

cnf(f_1009_3,plain,
    ( hAPP(fun(nat,bool),U_4141,hAPP(fun(nat,U_4141),fun(fun(nat,bool),U_4141),big_co1399186613setsum(nat,U_4141),U_4140),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,U_4139)),hAPP(nat,nat,suc,U_4138))) = hAPP(fun(nat,bool),U_4141,hAPP(fun(nat,U_4141),fun(fun(nat,bool),U_4141),big_co1399186613setsum(nat,U_4141),hAPP(fun(nat,nat),fun(nat,U_4141),hAPP(fun(nat,U_4141),fun(fun(nat,nat),fun(nat,U_4141)),combb(nat,U_4141,nat),U_4140),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4139),U_4138))
    | ~ comm_monoid_add(U_4141) ),
    inference(clausify,[status(thm)],[f_1009_2]) ).

fof(f_1010_1,plain,
    ! [X_a] :
      ( ! [X,A_2,B_1] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_1))
            & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2)) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1))) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_920_le__infE]) ).

fof(f_1010_2,plain,
    ! [U_4145] :
      ( ! [U_4144,U_4143,U_4142] :
          ( ( hBOOL(hAPP(U_4145,bool,hAPP(U_4145,fun(U_4145,bool),ord_less_eq(U_4145),U_4144),U_4142))
            & hBOOL(hAPP(U_4145,bool,hAPP(U_4145,fun(U_4145,bool),ord_less_eq(U_4145),U_4144),U_4143)) )
          | ~ hBOOL(hAPP(U_4145,bool,hAPP(U_4145,fun(U_4145,bool),ord_less_eq(U_4145),U_4144),hAPP(U_4145,U_4145,hAPP(U_4145,fun(U_4145,U_4145),semilattice_inf_inf(U_4145),U_4143),U_4142))) )
      | ~ semilattice_inf(U_4145) ),
    inference(variable_rename,[status(thm)],[f_1010_1]) ).

cnf(f_1010_3,plain,
    ( hBOOL(hAPP(U_4145,bool,hAPP(U_4145,fun(U_4145,bool),ord_less_eq(U_4145),U_4144),U_4143))
    | ~ hBOOL(hAPP(U_4145,bool,hAPP(U_4145,fun(U_4145,bool),ord_less_eq(U_4145),U_4144),hAPP(U_4145,U_4145,hAPP(U_4145,fun(U_4145,U_4145),semilattice_inf_inf(U_4145),U_4143),U_4142)))
    | ~ semilattice_inf(U_4145) ),
    inference(clausify,[status(thm)],[f_1010_2]) ).

cnf(f_1010_4,plain,
    ( hBOOL(hAPP(U_4145,bool,hAPP(U_4145,fun(U_4145,bool),ord_less_eq(U_4145),U_4144),U_4142))
    | ~ hBOOL(hAPP(U_4145,bool,hAPP(U_4145,fun(U_4145,bool),ord_less_eq(U_4145),U_4144),hAPP(U_4145,U_4145,hAPP(U_4145,fun(U_4145,U_4145),semilattice_inf_inf(U_4145),U_4143),U_4142)))
    | ~ semilattice_inf(U_4145) ),
    inference(clausify,[status(thm)],[f_1010_2]) ).

fof(f_1011_1,plain,
    ! [X_a] :
      ( ! [B_1,D,A_2,C_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),C_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1)) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_921_inf__mono]) ).

fof(f_1011_2,plain,
    ! [U_4150] :
      ( ! [U_4149,U_4148,U_4147,U_4146] :
          ( hBOOL(hAPP(U_4150,bool,hAPP(U_4150,fun(U_4150,bool),ord_less_eq(U_4150),hAPP(U_4150,U_4150,hAPP(U_4150,fun(U_4150,U_4150),semilattice_inf_inf(U_4150),U_4147),U_4149)),hAPP(U_4150,U_4150,hAPP(U_4150,fun(U_4150,U_4150),semilattice_inf_inf(U_4150),U_4146),U_4148)))
          | ~ hBOOL(hAPP(U_4150,bool,hAPP(U_4150,fun(U_4150,bool),ord_less_eq(U_4150),U_4149),U_4148))
          | ~ hBOOL(hAPP(U_4150,bool,hAPP(U_4150,fun(U_4150,bool),ord_less_eq(U_4150),U_4147),U_4146)) )
      | ~ semilattice_inf(U_4150) ),
    inference(variable_rename,[status(thm)],[f_1011_1]) ).

cnf(f_1011_3,plain,
    ( hBOOL(hAPP(U_4150,bool,hAPP(U_4150,fun(U_4150,bool),ord_less_eq(U_4150),hAPP(U_4150,U_4150,hAPP(U_4150,fun(U_4150,U_4150),semilattice_inf_inf(U_4150),U_4147),U_4149)),hAPP(U_4150,U_4150,hAPP(U_4150,fun(U_4150,U_4150),semilattice_inf_inf(U_4150),U_4146),U_4148)))
    | ~ hBOOL(hAPP(U_4150,bool,hAPP(U_4150,fun(U_4150,bool),ord_less_eq(U_4150),U_4149),U_4148))
    | ~ hBOOL(hAPP(U_4150,bool,hAPP(U_4150,fun(U_4150,bool),ord_less_eq(U_4150),U_4147),U_4146))
    | ~ semilattice_inf(U_4150) ),
    inference(clausify,[status(thm)],[f_1011_2]) ).

fof(f_1012_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_922_inf__greatest]) ).

fof(f_1012_2,plain,
    ! [U_4154] :
      ( ! [U_4153,U_4152,U_4151] :
          ( hBOOL(hAPP(U_4154,bool,hAPP(U_4154,fun(U_4154,bool),ord_less_eq(U_4154),U_4152),hAPP(U_4154,U_4154,hAPP(U_4154,fun(U_4154,U_4154),semilattice_inf_inf(U_4154),U_4151),U_4153)))
          | ~ hBOOL(hAPP(U_4154,bool,hAPP(U_4154,fun(U_4154,bool),ord_less_eq(U_4154),U_4152),U_4153))
          | ~ hBOOL(hAPP(U_4154,bool,hAPP(U_4154,fun(U_4154,bool),ord_less_eq(U_4154),U_4152),U_4151)) )
      | ~ semilattice_inf(U_4154) ),
    inference(variable_rename,[status(thm)],[f_1012_1]) ).

cnf(f_1012_3,plain,
    ( hBOOL(hAPP(U_4154,bool,hAPP(U_4154,fun(U_4154,bool),ord_less_eq(U_4154),U_4152),hAPP(U_4154,U_4154,hAPP(U_4154,fun(U_4154,U_4154),semilattice_inf_inf(U_4154),U_4151),U_4153)))
    | ~ hBOOL(hAPP(U_4154,bool,hAPP(U_4154,fun(U_4154,bool),ord_less_eq(U_4154),U_4152),U_4153))
    | ~ hBOOL(hAPP(U_4154,bool,hAPP(U_4154,fun(U_4154,bool),ord_less_eq(U_4154),U_4152),U_4151))
    | ~ semilattice_inf(U_4154) ),
    inference(clausify,[status(thm)],[f_1012_2]) ).

fof(f_1013_1,plain,
    ! [X_a] :
      ( ! [B_1,X,A_2] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_2)) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_923_le__infI]) ).

fof(f_1013_2,plain,
    ! [U_4158] :
      ( ! [U_4157,U_4156,U_4155] :
          ( hBOOL(hAPP(U_4158,bool,hAPP(U_4158,fun(U_4158,bool),ord_less_eq(U_4158),U_4156),hAPP(U_4158,U_4158,hAPP(U_4158,fun(U_4158,U_4158),semilattice_inf_inf(U_4158),U_4155),U_4157)))
          | ~ hBOOL(hAPP(U_4158,bool,hAPP(U_4158,fun(U_4158,bool),ord_less_eq(U_4158),U_4156),U_4157))
          | ~ hBOOL(hAPP(U_4158,bool,hAPP(U_4158,fun(U_4158,bool),ord_less_eq(U_4158),U_4156),U_4155)) )
      | ~ semilattice_inf(U_4158) ),
    inference(variable_rename,[status(thm)],[f_1013_1]) ).

cnf(f_1013_3,plain,
    ( hBOOL(hAPP(U_4158,bool,hAPP(U_4158,fun(U_4158,bool),ord_less_eq(U_4158),U_4156),hAPP(U_4158,U_4158,hAPP(U_4158,fun(U_4158,U_4158),semilattice_inf_inf(U_4158),U_4155),U_4157)))
    | ~ hBOOL(hAPP(U_4158,bool,hAPP(U_4158,fun(U_4158,bool),ord_less_eq(U_4158),U_4156),U_4157))
    | ~ hBOOL(hAPP(U_4158,bool,hAPP(U_4158,fun(U_4158,bool),ord_less_eq(U_4158),U_4156),U_4155))
    | ~ semilattice_inf(U_4158) ),
    inference(clausify,[status(thm)],[f_1013_2]) ).

fof(f_1014_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = ti(X_a,Y)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_924_inf__absorb2]) ).

fof(f_1014_2,plain,
    ! [U_4161] :
      ( ! [U_4160,U_4159] :
          ( hAPP(U_4161,U_4161,hAPP(U_4161,fun(U_4161,U_4161),semilattice_inf_inf(U_4161),U_4159),U_4160) = ti(U_4161,U_4160)
          | ~ hBOOL(hAPP(U_4161,bool,hAPP(U_4161,fun(U_4161,bool),ord_less_eq(U_4161),U_4160),U_4159)) )
      | ~ semilattice_inf(U_4161) ),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

cnf(f_1014_3,plain,
    ( hAPP(U_4161,U_4161,hAPP(U_4161,fun(U_4161,U_4161),semilattice_inf_inf(U_4161),U_4159),U_4160) = ti(U_4161,U_4160)
    | ~ hBOOL(hAPP(U_4161,bool,hAPP(U_4161,fun(U_4161,bool),ord_less_eq(U_4161),U_4160),U_4159))
    | ~ semilattice_inf(U_4161) ),
    inference(clausify,[status(thm)],[f_1014_2]) ).

fof(f_1015_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = ti(X_a,X)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_925_inf__absorb1]) ).

fof(f_1015_2,plain,
    ! [U_4164] :
      ( ! [U_4163,U_4162] :
          ( hAPP(U_4164,U_4164,hAPP(U_4164,fun(U_4164,U_4164),semilattice_inf_inf(U_4164),U_4163),U_4162) = ti(U_4164,U_4163)
          | ~ hBOOL(hAPP(U_4164,bool,hAPP(U_4164,fun(U_4164,bool),ord_less_eq(U_4164),U_4163),U_4162)) )
      | ~ semilattice_inf(U_4164) ),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

cnf(f_1015_3,plain,
    ( hAPP(U_4164,U_4164,hAPP(U_4164,fun(U_4164,U_4164),semilattice_inf_inf(U_4164),U_4163),U_4162) = ti(U_4164,U_4163)
    | ~ hBOOL(hAPP(U_4164,bool,hAPP(U_4164,fun(U_4164,bool),ord_less_eq(U_4164),U_4163),U_4162))
    | ~ semilattice_inf(U_4164) ),
    inference(clausify,[status(thm)],[f_1015_2]) ).

fof(f_1016_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),X)) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_926_le__infI2]) ).

fof(f_1016_2,plain,
    ! [U_4168] :
      ( ! [U_4167,U_4166,U_4165] :
          ( hBOOL(hAPP(U_4168,bool,hAPP(U_4168,fun(U_4168,bool),ord_less_eq(U_4168),hAPP(U_4168,U_4168,hAPP(U_4168,fun(U_4168,U_4168),semilattice_inf_inf(U_4168),U_4167),U_4166)),U_4165))
          | ~ hBOOL(hAPP(U_4168,bool,hAPP(U_4168,fun(U_4168,bool),ord_less_eq(U_4168),U_4166),U_4165)) )
      | ~ semilattice_inf(U_4168) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

cnf(f_1016_3,plain,
    ( hBOOL(hAPP(U_4168,bool,hAPP(U_4168,fun(U_4168,bool),ord_less_eq(U_4168),hAPP(U_4168,U_4168,hAPP(U_4168,fun(U_4168,U_4168),semilattice_inf_inf(U_4168),U_4167),U_4166)),U_4165))
    | ~ hBOOL(hAPP(U_4168,bool,hAPP(U_4168,fun(U_4168,bool),ord_less_eq(U_4168),U_4166),U_4165))
    | ~ semilattice_inf(U_4168) ),
    inference(clausify,[status(thm)],[f_1016_2]) ).

fof(f_1017_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),X)) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_927_le__infI1]) ).

fof(f_1017_2,plain,
    ! [U_4172] :
      ( ! [U_4171,U_4170,U_4169] :
          ( hBOOL(hAPP(U_4172,bool,hAPP(U_4172,fun(U_4172,bool),ord_less_eq(U_4172),hAPP(U_4172,U_4172,hAPP(U_4172,fun(U_4172,U_4172),semilattice_inf_inf(U_4172),U_4170),U_4171)),U_4169))
          | ~ hBOOL(hAPP(U_4172,bool,hAPP(U_4172,fun(U_4172,bool),ord_less_eq(U_4172),U_4170),U_4169)) )
      | ~ semilattice_inf(U_4172) ),
    inference(variable_rename,[status(thm)],[f_1017_1]) ).

cnf(f_1017_3,plain,
    ( hBOOL(hAPP(U_4172,bool,hAPP(U_4172,fun(U_4172,bool),ord_less_eq(U_4172),hAPP(U_4172,U_4172,hAPP(U_4172,fun(U_4172,U_4172),semilattice_inf_inf(U_4172),U_4170),U_4171)),U_4169))
    | ~ hBOOL(hAPP(U_4172,bool,hAPP(U_4172,fun(U_4172,bool),ord_less_eq(U_4172),U_4170),U_4169))
    | ~ semilattice_inf(U_4172) ),
    inference(clausify,[status(thm)],[f_1017_2]) ).

fof(f_1018_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1,Z_1] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y_1),Z_1)))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1))
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) )
          & ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) )
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y_1),Z_1))) ) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_928_le__inf__iff]) ).

fof(f_1018_2,plain,
    ! [U_4176] :
      ( ! [U_4175,U_4174,U_4173] :
          ( ( hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4175),hAPP(U_4176,U_4176,hAPP(U_4176,fun(U_4176,U_4176),semilattice_inf_inf(U_4176),U_4174),U_4173)))
            | ~ hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4175),U_4173))
            | ~ hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4175),U_4174)) )
          & ( ( hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4175),U_4173))
              & hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4175),U_4174)) )
            | ~ hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4175),hAPP(U_4176,U_4176,hAPP(U_4176,fun(U_4176,U_4176),semilattice_inf_inf(U_4176),U_4174),U_4173))) ) )
      | ~ semilattice_inf(U_4176) ),
    inference(variable_rename,[status(thm)],[f_1018_1]) ).

fof(f_1018_3,plain,
    ! [U_4176] :
      ( ( ! [U_4182,U_4180,U_4178] :
            ( hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4182),hAPP(U_4176,U_4176,hAPP(U_4176,fun(U_4176,U_4176),semilattice_inf_inf(U_4176),U_4180),U_4178)))
            | ~ hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4182),U_4178))
            | ~ hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4182),U_4180)) )
        & ! [U_4181,U_4179,U_4177] :
            ( ( hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4181),U_4177))
              & hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4181),U_4179)) )
            | ~ hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4181),hAPP(U_4176,U_4176,hAPP(U_4176,fun(U_4176,U_4176),semilattice_inf_inf(U_4176),U_4179),U_4177))) ) )
      | ~ semilattice_inf(U_4176) ),
    inference(miniscope,[status(thm)],[f_1018_2]) ).

cnf(f_1018_4,plain,
    ( hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4181),U_4179))
    | ~ hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4181),hAPP(U_4176,U_4176,hAPP(U_4176,fun(U_4176,U_4176),semilattice_inf_inf(U_4176),U_4179),U_4177)))
    | ~ semilattice_inf(U_4176) ),
    inference(clausify,[status(thm)],[f_1018_3]) ).

cnf(f_1018_5,plain,
    ( hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4181),U_4177))
    | ~ hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4181),hAPP(U_4176,U_4176,hAPP(U_4176,fun(U_4176,U_4176),semilattice_inf_inf(U_4176),U_4179),U_4177)))
    | ~ semilattice_inf(U_4176) ),
    inference(clausify,[status(thm)],[f_1018_3]) ).

cnf(f_1018_6,plain,
    ( hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4182),hAPP(U_4176,U_4176,hAPP(U_4176,fun(U_4176,U_4176),semilattice_inf_inf(U_4176),U_4180),U_4178)))
    | ~ hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4182),U_4178))
    | ~ hBOOL(hAPP(U_4176,bool,hAPP(U_4176,fun(U_4176,bool),ord_less_eq(U_4176),U_4182),U_4180))
    | ~ semilattice_inf(U_4176) ),
    inference(clausify,[status(thm)],[f_1018_3]) ).

fof(f_1019_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1))
            | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),Y_1) != ti(X_a,X_2) )
          & ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),Y_1) = ti(X_a,X_2)
            | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_1)) ) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_929_le__iff__inf]) ).

fof(f_1019_2,plain,
    ! [U_4185] :
      ( ! [U_4184,U_4183] :
          ( ( hBOOL(hAPP(U_4185,bool,hAPP(U_4185,fun(U_4185,bool),ord_less_eq(U_4185),U_4184),U_4183))
            | hAPP(U_4185,U_4185,hAPP(U_4185,fun(U_4185,U_4185),semilattice_inf_inf(U_4185),U_4184),U_4183) != ti(U_4185,U_4184) )
          & ( hAPP(U_4185,U_4185,hAPP(U_4185,fun(U_4185,U_4185),semilattice_inf_inf(U_4185),U_4184),U_4183) = ti(U_4185,U_4184)
            | ~ hBOOL(hAPP(U_4185,bool,hAPP(U_4185,fun(U_4185,bool),ord_less_eq(U_4185),U_4184),U_4183)) ) )
      | ~ semilattice_inf(U_4185) ),
    inference(variable_rename,[status(thm)],[f_1019_1]) ).

fof(f_1019_3,plain,
    ! [U_4185] :
      ( ( ! [U_4189,U_4187] :
            ( hBOOL(hAPP(U_4185,bool,hAPP(U_4185,fun(U_4185,bool),ord_less_eq(U_4185),U_4189),U_4187))
            | hAPP(U_4185,U_4185,hAPP(U_4185,fun(U_4185,U_4185),semilattice_inf_inf(U_4185),U_4189),U_4187) != ti(U_4185,U_4189) )
        & ! [U_4188,U_4186] :
            ( hAPP(U_4185,U_4185,hAPP(U_4185,fun(U_4185,U_4185),semilattice_inf_inf(U_4185),U_4188),U_4186) = ti(U_4185,U_4188)
            | ~ hBOOL(hAPP(U_4185,bool,hAPP(U_4185,fun(U_4185,bool),ord_less_eq(U_4185),U_4188),U_4186)) ) )
      | ~ semilattice_inf(U_4185) ),
    inference(miniscope,[status(thm)],[f_1019_2]) ).

cnf(f_1019_4,plain,
    ( hAPP(U_4185,U_4185,hAPP(U_4185,fun(U_4185,U_4185),semilattice_inf_inf(U_4185),U_4188),U_4186) = ti(U_4185,U_4188)
    | ~ hBOOL(hAPP(U_4185,bool,hAPP(U_4185,fun(U_4185,bool),ord_less_eq(U_4185),U_4188),U_4186))
    | ~ semilattice_inf(U_4185) ),
    inference(clausify,[status(thm)],[f_1019_3]) ).

cnf(f_1019_5,plain,
    ( hBOOL(hAPP(U_4185,bool,hAPP(U_4185,fun(U_4185,bool),ord_less_eq(U_4185),U_4189),U_4187))
    | hAPP(U_4185,U_4185,hAPP(U_4185,fun(U_4185,U_4185),semilattice_inf_inf(U_4185),U_4189),U_4187) != ti(U_4185,U_4189)
    | ~ semilattice_inf(U_4185) ),
    inference(clausify,[status(thm)],[f_1019_3]) ).

fof(f_1020_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Y))
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_930_inf__le2]) ).

fof(f_1020_2,plain,
    ! [U_4192] :
      ( ! [U_4191,U_4190] : hBOOL(hAPP(U_4192,bool,hAPP(U_4192,fun(U_4192,bool),ord_less_eq(U_4192),hAPP(U_4192,U_4192,hAPP(U_4192,fun(U_4192,U_4192),semilattice_inf_inf(U_4192),U_4191),U_4190)),U_4190))
      | ~ semilattice_inf(U_4192) ),
    inference(variable_rename,[status(thm)],[f_1020_1]) ).

cnf(f_1020_3,plain,
    ( hBOOL(hAPP(U_4192,bool,hAPP(U_4192,fun(U_4192,bool),ord_less_eq(U_4192),hAPP(U_4192,U_4192,hAPP(U_4192,fun(U_4192,U_4192),semilattice_inf_inf(U_4192),U_4191),U_4190)),U_4190))
    | ~ semilattice_inf(U_4192) ),
    inference(clausify,[status(thm)],[f_1020_2]) ).

fof(f_1021_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Y))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_931_inf__sup__ord_I2_J]) ).

fof(f_1021_2,plain,
    ! [U_4195] :
      ( ! [U_4194,U_4193] : hBOOL(hAPP(U_4195,bool,hAPP(U_4195,fun(U_4195,bool),ord_less_eq(U_4195),hAPP(U_4195,U_4195,hAPP(U_4195,fun(U_4195,U_4195),semilattice_inf_inf(U_4195),U_4194),U_4193)),U_4193))
      | ~ lattice(U_4195) ),
    inference(variable_rename,[status(thm)],[f_1021_1]) ).

cnf(f_1021_3,plain,
    ( hBOOL(hAPP(U_4195,bool,hAPP(U_4195,fun(U_4195,bool),ord_less_eq(U_4195),hAPP(U_4195,U_4195,hAPP(U_4195,fun(U_4195,U_4195),semilattice_inf_inf(U_4195),U_4194),U_4193)),U_4193))
    | ~ lattice(U_4195) ),
    inference(clausify,[status(thm)],[f_1021_2]) ).

fof(f_1022_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),X))
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_932_inf__le1]) ).

fof(f_1022_2,plain,
    ! [U_4198] :
      ( ! [U_4197,U_4196] : hBOOL(hAPP(U_4198,bool,hAPP(U_4198,fun(U_4198,bool),ord_less_eq(U_4198),hAPP(U_4198,U_4198,hAPP(U_4198,fun(U_4198,U_4198),semilattice_inf_inf(U_4198),U_4197),U_4196)),U_4197))
      | ~ semilattice_inf(U_4198) ),
    inference(variable_rename,[status(thm)],[f_1022_1]) ).

cnf(f_1022_3,plain,
    ( hBOOL(hAPP(U_4198,bool,hAPP(U_4198,fun(U_4198,bool),ord_less_eq(U_4198),hAPP(U_4198,U_4198,hAPP(U_4198,fun(U_4198,U_4198),semilattice_inf_inf(U_4198),U_4197),U_4196)),U_4197))
    | ~ semilattice_inf(U_4198) ),
    inference(clausify,[status(thm)],[f_1022_2]) ).

fof(f_1023_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),X))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_933_inf__sup__ord_I1_J]) ).

fof(f_1023_2,plain,
    ! [U_4201] :
      ( ! [U_4200,U_4199] : hBOOL(hAPP(U_4201,bool,hAPP(U_4201,fun(U_4201,bool),ord_less_eq(U_4201),hAPP(U_4201,U_4201,hAPP(U_4201,fun(U_4201,U_4201),semilattice_inf_inf(U_4201),U_4200),U_4199)),U_4200))
      | ~ lattice(U_4201) ),
    inference(variable_rename,[status(thm)],[f_1023_1]) ).

cnf(f_1023_3,plain,
    ( hBOOL(hAPP(U_4201,bool,hAPP(U_4201,fun(U_4201,bool),ord_less_eq(U_4201),hAPP(U_4201,U_4201,hAPP(U_4201,fun(U_4201,U_4201),semilattice_inf_inf(U_4201),U_4200),U_4199)),U_4200))
    | ~ lattice(U_4201) ),
    inference(clausify,[status(thm)],[f_1023_2]) ).

fof(f_1024_1,plain,
    ! [X_a] :
      ( ! [X_2,Y_1] :
          ( ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),Y_1) = top_top(X_a)
            | ti(X_a,Y_1) != top_top(X_a)
            | ti(X_a,X_2) != top_top(X_a) )
          & ( ( ti(X_a,Y_1) = top_top(X_a)
              & ti(X_a,X_2) = top_top(X_a) )
            | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),Y_1) != top_top(X_a) ) )
      | ~ bounded_lattice_top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_934_inf__eq__top__iff]) ).

fof(f_1024_2,plain,
    ! [U_4204] :
      ( ! [U_4203,U_4202] :
          ( ( hAPP(U_4204,U_4204,hAPP(U_4204,fun(U_4204,U_4204),semilattice_inf_inf(U_4204),U_4203),U_4202) = top_top(U_4204)
            | ti(U_4204,U_4202) != top_top(U_4204)
            | ti(U_4204,U_4203) != top_top(U_4204) )
          & ( ( ti(U_4204,U_4202) = top_top(U_4204)
              & ti(U_4204,U_4203) = top_top(U_4204) )
            | hAPP(U_4204,U_4204,hAPP(U_4204,fun(U_4204,U_4204),semilattice_inf_inf(U_4204),U_4203),U_4202) != top_top(U_4204) ) )
      | ~ bounded_lattice_top(U_4204) ),
    inference(variable_rename,[status(thm)],[f_1024_1]) ).

fof(f_1024_3,plain,
    ! [U_4204] :
      ( ( ! [U_4208,U_4206] :
            ( hAPP(U_4204,U_4204,hAPP(U_4204,fun(U_4204,U_4204),semilattice_inf_inf(U_4204),U_4208),U_4206) = top_top(U_4204)
            | ti(U_4204,U_4206) != top_top(U_4204)
            | ti(U_4204,U_4208) != top_top(U_4204) )
        & ! [U_4207,U_4205] :
            ( ( ti(U_4204,U_4205) = top_top(U_4204)
              & ti(U_4204,U_4207) = top_top(U_4204) )
            | hAPP(U_4204,U_4204,hAPP(U_4204,fun(U_4204,U_4204),semilattice_inf_inf(U_4204),U_4207),U_4205) != top_top(U_4204) ) )
      | ~ bounded_lattice_top(U_4204) ),
    inference(miniscope,[status(thm)],[f_1024_2]) ).

cnf(f_1024_4,plain,
    ( ti(U_4204,U_4207) = top_top(U_4204)
    | hAPP(U_4204,U_4204,hAPP(U_4204,fun(U_4204,U_4204),semilattice_inf_inf(U_4204),U_4207),U_4205) != top_top(U_4204)
    | ~ bounded_lattice_top(U_4204) ),
    inference(clausify,[status(thm)],[f_1024_3]) ).

cnf(f_1024_5,plain,
    ( ti(U_4204,U_4205) = top_top(U_4204)
    | hAPP(U_4204,U_4204,hAPP(U_4204,fun(U_4204,U_4204),semilattice_inf_inf(U_4204),U_4207),U_4205) != top_top(U_4204)
    | ~ bounded_lattice_top(U_4204) ),
    inference(clausify,[status(thm)],[f_1024_3]) ).

cnf(f_1024_6,plain,
    ( hAPP(U_4204,U_4204,hAPP(U_4204,fun(U_4204,U_4204),semilattice_inf_inf(U_4204),U_4208),U_4206) = top_top(U_4204)
    | ti(U_4204,U_4206) != top_top(U_4204)
    | ti(U_4204,U_4208) != top_top(U_4204)
    | ~ bounded_lattice_top(U_4204) ),
    inference(clausify,[status(thm)],[f_1024_3]) ).

fof(f_1025_1,plain,
    ! [X_a] :
      ( ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),top_top(X_a)) = ti(X_a,X)
      | ~ bounded_lattice_top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_935_inf__top__right]) ).

fof(f_1025_2,plain,
    ! [U_4210] :
      ( ! [U_4209] : hAPP(U_4210,U_4210,hAPP(U_4210,fun(U_4210,U_4210),semilattice_inf_inf(U_4210),U_4209),top_top(U_4210)) = ti(U_4210,U_4209)
      | ~ bounded_lattice_top(U_4210) ),
    inference(variable_rename,[status(thm)],[f_1025_1]) ).

cnf(f_1025_3,plain,
    ( hAPP(U_4210,U_4210,hAPP(U_4210,fun(U_4210,U_4210),semilattice_inf_inf(U_4210),U_4209),top_top(U_4210)) = ti(U_4210,U_4209)
    | ~ bounded_lattice_top(U_4210) ),
    inference(clausify,[status(thm)],[f_1025_2]) ).

fof(f_1026_1,plain,
    ! [X_a] :
      ( ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),top_top(X_a)),X) = ti(X_a,X)
      | ~ bounded_lattice_top(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_936_inf__top__left]) ).

fof(f_1026_2,plain,
    ! [U_4212] :
      ( ! [U_4211] : hAPP(U_4212,U_4212,hAPP(U_4212,fun(U_4212,U_4212),semilattice_inf_inf(U_4212),top_top(U_4212)),U_4211) = ti(U_4212,U_4211)
      | ~ bounded_lattice_top(U_4212) ),
    inference(variable_rename,[status(thm)],[f_1026_1]) ).

cnf(f_1026_3,plain,
    ( hAPP(U_4212,U_4212,hAPP(U_4212,fun(U_4212,U_4212),semilattice_inf_inf(U_4212),top_top(U_4212)),U_4211) = ti(U_4212,U_4211)
    | ~ bounded_lattice_top(U_4212) ),
    inference(clausify,[status(thm)],[f_1026_2]) ).

fof(f_1027_1,plain,
    ! [X_b,X_a] :
      ( ! [F,G,X_2] : hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),semilattice_inf_inf(fun(X_b,X_a)),F),G),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,G,X_2))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_937_inf__apply]) ).

fof(f_1027_2,plain,
    ! [U_4217,U_4216] :
      ( ! [U_4215,U_4214,U_4213] : hAPP(U_4217,U_4216,hAPP(fun(U_4217,U_4216),fun(U_4217,U_4216),hAPP(fun(U_4217,U_4216),fun(fun(U_4217,U_4216),fun(U_4217,U_4216)),semilattice_inf_inf(fun(U_4217,U_4216)),U_4215),U_4214),U_4213) = hAPP(U_4216,U_4216,hAPP(U_4216,fun(U_4216,U_4216),semilattice_inf_inf(U_4216),hAPP(U_4217,U_4216,U_4215,U_4213)),hAPP(U_4217,U_4216,U_4214,U_4213))
      | ~ lattice(U_4216) ),
    inference(variable_rename,[status(thm)],[f_1027_1]) ).

cnf(f_1027_3,plain,
    ( hAPP(U_4217,U_4216,hAPP(fun(U_4217,U_4216),fun(U_4217,U_4216),hAPP(fun(U_4217,U_4216),fun(fun(U_4217,U_4216),fun(U_4217,U_4216)),semilattice_inf_inf(fun(U_4217,U_4216)),U_4215),U_4214),U_4213) = hAPP(U_4216,U_4216,hAPP(U_4216,fun(U_4216,U_4216),semilattice_inf_inf(U_4216),hAPP(U_4217,U_4216,U_4215,U_4213)),hAPP(U_4217,U_4216,U_4214,U_4213))
    | ~ lattice(U_4216) ),
    inference(clausify,[status(thm)],[f_1027_2]) ).

fof(f_1028_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_938_inf__assoc]) ).

fof(f_1028_2,plain,
    ! [U_4221] :
      ( ! [U_4220,U_4219,U_4218] : hAPP(U_4221,U_4221,hAPP(U_4221,fun(U_4221,U_4221),semilattice_inf_inf(U_4221),hAPP(U_4221,U_4221,hAPP(U_4221,fun(U_4221,U_4221),semilattice_inf_inf(U_4221),U_4220),U_4219)),U_4218) = hAPP(U_4221,U_4221,hAPP(U_4221,fun(U_4221,U_4221),semilattice_inf_inf(U_4221),U_4220),hAPP(U_4221,U_4221,hAPP(U_4221,fun(U_4221,U_4221),semilattice_inf_inf(U_4221),U_4219),U_4218))
      | ~ semilattice_inf(U_4221) ),
    inference(variable_rename,[status(thm)],[f_1028_1]) ).

cnf(f_1028_3,plain,
    ( hAPP(U_4221,U_4221,hAPP(U_4221,fun(U_4221,U_4221),semilattice_inf_inf(U_4221),hAPP(U_4221,U_4221,hAPP(U_4221,fun(U_4221,U_4221),semilattice_inf_inf(U_4221),U_4220),U_4219)),U_4218) = hAPP(U_4221,U_4221,hAPP(U_4221,fun(U_4221,U_4221),semilattice_inf_inf(U_4221),U_4220),hAPP(U_4221,U_4221,hAPP(U_4221,fun(U_4221,U_4221),semilattice_inf_inf(U_4221),U_4219),U_4218))
    | ~ semilattice_inf(U_4221) ),
    inference(clausify,[status(thm)],[f_1028_2]) ).

fof(f_1029_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_939_inf__sup__aci_I2_J]) ).

fof(f_1029_2,plain,
    ! [U_4225] :
      ( ! [U_4224,U_4223,U_4222] : hAPP(U_4225,U_4225,hAPP(U_4225,fun(U_4225,U_4225),semilattice_inf_inf(U_4225),hAPP(U_4225,U_4225,hAPP(U_4225,fun(U_4225,U_4225),semilattice_inf_inf(U_4225),U_4224),U_4223)),U_4222) = hAPP(U_4225,U_4225,hAPP(U_4225,fun(U_4225,U_4225),semilattice_inf_inf(U_4225),U_4224),hAPP(U_4225,U_4225,hAPP(U_4225,fun(U_4225,U_4225),semilattice_inf_inf(U_4225),U_4223),U_4222))
      | ~ lattice(U_4225) ),
    inference(variable_rename,[status(thm)],[f_1029_1]) ).

cnf(f_1029_3,plain,
    ( hAPP(U_4225,U_4225,hAPP(U_4225,fun(U_4225,U_4225),semilattice_inf_inf(U_4225),hAPP(U_4225,U_4225,hAPP(U_4225,fun(U_4225,U_4225),semilattice_inf_inf(U_4225),U_4224),U_4223)),U_4222) = hAPP(U_4225,U_4225,hAPP(U_4225,fun(U_4225,U_4225),semilattice_inf_inf(U_4225),U_4224),hAPP(U_4225,U_4225,hAPP(U_4225,fun(U_4225,U_4225),semilattice_inf_inf(U_4225),U_4223),U_4222))
    | ~ lattice(U_4225) ),
    inference(clausify,[status(thm)],[f_1029_2]) ).

fof(f_1030_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),C_1))
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_940_inf_Oassoc]) ).

fof(f_1030_2,plain,
    ! [U_4229] :
      ( ! [U_4228,U_4227,U_4226] : hAPP(U_4229,U_4229,hAPP(U_4229,fun(U_4229,U_4229),semilattice_inf_inf(U_4229),hAPP(U_4229,U_4229,hAPP(U_4229,fun(U_4229,U_4229),semilattice_inf_inf(U_4229),U_4228),U_4227)),U_4226) = hAPP(U_4229,U_4229,hAPP(U_4229,fun(U_4229,U_4229),semilattice_inf_inf(U_4229),U_4228),hAPP(U_4229,U_4229,hAPP(U_4229,fun(U_4229,U_4229),semilattice_inf_inf(U_4229),U_4227),U_4226))
      | ~ semilattice_inf(U_4229) ),
    inference(variable_rename,[status(thm)],[f_1030_1]) ).

cnf(f_1030_3,plain,
    ( hAPP(U_4229,U_4229,hAPP(U_4229,fun(U_4229,U_4229),semilattice_inf_inf(U_4229),hAPP(U_4229,U_4229,hAPP(U_4229,fun(U_4229,U_4229),semilattice_inf_inf(U_4229),U_4228),U_4227)),U_4226) = hAPP(U_4229,U_4229,hAPP(U_4229,fun(U_4229,U_4229),semilattice_inf_inf(U_4229),U_4228),hAPP(U_4229,U_4229,hAPP(U_4229,fun(U_4229,U_4229),semilattice_inf_inf(U_4229),U_4227),U_4226))
    | ~ semilattice_inf(U_4229) ),
    inference(clausify,[status(thm)],[f_1030_2]) ).

fof(f_1031_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z))
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_941_inf__left__commute]) ).

fof(f_1031_2,plain,
    ! [U_4233] :
      ( ! [U_4232,U_4231,U_4230] : hAPP(U_4233,U_4233,hAPP(U_4233,fun(U_4233,U_4233),semilattice_inf_inf(U_4233),U_4232),hAPP(U_4233,U_4233,hAPP(U_4233,fun(U_4233,U_4233),semilattice_inf_inf(U_4233),U_4231),U_4230)) = hAPP(U_4233,U_4233,hAPP(U_4233,fun(U_4233,U_4233),semilattice_inf_inf(U_4233),U_4231),hAPP(U_4233,U_4233,hAPP(U_4233,fun(U_4233,U_4233),semilattice_inf_inf(U_4233),U_4232),U_4230))
      | ~ semilattice_inf(U_4233) ),
    inference(variable_rename,[status(thm)],[f_1031_1]) ).

cnf(f_1031_3,plain,
    ( hAPP(U_4233,U_4233,hAPP(U_4233,fun(U_4233,U_4233),semilattice_inf_inf(U_4233),U_4232),hAPP(U_4233,U_4233,hAPP(U_4233,fun(U_4233,U_4233),semilattice_inf_inf(U_4233),U_4231),U_4230)) = hAPP(U_4233,U_4233,hAPP(U_4233,fun(U_4233,U_4233),semilattice_inf_inf(U_4233),U_4231),hAPP(U_4233,U_4233,hAPP(U_4233,fun(U_4233,U_4233),semilattice_inf_inf(U_4233),U_4232),U_4230))
    | ~ semilattice_inf(U_4233) ),
    inference(clausify,[status(thm)],[f_1031_2]) ).

fof(f_1032_1,plain,
    ! [X_a] :
      ( ! [X,Y,Z] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z))
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_942_inf__sup__aci_I3_J]) ).

fof(f_1032_2,plain,
    ! [U_4237] :
      ( ! [U_4236,U_4235,U_4234] : hAPP(U_4237,U_4237,hAPP(U_4237,fun(U_4237,U_4237),semilattice_inf_inf(U_4237),U_4236),hAPP(U_4237,U_4237,hAPP(U_4237,fun(U_4237,U_4237),semilattice_inf_inf(U_4237),U_4235),U_4234)) = hAPP(U_4237,U_4237,hAPP(U_4237,fun(U_4237,U_4237),semilattice_inf_inf(U_4237),U_4235),hAPP(U_4237,U_4237,hAPP(U_4237,fun(U_4237,U_4237),semilattice_inf_inf(U_4237),U_4236),U_4234))
      | ~ lattice(U_4237) ),
    inference(variable_rename,[status(thm)],[f_1032_1]) ).

cnf(f_1032_3,plain,
    ( hAPP(U_4237,U_4237,hAPP(U_4237,fun(U_4237,U_4237),semilattice_inf_inf(U_4237),U_4236),hAPP(U_4237,U_4237,hAPP(U_4237,fun(U_4237,U_4237),semilattice_inf_inf(U_4237),U_4235),U_4234)) = hAPP(U_4237,U_4237,hAPP(U_4237,fun(U_4237,U_4237),semilattice_inf_inf(U_4237),U_4235),hAPP(U_4237,U_4237,hAPP(U_4237,fun(U_4237,U_4237),semilattice_inf_inf(U_4237),U_4236),U_4234))
    | ~ lattice(U_4237) ),
    inference(clausify,[status(thm)],[f_1032_2]) ).

fof(f_1033_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2,C_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),C_1))
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_943_inf_Oleft__commute]) ).

fof(f_1033_2,plain,
    ! [U_4241] :
      ( ! [U_4240,U_4239,U_4238] : hAPP(U_4241,U_4241,hAPP(U_4241,fun(U_4241,U_4241),semilattice_inf_inf(U_4241),U_4240),hAPP(U_4241,U_4241,hAPP(U_4241,fun(U_4241,U_4241),semilattice_inf_inf(U_4241),U_4239),U_4238)) = hAPP(U_4241,U_4241,hAPP(U_4241,fun(U_4241,U_4241),semilattice_inf_inf(U_4241),U_4239),hAPP(U_4241,U_4241,hAPP(U_4241,fun(U_4241,U_4241),semilattice_inf_inf(U_4241),U_4240),U_4238))
      | ~ semilattice_inf(U_4241) ),
    inference(variable_rename,[status(thm)],[f_1033_1]) ).

cnf(f_1033_3,plain,
    ( hAPP(U_4241,U_4241,hAPP(U_4241,fun(U_4241,U_4241),semilattice_inf_inf(U_4241),U_4240),hAPP(U_4241,U_4241,hAPP(U_4241,fun(U_4241,U_4241),semilattice_inf_inf(U_4241),U_4239),U_4238)) = hAPP(U_4241,U_4241,hAPP(U_4241,fun(U_4241,U_4241),semilattice_inf_inf(U_4241),U_4239),hAPP(U_4241,U_4241,hAPP(U_4241,fun(U_4241,U_4241),semilattice_inf_inf(U_4241),U_4240),U_4238))
    | ~ semilattice_inf(U_4241) ),
    inference(clausify,[status(thm)],[f_1033_2]) ).

fof(f_1034_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_944_inf__left__idem]) ).

fof(f_1034_2,plain,
    ! [U_4244] :
      ( ! [U_4243,U_4242] : hAPP(U_4244,U_4244,hAPP(U_4244,fun(U_4244,U_4244),semilattice_inf_inf(U_4244),U_4243),hAPP(U_4244,U_4244,hAPP(U_4244,fun(U_4244,U_4244),semilattice_inf_inf(U_4244),U_4243),U_4242)) = hAPP(U_4244,U_4244,hAPP(U_4244,fun(U_4244,U_4244),semilattice_inf_inf(U_4244),U_4243),U_4242)
      | ~ semilattice_inf(U_4244) ),
    inference(variable_rename,[status(thm)],[f_1034_1]) ).

cnf(f_1034_3,plain,
    ( hAPP(U_4244,U_4244,hAPP(U_4244,fun(U_4244,U_4244),semilattice_inf_inf(U_4244),U_4243),hAPP(U_4244,U_4244,hAPP(U_4244,fun(U_4244,U_4244),semilattice_inf_inf(U_4244),U_4243),U_4242)) = hAPP(U_4244,U_4244,hAPP(U_4244,fun(U_4244,U_4244),semilattice_inf_inf(U_4244),U_4243),U_4242)
    | ~ semilattice_inf(U_4244) ),
    inference(clausify,[status(thm)],[f_1034_2]) ).

fof(f_1035_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_945_inf__sup__aci_I4_J]) ).

fof(f_1035_2,plain,
    ! [U_4247] :
      ( ! [U_4246,U_4245] : hAPP(U_4247,U_4247,hAPP(U_4247,fun(U_4247,U_4247),semilattice_inf_inf(U_4247),U_4246),hAPP(U_4247,U_4247,hAPP(U_4247,fun(U_4247,U_4247),semilattice_inf_inf(U_4247),U_4246),U_4245)) = hAPP(U_4247,U_4247,hAPP(U_4247,fun(U_4247,U_4247),semilattice_inf_inf(U_4247),U_4246),U_4245)
      | ~ lattice(U_4247) ),
    inference(variable_rename,[status(thm)],[f_1035_1]) ).

cnf(f_1035_3,plain,
    ( hAPP(U_4247,U_4247,hAPP(U_4247,fun(U_4247,U_4247),semilattice_inf_inf(U_4247),U_4246),hAPP(U_4247,U_4247,hAPP(U_4247,fun(U_4247,U_4247),semilattice_inf_inf(U_4247),U_4246),U_4245)) = hAPP(U_4247,U_4247,hAPP(U_4247,fun(U_4247,U_4247),semilattice_inf_inf(U_4247),U_4246),U_4245)
    | ~ lattice(U_4247) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

fof(f_1036_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_946_inf_Oleft__idem]) ).

fof(f_1036_2,plain,
    ! [U_4250] :
      ( ! [U_4249,U_4248] : hAPP(U_4250,U_4250,hAPP(U_4250,fun(U_4250,U_4250),semilattice_inf_inf(U_4250),U_4249),hAPP(U_4250,U_4250,hAPP(U_4250,fun(U_4250,U_4250),semilattice_inf_inf(U_4250),U_4249),U_4248)) = hAPP(U_4250,U_4250,hAPP(U_4250,fun(U_4250,U_4250),semilattice_inf_inf(U_4250),U_4249),U_4248)
      | ~ semilattice_inf(U_4250) ),
    inference(variable_rename,[status(thm)],[f_1036_1]) ).

cnf(f_1036_3,plain,
    ( hAPP(U_4250,U_4250,hAPP(U_4250,fun(U_4250,U_4250),semilattice_inf_inf(U_4250),U_4249),hAPP(U_4250,U_4250,hAPP(U_4250,fun(U_4250,U_4250),semilattice_inf_inf(U_4250),U_4249),U_4248)) = hAPP(U_4250,U_4250,hAPP(U_4250,fun(U_4250,U_4250),semilattice_inf_inf(U_4250),U_4249),U_4248)
    | ~ semilattice_inf(U_4250) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

fof(f_1037_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X)
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_947_inf__commute]) ).

fof(f_1037_2,plain,
    ! [U_4253] :
      ( ! [U_4252,U_4251] : hAPP(U_4253,U_4253,hAPP(U_4253,fun(U_4253,U_4253),semilattice_inf_inf(U_4253),U_4252),U_4251) = hAPP(U_4253,U_4253,hAPP(U_4253,fun(U_4253,U_4253),semilattice_inf_inf(U_4253),U_4251),U_4252)
      | ~ semilattice_inf(U_4253) ),
    inference(variable_rename,[status(thm)],[f_1037_1]) ).

cnf(f_1037_3,plain,
    ( hAPP(U_4253,U_4253,hAPP(U_4253,fun(U_4253,U_4253),semilattice_inf_inf(U_4253),U_4252),U_4251) = hAPP(U_4253,U_4253,hAPP(U_4253,fun(U_4253,U_4253),semilattice_inf_inf(U_4253),U_4251),U_4252)
    | ~ semilattice_inf(U_4253) ),
    inference(clausify,[status(thm)],[f_1037_2]) ).

fof(f_1038_1,plain,
    ! [X_a] :
      ( ! [X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X)
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_948_inf__sup__aci_I1_J]) ).

fof(f_1038_2,plain,
    ! [U_4256] :
      ( ! [U_4255,U_4254] : hAPP(U_4256,U_4256,hAPP(U_4256,fun(U_4256,U_4256),semilattice_inf_inf(U_4256),U_4255),U_4254) = hAPP(U_4256,U_4256,hAPP(U_4256,fun(U_4256,U_4256),semilattice_inf_inf(U_4256),U_4254),U_4255)
      | ~ lattice(U_4256) ),
    inference(variable_rename,[status(thm)],[f_1038_1]) ).

cnf(f_1038_3,plain,
    ( hAPP(U_4256,U_4256,hAPP(U_4256,fun(U_4256,U_4256),semilattice_inf_inf(U_4256),U_4255),U_4254) = hAPP(U_4256,U_4256,hAPP(U_4256,fun(U_4256,U_4256),semilattice_inf_inf(U_4256),U_4254),U_4255)
    | ~ lattice(U_4256) ),
    inference(clausify,[status(thm)],[f_1038_2]) ).

fof(f_1039_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_1),A_2)
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_949_inf_Ocommute]) ).

fof(f_1039_2,plain,
    ! [U_4259] :
      ( ! [U_4258,U_4257] : hAPP(U_4259,U_4259,hAPP(U_4259,fun(U_4259,U_4259),semilattice_inf_inf(U_4259),U_4258),U_4257) = hAPP(U_4259,U_4259,hAPP(U_4259,fun(U_4259,U_4259),semilattice_inf_inf(U_4259),U_4257),U_4258)
      | ~ semilattice_inf(U_4259) ),
    inference(variable_rename,[status(thm)],[f_1039_1]) ).

cnf(f_1039_3,plain,
    ( hAPP(U_4259,U_4259,hAPP(U_4259,fun(U_4259,U_4259),semilattice_inf_inf(U_4259),U_4258),U_4257) = hAPP(U_4259,U_4259,hAPP(U_4259,fun(U_4259,U_4259),semilattice_inf_inf(U_4259),U_4257),U_4258)
    | ~ semilattice_inf(U_4259) ),
    inference(clausify,[status(thm)],[f_1039_2]) ).

fof(f_1040_1,plain,
    ! [X_a,X_b] :
      ( ! [F,G,X_1] : hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),semilattice_inf_inf(fun(X_a,X_b)),F),G),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))
      | ~ lattice(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_950_inf__fun__def]) ).

fof(f_1040_2,plain,
    ! [U_4264,U_4263] :
      ( ! [U_4262,U_4261,U_4260] : hAPP(U_4264,U_4263,hAPP(fun(U_4264,U_4263),fun(U_4264,U_4263),hAPP(fun(U_4264,U_4263),fun(fun(U_4264,U_4263),fun(U_4264,U_4263)),semilattice_inf_inf(fun(U_4264,U_4263)),U_4262),U_4261),U_4260) = hAPP(U_4263,U_4263,hAPP(U_4263,fun(U_4263,U_4263),semilattice_inf_inf(U_4263),hAPP(U_4264,U_4263,U_4262,U_4260)),hAPP(U_4264,U_4263,U_4261,U_4260))
      | ~ lattice(U_4263) ),
    inference(variable_rename,[status(thm)],[f_1040_1]) ).

cnf(f_1040_3,plain,
    ( hAPP(U_4264,U_4263,hAPP(fun(U_4264,U_4263),fun(U_4264,U_4263),hAPP(fun(U_4264,U_4263),fun(fun(U_4264,U_4263),fun(U_4264,U_4263)),semilattice_inf_inf(fun(U_4264,U_4263)),U_4262),U_4261),U_4260) = hAPP(U_4263,U_4263,hAPP(U_4263,fun(U_4263,U_4263),semilattice_inf_inf(U_4263),hAPP(U_4264,U_4263,U_4262,U_4260)),hAPP(U_4264,U_4263,U_4261,U_4260))
    | ~ lattice(U_4263) ),
    inference(clausify,[status(thm)],[f_1040_2]) ).

fof(f_1041_1,plain,
    ! [X_a] :
      ( ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),X) = ti(X_a,X)
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_951_inf__idem]) ).

fof(f_1041_2,plain,
    ! [U_4266] :
      ( ! [U_4265] : hAPP(U_4266,U_4266,hAPP(U_4266,fun(U_4266,U_4266),semilattice_inf_inf(U_4266),U_4265),U_4265) = ti(U_4266,U_4265)
      | ~ semilattice_inf(U_4266) ),
    inference(variable_rename,[status(thm)],[f_1041_1]) ).

cnf(f_1041_3,plain,
    ( hAPP(U_4266,U_4266,hAPP(U_4266,fun(U_4266,U_4266),semilattice_inf_inf(U_4266),U_4265),U_4265) = ti(U_4266,U_4265)
    | ~ semilattice_inf(U_4266) ),
    inference(clausify,[status(thm)],[f_1041_2]) ).

fof(f_1042_1,plain,
    ! [X_a] :
      ( ! [A_2] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),A_2) = ti(X_a,A_2)
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_952_inf_Oidem]) ).

fof(f_1042_2,plain,
    ! [U_4268] :
      ( ! [U_4267] : hAPP(U_4268,U_4268,hAPP(U_4268,fun(U_4268,U_4268),semilattice_inf_inf(U_4268),U_4267),U_4267) = ti(U_4268,U_4267)
      | ~ semilattice_inf(U_4268) ),
    inference(variable_rename,[status(thm)],[f_1042_1]) ).

cnf(f_1042_3,plain,
    ( hAPP(U_4268,U_4268,hAPP(U_4268,fun(U_4268,U_4268),semilattice_inf_inf(U_4268),U_4267),U_4267) = ti(U_4268,U_4267)
    | ~ semilattice_inf(U_4268) ),
    inference(clausify,[status(thm)],[f_1042_2]) ).

fof(f_1043_1,plain,
    ! [X_a] :
      ( ! [B_1,A_2,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),X)) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_953_less__infI1]) ).

fof(f_1043_2,plain,
    ! [U_4272] :
      ( ! [U_4271,U_4270,U_4269] :
          ( hBOOL(hAPP(U_4272,bool,hAPP(U_4272,fun(U_4272,bool),ord_less(U_4272),hAPP(U_4272,U_4272,hAPP(U_4272,fun(U_4272,U_4272),semilattice_inf_inf(U_4272),U_4270),U_4271)),U_4269))
          | ~ hBOOL(hAPP(U_4272,bool,hAPP(U_4272,fun(U_4272,bool),ord_less(U_4272),U_4270),U_4269)) )
      | ~ semilattice_inf(U_4272) ),
    inference(variable_rename,[status(thm)],[f_1043_1]) ).

cnf(f_1043_3,plain,
    ( hBOOL(hAPP(U_4272,bool,hAPP(U_4272,fun(U_4272,bool),ord_less(U_4272),hAPP(U_4272,U_4272,hAPP(U_4272,fun(U_4272,U_4272),semilattice_inf_inf(U_4272),U_4270),U_4271)),U_4269))
    | ~ hBOOL(hAPP(U_4272,bool,hAPP(U_4272,fun(U_4272,bool),ord_less(U_4272),U_4270),U_4269))
    | ~ semilattice_inf(U_4272) ),
    inference(clausify,[status(thm)],[f_1043_2]) ).

fof(f_1044_1,plain,
    ! [X_a] :
      ( ! [A_2,B_1,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_2),B_1)),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),X)) )
      | ~ semilattice_inf(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_954_less__infI2]) ).

fof(f_1044_2,plain,
    ! [U_4276] :
      ( ! [U_4275,U_4274,U_4273] :
          ( hBOOL(hAPP(U_4276,bool,hAPP(U_4276,fun(U_4276,bool),ord_less(U_4276),hAPP(U_4276,U_4276,hAPP(U_4276,fun(U_4276,U_4276),semilattice_inf_inf(U_4276),U_4275),U_4274)),U_4273))
          | ~ hBOOL(hAPP(U_4276,bool,hAPP(U_4276,fun(U_4276,bool),ord_less(U_4276),U_4274),U_4273)) )
      | ~ semilattice_inf(U_4276) ),
    inference(variable_rename,[status(thm)],[f_1044_1]) ).

cnf(f_1044_3,plain,
    ( hBOOL(hAPP(U_4276,bool,hAPP(U_4276,fun(U_4276,bool),ord_less(U_4276),hAPP(U_4276,U_4276,hAPP(U_4276,fun(U_4276,U_4276),semilattice_inf_inf(U_4276),U_4275),U_4274)),U_4273))
    | ~ hBOOL(hAPP(U_4276,bool,hAPP(U_4276,fun(U_4276,bool),ord_less(U_4276),U_4274),U_4273))
    | ~ semilattice_inf(U_4276) ),
    inference(clausify,[status(thm)],[f_1044_2]) ).

fof(f_1045_1,plain,
    ! [X_a] :
      ( ! [F,P_1,M,Na] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Na))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Na),P_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),P_1))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),P_1))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_955_setsum__add__nat__ivl]) ).

fof(f_1045_2,plain,
    ! [U_4281] :
      ( ! [U_4280,U_4279,U_4278,U_4277] :
          ( hAPP(U_4281,U_4281,hAPP(U_4281,fun(U_4281,U_4281),plus_plus(U_4281),hAPP(fun(nat,bool),U_4281,hAPP(fun(nat,U_4281),fun(fun(nat,bool),U_4281),big_co1399186613setsum(nat,U_4281),U_4280),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4278),U_4277))),hAPP(fun(nat,bool),U_4281,hAPP(fun(nat,U_4281),fun(fun(nat,bool),U_4281),big_co1399186613setsum(nat,U_4281),U_4280),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4277),U_4279))) = hAPP(fun(nat,bool),U_4281,hAPP(fun(nat,U_4281),fun(fun(nat,bool),U_4281),big_co1399186613setsum(nat,U_4281),U_4280),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4278),U_4279))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_4277),U_4279))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_4278),U_4277)) )
      | ~ comm_monoid_add(U_4281) ),
    inference(variable_rename,[status(thm)],[f_1045_1]) ).

cnf(f_1045_3,plain,
    ( hAPP(U_4281,U_4281,hAPP(U_4281,fun(U_4281,U_4281),plus_plus(U_4281),hAPP(fun(nat,bool),U_4281,hAPP(fun(nat,U_4281),fun(fun(nat,bool),U_4281),big_co1399186613setsum(nat,U_4281),U_4280),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4278),U_4277))),hAPP(fun(nat,bool),U_4281,hAPP(fun(nat,U_4281),fun(fun(nat,bool),U_4281),big_co1399186613setsum(nat,U_4281),U_4280),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4277),U_4279))) = hAPP(fun(nat,bool),U_4281,hAPP(fun(nat,U_4281),fun(fun(nat,bool),U_4281),big_co1399186613setsum(nat,U_4281),U_4280),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4278),U_4279))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_4277),U_4279))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_4278),U_4277))
    | ~ comm_monoid_add(U_4281) ),
    inference(clausify,[status(thm)],[f_1045_2]) ).

fof(f_1046_1,plain,
    ! [K,F] :
      ( hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),K))
      | hAPP(nat,nat,F,zero_zero(nat)) != zero_zero(nat) ),
    inference(fof_nnf,[status(thm)],[fact_956_setsum__shift__lb__Suc0__0]) ).

fof(f_1046_2,plain,
    ! [U_4283,U_4282] :
      ( hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),U_4282),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_4283)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),U_4282),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_4283))
      | hAPP(nat,nat,U_4282,zero_zero(nat)) != zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[f_1046_1]) ).

cnf(f_1046_3,plain,
    ( hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),U_4282),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_4283)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),U_4282),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),U_4283))
    | hAPP(nat,nat,U_4282,zero_zero(nat)) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_1046_2]) ).

fof(f_1047_1,plain,
    ! [X_a,X_b,B,A_1,F,C] :
      ( hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),C)) ),
    inference(fof_nnf,[status(thm)],[fact_957_inj__on__image__Int]) ).

fof(f_1047_2,plain,
    ! [U_4289,U_4288,U_4287,U_4286,U_4285,U_4284] :
      ( hAPP(fun(U_4289,bool),fun(U_4288,bool),hAPP(fun(U_4289,U_4288),fun(fun(U_4289,bool),fun(U_4288,bool)),image(U_4289,U_4288),U_4285),hAPP(fun(U_4289,bool),fun(U_4289,bool),hAPP(fun(U_4289,bool),fun(fun(U_4289,bool),fun(U_4289,bool)),semilattice_inf_inf(fun(U_4289,bool)),U_4286),U_4287)) = hAPP(fun(U_4288,bool),fun(U_4288,bool),hAPP(fun(U_4288,bool),fun(fun(U_4288,bool),fun(U_4288,bool)),semilattice_inf_inf(fun(U_4288,bool)),hAPP(fun(U_4289,bool),fun(U_4288,bool),hAPP(fun(U_4289,U_4288),fun(fun(U_4289,bool),fun(U_4288,bool)),image(U_4289,U_4288),U_4285),U_4286)),hAPP(fun(U_4289,bool),fun(U_4288,bool),hAPP(fun(U_4289,U_4288),fun(fun(U_4289,bool),fun(U_4288,bool)),image(U_4289,U_4288),U_4285),U_4287))
      | ~ hBOOL(hAPP(fun(U_4289,bool),bool,hAPP(fun(U_4289,bool),fun(fun(U_4289,bool),bool),ord_less_eq(fun(U_4289,bool)),U_4287),U_4284))
      | ~ hBOOL(hAPP(fun(U_4289,bool),bool,hAPP(fun(U_4289,bool),fun(fun(U_4289,bool),bool),ord_less_eq(fun(U_4289,bool)),U_4286),U_4284))
      | ~ hBOOL(hAPP(fun(U_4289,bool),bool,hAPP(fun(U_4289,U_4288),fun(fun(U_4289,bool),bool),inj_on(U_4289,U_4288),U_4285),U_4284)) ),
    inference(variable_rename,[status(thm)],[f_1047_1]) ).

cnf(f_1047_3,plain,
    ( hAPP(fun(U_4289,bool),fun(U_4288,bool),hAPP(fun(U_4289,U_4288),fun(fun(U_4289,bool),fun(U_4288,bool)),image(U_4289,U_4288),U_4285),hAPP(fun(U_4289,bool),fun(U_4289,bool),hAPP(fun(U_4289,bool),fun(fun(U_4289,bool),fun(U_4289,bool)),semilattice_inf_inf(fun(U_4289,bool)),U_4286),U_4287)) = hAPP(fun(U_4288,bool),fun(U_4288,bool),hAPP(fun(U_4288,bool),fun(fun(U_4288,bool),fun(U_4288,bool)),semilattice_inf_inf(fun(U_4288,bool)),hAPP(fun(U_4289,bool),fun(U_4288,bool),hAPP(fun(U_4289,U_4288),fun(fun(U_4289,bool),fun(U_4288,bool)),image(U_4289,U_4288),U_4285),U_4286)),hAPP(fun(U_4289,bool),fun(U_4288,bool),hAPP(fun(U_4289,U_4288),fun(fun(U_4289,bool),fun(U_4288,bool)),image(U_4289,U_4288),U_4285),U_4287))
    | ~ hBOOL(hAPP(fun(U_4289,bool),bool,hAPP(fun(U_4289,bool),fun(fun(U_4289,bool),bool),ord_less_eq(fun(U_4289,bool)),U_4287),U_4284))
    | ~ hBOOL(hAPP(fun(U_4289,bool),bool,hAPP(fun(U_4289,bool),fun(fun(U_4289,bool),bool),ord_less_eq(fun(U_4289,bool)),U_4286),U_4284))
    | ~ hBOOL(hAPP(fun(U_4289,bool),bool,hAPP(fun(U_4289,U_4288),fun(fun(U_4289,bool),bool),inj_on(U_4289,U_4288),U_4285),U_4284)) ),
    inference(clausify,[status(thm)],[f_1047_2]) ).

fof(f_1048_1,plain,
    ! [X_a,X_b,A_1,B,F] :
      ( hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
    inference(fof_nnf,[status(thm)],[fact_958_image__Int]) ).

fof(f_1048_2,plain,
    ! [U_4294,U_4293,U_4292,U_4291,U_4290] :
      ( hAPP(fun(U_4294,bool),fun(U_4293,bool),hAPP(fun(U_4294,U_4293),fun(fun(U_4294,bool),fun(U_4293,bool)),image(U_4294,U_4293),U_4290),hAPP(fun(U_4294,bool),fun(U_4294,bool),hAPP(fun(U_4294,bool),fun(fun(U_4294,bool),fun(U_4294,bool)),semilattice_inf_inf(fun(U_4294,bool)),U_4292),U_4291)) = hAPP(fun(U_4293,bool),fun(U_4293,bool),hAPP(fun(U_4293,bool),fun(fun(U_4293,bool),fun(U_4293,bool)),semilattice_inf_inf(fun(U_4293,bool)),hAPP(fun(U_4294,bool),fun(U_4293,bool),hAPP(fun(U_4294,U_4293),fun(fun(U_4294,bool),fun(U_4293,bool)),image(U_4294,U_4293),U_4290),U_4292)),hAPP(fun(U_4294,bool),fun(U_4293,bool),hAPP(fun(U_4294,U_4293),fun(fun(U_4294,bool),fun(U_4293,bool)),image(U_4294,U_4293),U_4290),U_4291))
      | ~ hBOOL(hAPP(fun(U_4294,bool),bool,hAPP(fun(U_4294,U_4293),fun(fun(U_4294,bool),bool),inj_on(U_4294,U_4293),U_4290),top_top(fun(U_4294,bool)))) ),
    inference(variable_rename,[status(thm)],[f_1048_1]) ).

cnf(f_1048_3,plain,
    ( hAPP(fun(U_4294,bool),fun(U_4293,bool),hAPP(fun(U_4294,U_4293),fun(fun(U_4294,bool),fun(U_4293,bool)),image(U_4294,U_4293),U_4290),hAPP(fun(U_4294,bool),fun(U_4294,bool),hAPP(fun(U_4294,bool),fun(fun(U_4294,bool),fun(U_4294,bool)),semilattice_inf_inf(fun(U_4294,bool)),U_4292),U_4291)) = hAPP(fun(U_4293,bool),fun(U_4293,bool),hAPP(fun(U_4293,bool),fun(fun(U_4293,bool),fun(U_4293,bool)),semilattice_inf_inf(fun(U_4293,bool)),hAPP(fun(U_4294,bool),fun(U_4293,bool),hAPP(fun(U_4294,U_4293),fun(fun(U_4294,bool),fun(U_4293,bool)),image(U_4294,U_4293),U_4290),U_4292)),hAPP(fun(U_4294,bool),fun(U_4293,bool),hAPP(fun(U_4294,U_4293),fun(fun(U_4294,bool),fun(U_4293,bool)),image(U_4294,U_4293),U_4290),U_4291))
    | ~ hBOOL(hAPP(fun(U_4294,bool),bool,hAPP(fun(U_4294,U_4293),fun(fun(U_4294,bool),bool),inj_on(U_4294,U_4293),U_4290),top_top(fun(U_4294,bool)))) ),
    inference(clausify,[status(thm)],[f_1048_2]) ).

fof(f_1049_1,plain,
    ! [X_a] :
      ( ! [K,F] :
          ( hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))
          | hAPP(nat,X_a,F,zero_zero(nat)) != zero_zero(X_a) )
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_959_setsum__shift__lb__Suc0__0__upt]) ).

fof(f_1049_2,plain,
    ! [U_4297] :
      ( ! [U_4296,U_4295] :
          ( hAPP(fun(nat,bool),U_4297,hAPP(fun(nat,U_4297),fun(fun(nat,bool),U_4297),big_co1399186613setsum(nat,U_4297),U_4295),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_4296)) = hAPP(fun(nat,bool),U_4297,hAPP(fun(nat,U_4297),fun(fun(nat,bool),U_4297),big_co1399186613setsum(nat,U_4297),U_4295),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_4296))
          | hAPP(nat,U_4297,U_4295,zero_zero(nat)) != zero_zero(U_4297) )
      | ~ comm_monoid_add(U_4297) ),
    inference(variable_rename,[status(thm)],[f_1049_1]) ).

cnf(f_1049_3,plain,
    ( hAPP(fun(nat,bool),U_4297,hAPP(fun(nat,U_4297),fun(fun(nat,bool),U_4297),big_co1399186613setsum(nat,U_4297),U_4295),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),U_4296)) = hAPP(fun(nat,bool),U_4297,hAPP(fun(nat,U_4297),fun(fun(nat,bool),U_4297),big_co1399186613setsum(nat,U_4297),U_4295),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),U_4296))
    | hAPP(nat,U_4297,U_4295,zero_zero(nat)) != zero_zero(U_4297)
    | ~ comm_monoid_add(U_4297) ),
    inference(clausify,[status(thm)],[f_1049_2]) ).

fof(f_1050_1,plain,
    ! [X_a] :
      ( ! [F,M,Na] :
          ( hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Na)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,M)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,M)),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) )
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_960_setsum__head__upt__Suc]) ).

fof(f_1050_2,plain,
    ! [U_4301] :
      ( ! [U_4300,U_4299,U_4298] :
          ( hAPP(fun(nat,bool),U_4301,hAPP(fun(nat,U_4301),fun(fun(nat,bool),U_4301),big_co1399186613setsum(nat,U_4301),U_4300),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4299),U_4298)) = hAPP(U_4301,U_4301,hAPP(U_4301,fun(U_4301,U_4301),plus_plus(U_4301),hAPP(nat,U_4301,U_4300,U_4299)),hAPP(fun(nat,bool),U_4301,hAPP(fun(nat,U_4301),fun(fun(nat,bool),U_4301),big_co1399186613setsum(nat,U_4301),U_4300),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,U_4299)),U_4298)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_4299),U_4298)) )
      | ~ comm_monoid_add(U_4301) ),
    inference(variable_rename,[status(thm)],[f_1050_1]) ).

cnf(f_1050_3,plain,
    ( hAPP(fun(nat,bool),U_4301,hAPP(fun(nat,U_4301),fun(fun(nat,bool),U_4301),big_co1399186613setsum(nat,U_4301),U_4300),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4299),U_4298)) = hAPP(U_4301,U_4301,hAPP(U_4301,fun(U_4301,U_4301),plus_plus(U_4301),hAPP(nat,U_4301,U_4300,U_4299)),hAPP(fun(nat,bool),U_4301,hAPP(fun(nat,U_4301),fun(fun(nat,bool),U_4301),big_co1399186613setsum(nat,U_4301),U_4300),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,U_4299)),U_4298)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_4299),U_4298))
    | ~ comm_monoid_add(U_4301) ),
    inference(clausify,[status(thm)],[f_1050_2]) ).

fof(f_1051_1,plain,
    ! [X_a] :
      ( ! [F,M,Na] :
          ( hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,M)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,M)),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_961_setsum__head__Suc]) ).

fof(f_1051_2,plain,
    ! [U_4305] :
      ( ! [U_4304,U_4303,U_4302] :
          ( hAPP(fun(nat,bool),U_4305,hAPP(fun(nat,U_4305),fun(fun(nat,bool),U_4305),big_co1399186613setsum(nat,U_4305),U_4304),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4303),U_4302)) = hAPP(U_4305,U_4305,hAPP(U_4305,fun(U_4305,U_4305),plus_plus(U_4305),hAPP(nat,U_4305,U_4304,U_4303)),hAPP(fun(nat,bool),U_4305,hAPP(fun(nat,U_4305),fun(fun(nat,bool),U_4305),big_co1399186613setsum(nat,U_4305),U_4304),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,U_4303)),U_4302)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_4303),U_4302)) )
      | ~ comm_monoid_add(U_4305) ),
    inference(variable_rename,[status(thm)],[f_1051_1]) ).

cnf(f_1051_3,plain,
    ( hAPP(fun(nat,bool),U_4305,hAPP(fun(nat,U_4305),fun(fun(nat,bool),U_4305),big_co1399186613setsum(nat,U_4305),U_4304),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4303),U_4302)) = hAPP(U_4305,U_4305,hAPP(U_4305,fun(U_4305,U_4305),plus_plus(U_4305),hAPP(nat,U_4305,U_4304,U_4303)),hAPP(fun(nat,bool),U_4305,hAPP(fun(nat,U_4305),fun(fun(nat,bool),U_4305),big_co1399186613setsum(nat,U_4305),U_4304),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,U_4303)),U_4302)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_4303),U_4302))
    | ~ comm_monoid_add(U_4305) ),
    inference(clausify,[status(thm)],[f_1051_2]) ).

fof(f_1052_1,plain,
    ! [X_a,B,A_1] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_962_card__Un__Int]) ).

fof(f_1052_2,plain,
    ! [U_4308,U_4307,U_4306] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4308,bool),nat,finite_card(U_4308),U_4306)),hAPP(fun(U_4308,bool),nat,finite_card(U_4308),U_4307)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4308,bool),nat,finite_card(U_4308),hAPP(fun(U_4308,bool),fun(U_4308,bool),hAPP(fun(U_4308,bool),fun(fun(U_4308,bool),fun(U_4308,bool)),semilattice_sup_sup(fun(U_4308,bool)),U_4306),U_4307))),hAPP(fun(U_4308,bool),nat,finite_card(U_4308),hAPP(fun(U_4308,bool),fun(U_4308,bool),hAPP(fun(U_4308,bool),fun(fun(U_4308,bool),fun(U_4308,bool)),semilattice_inf_inf(fun(U_4308,bool)),U_4306),U_4307)))
      | ~ hBOOL(hAPP(fun(U_4308,bool),bool,finite_finite_1(U_4308),U_4307))
      | ~ hBOOL(hAPP(fun(U_4308,bool),bool,finite_finite_1(U_4308),U_4306)) ),
    inference(variable_rename,[status(thm)],[f_1052_1]) ).

cnf(f_1052_3,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4308,bool),nat,finite_card(U_4308),U_4306)),hAPP(fun(U_4308,bool),nat,finite_card(U_4308),U_4307)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4308,bool),nat,finite_card(U_4308),hAPP(fun(U_4308,bool),fun(U_4308,bool),hAPP(fun(U_4308,bool),fun(fun(U_4308,bool),fun(U_4308,bool)),semilattice_sup_sup(fun(U_4308,bool)),U_4306),U_4307))),hAPP(fun(U_4308,bool),nat,finite_card(U_4308),hAPP(fun(U_4308,bool),fun(U_4308,bool),hAPP(fun(U_4308,bool),fun(fun(U_4308,bool),fun(U_4308,bool)),semilattice_inf_inf(fun(U_4308,bool)),U_4306),U_4307)))
    | ~ hBOOL(hAPP(fun(U_4308,bool),bool,finite_finite_1(U_4308),U_4307))
    | ~ hBOOL(hAPP(fun(U_4308,bool),bool,finite_finite_1(U_4308),U_4306)) ),
    inference(clausify,[status(thm)],[f_1052_2]) ).

fof(f_1053_1,plain,
    ! [X_a,B,A_1] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_963_card_Ounion__inter]) ).

fof(f_1053_2,plain,
    ! [U_4311,U_4310,U_4309] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4311,bool),nat,finite_card(U_4311),hAPP(fun(U_4311,bool),fun(U_4311,bool),hAPP(fun(U_4311,bool),fun(fun(U_4311,bool),fun(U_4311,bool)),semilattice_sup_sup(fun(U_4311,bool)),U_4309),U_4310))),hAPP(fun(U_4311,bool),nat,finite_card(U_4311),hAPP(fun(U_4311,bool),fun(U_4311,bool),hAPP(fun(U_4311,bool),fun(fun(U_4311,bool),fun(U_4311,bool)),semilattice_inf_inf(fun(U_4311,bool)),U_4309),U_4310))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4311,bool),nat,finite_card(U_4311),U_4309)),hAPP(fun(U_4311,bool),nat,finite_card(U_4311),U_4310))
      | ~ hBOOL(hAPP(fun(U_4311,bool),bool,finite_finite_1(U_4311),U_4310))
      | ~ hBOOL(hAPP(fun(U_4311,bool),bool,finite_finite_1(U_4311),U_4309)) ),
    inference(variable_rename,[status(thm)],[f_1053_1]) ).

cnf(f_1053_3,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4311,bool),nat,finite_card(U_4311),hAPP(fun(U_4311,bool),fun(U_4311,bool),hAPP(fun(U_4311,bool),fun(fun(U_4311,bool),fun(U_4311,bool)),semilattice_sup_sup(fun(U_4311,bool)),U_4309),U_4310))),hAPP(fun(U_4311,bool),nat,finite_card(U_4311),hAPP(fun(U_4311,bool),fun(U_4311,bool),hAPP(fun(U_4311,bool),fun(fun(U_4311,bool),fun(U_4311,bool)),semilattice_inf_inf(fun(U_4311,bool)),U_4309),U_4310))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4311,bool),nat,finite_card(U_4311),U_4309)),hAPP(fun(U_4311,bool),nat,finite_card(U_4311),U_4310))
    | ~ hBOOL(hAPP(fun(U_4311,bool),bool,finite_finite_1(U_4311),U_4310))
    | ~ hBOOL(hAPP(fun(U_4311,bool),bool,finite_finite_1(U_4311),U_4309)) ),
    inference(clausify,[status(thm)],[f_1053_2]) ).

fof(f_1054_1,plain,
    ! [X_a] :
      ( ! [F,Na,M] :
          ( ( hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),hAPP(nat,nat,suc,Na))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Na))),hAPP(nat,X_a,F,Na))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) )
          & ( hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),hAPP(nat,nat,suc,Na))) = zero_zero(X_a)
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) ) )
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_964_setsum__op__ivl__Suc]) ).

fof(f_1054_2,plain,
    ! [U_4315] :
      ( ! [U_4314,U_4313,U_4312] :
          ( ( hAPP(fun(nat,bool),U_4315,hAPP(fun(nat,U_4315),fun(fun(nat,bool),U_4315),big_co1399186613setsum(nat,U_4315),U_4314),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4312),hAPP(nat,nat,suc,U_4313))) = hAPP(U_4315,U_4315,hAPP(U_4315,fun(U_4315,U_4315),plus_plus(U_4315),hAPP(fun(nat,bool),U_4315,hAPP(fun(nat,U_4315),fun(fun(nat,bool),U_4315),big_co1399186613setsum(nat,U_4315),U_4314),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4312),U_4313))),hAPP(nat,U_4315,U_4314,U_4313))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_4313),U_4312)) )
          & ( hAPP(fun(nat,bool),U_4315,hAPP(fun(nat,U_4315),fun(fun(nat,bool),U_4315),big_co1399186613setsum(nat,U_4315),U_4314),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4312),hAPP(nat,nat,suc,U_4313))) = zero_zero(U_4315)
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_4313),U_4312)) ) )
      | ~ comm_monoid_add(U_4315) ),
    inference(variable_rename,[status(thm)],[f_1054_1]) ).

fof(f_1054_3,plain,
    ! [U_4315] :
      ( ( ! [U_4321,U_4319,U_4317] :
            ( hAPP(fun(nat,bool),U_4315,hAPP(fun(nat,U_4315),fun(fun(nat,bool),U_4315),big_co1399186613setsum(nat,U_4315),U_4321),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4317),hAPP(nat,nat,suc,U_4319))) = hAPP(U_4315,U_4315,hAPP(U_4315,fun(U_4315,U_4315),plus_plus(U_4315),hAPP(fun(nat,bool),U_4315,hAPP(fun(nat,U_4315),fun(fun(nat,bool),U_4315),big_co1399186613setsum(nat,U_4315),U_4321),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4317),U_4319))),hAPP(nat,U_4315,U_4321,U_4319))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_4319),U_4317)) )
        & ! [U_4320,U_4318,U_4316] :
            ( hAPP(fun(nat,bool),U_4315,hAPP(fun(nat,U_4315),fun(fun(nat,bool),U_4315),big_co1399186613setsum(nat,U_4315),U_4320),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4316),hAPP(nat,nat,suc,U_4318))) = zero_zero(U_4315)
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_4318),U_4316)) ) )
      | ~ comm_monoid_add(U_4315) ),
    inference(miniscope,[status(thm)],[f_1054_2]) ).

cnf(f_1054_4,plain,
    ( hAPP(fun(nat,bool),U_4315,hAPP(fun(nat,U_4315),fun(fun(nat,bool),U_4315),big_co1399186613setsum(nat,U_4315),U_4320),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4316),hAPP(nat,nat,suc,U_4318))) = zero_zero(U_4315)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_4318),U_4316))
    | ~ comm_monoid_add(U_4315) ),
    inference(clausify,[status(thm)],[f_1054_3]) ).

cnf(f_1054_5,plain,
    ( hAPP(fun(nat,bool),U_4315,hAPP(fun(nat,U_4315),fun(fun(nat,bool),U_4315),big_co1399186613setsum(nat,U_4315),U_4321),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4317),hAPP(nat,nat,suc,U_4319))) = hAPP(U_4315,U_4315,hAPP(U_4315,fun(U_4315,U_4315),plus_plus(U_4315),hAPP(fun(nat,bool),U_4315,hAPP(fun(nat,U_4315),fun(fun(nat,bool),U_4315),big_co1399186613setsum(nat,U_4315),U_4321),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_4317),U_4319))),hAPP(nat,U_4315,U_4321,U_4319))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_4319),U_4317))
    | ~ comm_monoid_add(U_4315) ),
    inference(clausify,[status(thm)],[f_1054_3]) ).

fof(f_1055_1,plain,
    ! [X_a] :
      ( ! [F,Na,M] :
          ( ( hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,suc,Na))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,Na)))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Na)),M)) )
          & ( hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,suc,Na))) = zero_zero(X_a)
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Na)),M)) ) )
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_965_setsum__cl__ivl__Suc]) ).

fof(f_1055_2,plain,
    ! [U_4325] :
      ( ! [U_4324,U_4323,U_4322] :
          ( ( hAPP(fun(nat,bool),U_4325,hAPP(fun(nat,U_4325),fun(fun(nat,bool),U_4325),big_co1399186613setsum(nat,U_4325),U_4324),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4322),hAPP(nat,nat,suc,U_4323))) = hAPP(U_4325,U_4325,hAPP(U_4325,fun(U_4325,U_4325),plus_plus(U_4325),hAPP(fun(nat,bool),U_4325,hAPP(fun(nat,U_4325),fun(fun(nat,bool),U_4325),big_co1399186613setsum(nat,U_4325),U_4324),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4322),U_4323))),hAPP(nat,U_4325,U_4324,hAPP(nat,nat,suc,U_4323)))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_4323)),U_4322)) )
          & ( hAPP(fun(nat,bool),U_4325,hAPP(fun(nat,U_4325),fun(fun(nat,bool),U_4325),big_co1399186613setsum(nat,U_4325),U_4324),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4322),hAPP(nat,nat,suc,U_4323))) = zero_zero(U_4325)
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_4323)),U_4322)) ) )
      | ~ comm_monoid_add(U_4325) ),
    inference(variable_rename,[status(thm)],[f_1055_1]) ).

fof(f_1055_3,plain,
    ! [U_4325] :
      ( ( ! [U_4331,U_4329,U_4327] :
            ( hAPP(fun(nat,bool),U_4325,hAPP(fun(nat,U_4325),fun(fun(nat,bool),U_4325),big_co1399186613setsum(nat,U_4325),U_4331),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4327),hAPP(nat,nat,suc,U_4329))) = hAPP(U_4325,U_4325,hAPP(U_4325,fun(U_4325,U_4325),plus_plus(U_4325),hAPP(fun(nat,bool),U_4325,hAPP(fun(nat,U_4325),fun(fun(nat,bool),U_4325),big_co1399186613setsum(nat,U_4325),U_4331),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4327),U_4329))),hAPP(nat,U_4325,U_4331,hAPP(nat,nat,suc,U_4329)))
            | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_4329)),U_4327)) )
        & ! [U_4330,U_4328,U_4326] :
            ( hAPP(fun(nat,bool),U_4325,hAPP(fun(nat,U_4325),fun(fun(nat,bool),U_4325),big_co1399186613setsum(nat,U_4325),U_4330),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4326),hAPP(nat,nat,suc,U_4328))) = zero_zero(U_4325)
            | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_4328)),U_4326)) ) )
      | ~ comm_monoid_add(U_4325) ),
    inference(miniscope,[status(thm)],[f_1055_2]) ).

cnf(f_1055_4,plain,
    ( hAPP(fun(nat,bool),U_4325,hAPP(fun(nat,U_4325),fun(fun(nat,bool),U_4325),big_co1399186613setsum(nat,U_4325),U_4330),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4326),hAPP(nat,nat,suc,U_4328))) = zero_zero(U_4325)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_4328)),U_4326))
    | ~ comm_monoid_add(U_4325) ),
    inference(clausify,[status(thm)],[f_1055_3]) ).

cnf(f_1055_5,plain,
    ( hAPP(fun(nat,bool),U_4325,hAPP(fun(nat,U_4325),fun(fun(nat,bool),U_4325),big_co1399186613setsum(nat,U_4325),U_4331),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4327),hAPP(nat,nat,suc,U_4329))) = hAPP(U_4325,U_4325,hAPP(U_4325,fun(U_4325,U_4325),plus_plus(U_4325),hAPP(fun(nat,bool),U_4325,hAPP(fun(nat,U_4325),fun(fun(nat,bool),U_4325),big_co1399186613setsum(nat,U_4325),U_4331),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4327),U_4329))),hAPP(nat,U_4325,U_4331,hAPP(nat,nat,suc,U_4329)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_4329)),U_4327))
    | ~ comm_monoid_add(U_4325) ),
    inference(clausify,[status(thm)],[f_1055_3]) ).

fof(f_1056_1,plain,
    ! [X_a] :
      ( ! [Pa,M,Na] :
          ( hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),Pa),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),Na)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,Pa,M)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),Pa),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),M),Na)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) )
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_966_setsum__head]) ).

fof(f_1056_2,plain,
    ! [U_4335] :
      ( ! [U_4334,U_4333,U_4332] :
          ( hAPP(fun(nat,bool),U_4335,hAPP(fun(nat,U_4335),fun(fun(nat,bool),U_4335),big_co1399186613setsum(nat,U_4335),U_4334),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4333),U_4332)) = hAPP(U_4335,U_4335,hAPP(U_4335,fun(U_4335,U_4335),plus_plus(U_4335),hAPP(nat,U_4335,U_4334,U_4333)),hAPP(fun(nat,bool),U_4335,hAPP(fun(nat,U_4335),fun(fun(nat,bool),U_4335),big_co1399186613setsum(nat,U_4335),U_4334),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),U_4333),U_4332)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_4333),U_4332)) )
      | ~ comm_monoid_add(U_4335) ),
    inference(variable_rename,[status(thm)],[f_1056_1]) ).

cnf(f_1056_3,plain,
    ( hAPP(fun(nat,bool),U_4335,hAPP(fun(nat,U_4335),fun(fun(nat,bool),U_4335),big_co1399186613setsum(nat,U_4335),U_4334),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),U_4333),U_4332)) = hAPP(U_4335,U_4335,hAPP(U_4335,fun(U_4335,U_4335),plus_plus(U_4335),hAPP(nat,U_4335,U_4334,U_4333)),hAPP(fun(nat,bool),U_4335,hAPP(fun(nat,U_4335),fun(fun(nat,bool),U_4335),big_co1399186613setsum(nat,U_4335),U_4334),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),U_4333),U_4332)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_4333),U_4332))
    | ~ comm_monoid_add(U_4335) ),
    inference(clausify,[status(thm)],[f_1056_2]) ).

fof(f_1057_1,plain,
    ! [X_a,B,A_1] :
      ( hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B))
      | ( one_one(nat) != zero_zero(nat)
        & ? [X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_967_card_Ounion__inter__neutral]) ).

fof(f_1057_2,plain,
    ! [U_4339,U_4338,U_4337] :
      ( hAPP(fun(U_4339,bool),nat,finite_card(U_4339),hAPP(fun(U_4339,bool),fun(U_4339,bool),hAPP(fun(U_4339,bool),fun(fun(U_4339,bool),fun(U_4339,bool)),semilattice_sup_sup(fun(U_4339,bool)),U_4337),U_4338)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4339,bool),nat,finite_card(U_4339),U_4337)),hAPP(fun(U_4339,bool),nat,finite_card(U_4339),U_4338))
      | ( one_one(nat) != zero_zero(nat)
        & ? [U_4336] : hBOOL(hAPP(fun(U_4339,bool),bool,hAPP(U_4339,fun(fun(U_4339,bool),bool),member(U_4339),U_4336),hAPP(fun(U_4339,bool),fun(U_4339,bool),hAPP(fun(U_4339,bool),fun(fun(U_4339,bool),fun(U_4339,bool)),semilattice_inf_inf(fun(U_4339,bool)),U_4337),U_4338))) )
      | ~ hBOOL(hAPP(fun(U_4339,bool),bool,finite_finite_1(U_4339),U_4338))
      | ~ hBOOL(hAPP(fun(U_4339,bool),bool,finite_finite_1(U_4339),U_4337)) ),
    inference(variable_rename,[status(thm)],[f_1057_1]) ).

fof(f_1057_3,plain,
    ! [U_4339,U_4338,U_4337] :
      ( hAPP(fun(U_4339,bool),nat,finite_card(U_4339),hAPP(fun(U_4339,bool),fun(U_4339,bool),hAPP(fun(U_4339,bool),fun(fun(U_4339,bool),fun(U_4339,bool)),semilattice_sup_sup(fun(U_4339,bool)),U_4337),U_4338)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4339,bool),nat,finite_card(U_4339),U_4337)),hAPP(fun(U_4339,bool),nat,finite_card(U_4339),U_4338))
      | ( one_one(nat) != zero_zero(nat)
        & hBOOL(hAPP(fun(U_4339,bool),bool,hAPP(U_4339,fun(fun(U_4339,bool),bool),member(U_4339),sK180(U_4339,U_4338,U_4337)),hAPP(fun(U_4339,bool),fun(U_4339,bool),hAPP(fun(U_4339,bool),fun(fun(U_4339,bool),fun(U_4339,bool)),semilattice_inf_inf(fun(U_4339,bool)),U_4337),U_4338))) )
      | ~ hBOOL(hAPP(fun(U_4339,bool),bool,finite_finite_1(U_4339),U_4338))
      | ~ hBOOL(hAPP(fun(U_4339,bool),bool,finite_finite_1(U_4339),U_4337)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_4336,sK180(U_4339,U_4338,U_4337))],[f_1057_2]) ).

cnf(f_1057_4,plain,
    ( hBOOL(hAPP(fun(U_4339,bool),bool,hAPP(U_4339,fun(fun(U_4339,bool),bool),member(U_4339),sK180(U_4339,U_4338,U_4337)),hAPP(fun(U_4339,bool),fun(U_4339,bool),hAPP(fun(U_4339,bool),fun(fun(U_4339,bool),fun(U_4339,bool)),semilattice_inf_inf(fun(U_4339,bool)),U_4337),U_4338)))
    | hAPP(fun(U_4339,bool),nat,finite_card(U_4339),hAPP(fun(U_4339,bool),fun(U_4339,bool),hAPP(fun(U_4339,bool),fun(fun(U_4339,bool),fun(U_4339,bool)),semilattice_sup_sup(fun(U_4339,bool)),U_4337),U_4338)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4339,bool),nat,finite_card(U_4339),U_4337)),hAPP(fun(U_4339,bool),nat,finite_card(U_4339),U_4338))
    | ~ hBOOL(hAPP(fun(U_4339,bool),bool,finite_finite_1(U_4339),U_4338))
    | ~ hBOOL(hAPP(fun(U_4339,bool),bool,finite_finite_1(U_4339),U_4337)) ),
    inference(clausify,[status(thm)],[f_1057_3]) ).

cnf(f_1057_5,plain,
    ( one_one(nat) != zero_zero(nat)
    | hAPP(fun(U_4339,bool),nat,finite_card(U_4339),hAPP(fun(U_4339,bool),fun(U_4339,bool),hAPP(fun(U_4339,bool),fun(fun(U_4339,bool),fun(U_4339,bool)),semilattice_sup_sup(fun(U_4339,bool)),U_4337),U_4338)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_4339,bool),nat,finite_card(U_4339),U_4337)),hAPP(fun(U_4339,bool),nat,finite_card(U_4339),U_4338))
    | ~ hBOOL(hAPP(fun(U_4339,bool),bool,finite_finite_1(U_4339),U_4338))
    | ~ hBOOL(hAPP(fun(U_4339,bool),bool,finite_finite_1(U_4339),U_4337)) ),
    inference(clausify,[status(thm)],[f_1057_3]) ).

fof(f_1058_1,plain,
    ! [X_a,X_b] :
      ( ! [F,T_3,S] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),F),one_one(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),S),T_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),F),one_one(X_b)),S)),hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),times_times(X_b)),F),one_one(X_b)),T_3))
          | ? [X_1] :
              ( hAPP(X_a,X_b,F,X_1) != one_one(X_b)
              & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),S),T_3))) )
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) )
      | ~ comm_monoid_mult(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_968_fold__image__Un__one]) ).

fof(f_1058_2,plain,
    ! [U_4345,U_4344] :
      ( ! [U_4343,U_4342,U_4341] :
          ( hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),hAPP(fun(U_4345,bool),fun(U_4345,bool),hAPP(fun(U_4345,bool),fun(fun(U_4345,bool),fun(U_4345,bool)),semilattice_sup_sup(fun(U_4345,bool)),U_4341),U_4342)) = hAPP(U_4344,U_4344,hAPP(U_4344,fun(U_4344,U_4344),times_times(U_4344),hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),U_4341)),hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),U_4342))
          | ? [U_4340] :
              ( hAPP(U_4345,U_4344,U_4343,U_4340) != one_one(U_4344)
              & hBOOL(hAPP(fun(U_4345,bool),bool,hAPP(U_4345,fun(fun(U_4345,bool),bool),member(U_4345),U_4340),hAPP(fun(U_4345,bool),fun(U_4345,bool),hAPP(fun(U_4345,bool),fun(fun(U_4345,bool),fun(U_4345,bool)),semilattice_inf_inf(fun(U_4345,bool)),U_4341),U_4342))) )
          | ~ hBOOL(hAPP(fun(U_4345,bool),bool,finite_finite_1(U_4345),U_4342))
          | ~ hBOOL(hAPP(fun(U_4345,bool),bool,finite_finite_1(U_4345),U_4341)) )
      | ~ comm_monoid_mult(U_4344) ),
    inference(variable_rename,[status(thm)],[f_1058_1]) ).

fof(f_1058_3,plain,
    ! [U_4345,U_4344] :
      ( ! [U_4343,U_4342,U_4341] :
          ( hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),hAPP(fun(U_4345,bool),fun(U_4345,bool),hAPP(fun(U_4345,bool),fun(fun(U_4345,bool),fun(U_4345,bool)),semilattice_sup_sup(fun(U_4345,bool)),U_4341),U_4342)) = hAPP(U_4344,U_4344,hAPP(U_4344,fun(U_4344,U_4344),times_times(U_4344),hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),U_4341)),hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),U_4342))
          | ( hAPP(U_4345,U_4344,U_4343,sK181(U_4345,U_4344,U_4343,U_4342,U_4341)) != one_one(U_4344)
            & hBOOL(hAPP(fun(U_4345,bool),bool,hAPP(U_4345,fun(fun(U_4345,bool),bool),member(U_4345),sK181(U_4345,U_4344,U_4343,U_4342,U_4341)),hAPP(fun(U_4345,bool),fun(U_4345,bool),hAPP(fun(U_4345,bool),fun(fun(U_4345,bool),fun(U_4345,bool)),semilattice_inf_inf(fun(U_4345,bool)),U_4341),U_4342))) )
          | ~ hBOOL(hAPP(fun(U_4345,bool),bool,finite_finite_1(U_4345),U_4342))
          | ~ hBOOL(hAPP(fun(U_4345,bool),bool,finite_finite_1(U_4345),U_4341)) )
      | ~ comm_monoid_mult(U_4344) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_4340,sK181(U_4345,U_4344,U_4343,U_4342,U_4341))],[f_1058_2]) ).

cnf(f_1058_4,plain,
    ( hBOOL(hAPP(fun(U_4345,bool),bool,hAPP(U_4345,fun(fun(U_4345,bool),bool),member(U_4345),sK181(U_4345,U_4344,U_4343,U_4342,U_4341)),hAPP(fun(U_4345,bool),fun(U_4345,bool),hAPP(fun(U_4345,bool),fun(fun(U_4345,bool),fun(U_4345,bool)),semilattice_inf_inf(fun(U_4345,bool)),U_4341),U_4342)))
    | hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),hAPP(fun(U_4345,bool),fun(U_4345,bool),hAPP(fun(U_4345,bool),fun(fun(U_4345,bool),fun(U_4345,bool)),semilattice_sup_sup(fun(U_4345,bool)),U_4341),U_4342)) = hAPP(U_4344,U_4344,hAPP(U_4344,fun(U_4344,U_4344),times_times(U_4344),hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),U_4341)),hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),U_4342))
    | ~ hBOOL(hAPP(fun(U_4345,bool),bool,finite_finite_1(U_4345),U_4342))
    | ~ hBOOL(hAPP(fun(U_4345,bool),bool,finite_finite_1(U_4345),U_4341))
    | ~ comm_monoid_mult(U_4344) ),
    inference(clausify,[status(thm)],[f_1058_3]) ).

cnf(f_1058_5,plain,
    ( hAPP(U_4345,U_4344,U_4343,sK181(U_4345,U_4344,U_4343,U_4342,U_4341)) != one_one(U_4344)
    | hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),hAPP(fun(U_4345,bool),fun(U_4345,bool),hAPP(fun(U_4345,bool),fun(fun(U_4345,bool),fun(U_4345,bool)),semilattice_sup_sup(fun(U_4345,bool)),U_4341),U_4342)) = hAPP(U_4344,U_4344,hAPP(U_4344,fun(U_4344,U_4344),times_times(U_4344),hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),U_4341)),hAPP(fun(U_4345,bool),U_4344,hAPP(U_4344,fun(fun(U_4345,bool),U_4344),hAPP(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344)),hAPP(fun(U_4344,fun(U_4344,U_4344)),fun(fun(U_4345,U_4344),fun(U_4344,fun(fun(U_4345,bool),U_4344))),finite_fold_image(U_4344,U_4345),times_times(U_4344)),U_4343),one_one(U_4344)),U_4342))
    | ~ hBOOL(hAPP(fun(U_4345,bool),bool,finite_finite_1(U_4345),U_4342))
    | ~ hBOOL(hAPP(fun(U_4345,bool),bool,finite_finite_1(U_4345),U_4341))
    | ~ comm_monoid_mult(U_4344) ),
    inference(clausify,[status(thm)],[f_1058_3]) ).

fof(f_1059_1,plain,
    ! [X_b,X_a,R_2,S,X_1,Xa] :
      ( ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_2)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S)),X_1),Xa))
        | ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool)),semilattice_inf_inf(fun(product_prod(X_a,X_b),bool)),R_2),S))) )
      & ( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool)),semilattice_inf_inf(fun(product_prod(X_a,X_b),bool)),R_2),S)))
        | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_2)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S)),X_1),Xa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_969_inf__Int__eq2]) ).

fof(f_1059_2,plain,
    ! [U_4351,U_4350,U_4349,U_4348,U_4347,U_4346] :
      ( ( hBOOL(hAPP(U_4351,bool,hAPP(U_4350,fun(U_4351,bool),hAPP(fun(U_4350,fun(U_4351,bool)),fun(U_4350,fun(U_4351,bool)),hAPP(fun(U_4350,fun(U_4351,bool)),fun(fun(U_4350,fun(U_4351,bool)),fun(U_4350,fun(U_4351,bool))),semilattice_inf_inf(fun(U_4350,fun(U_4351,bool))),hAPP(fun(product_prod(U_4350,U_4351),bool),fun(U_4350,fun(U_4351,bool)),hAPP(fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4350,fun(U_4351,bool))),combc(U_4350,fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)),hAPP(fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),hAPP(fun(fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),fun(fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)))),combb(fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)),U_4350),combc(U_4351,fun(product_prod(U_4350,U_4351),bool),bool)),hAPP(fun(U_4350,fun(U_4351,product_prod(U_4350,U_4351))),fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),hAPP(fun(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(fun(U_4350,fun(U_4351,product_prod(U_4350,U_4351))),fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)))),combb(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),U_4350),hAPP(fun(product_prod(U_4350,U_4351),fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),combb(product_prod(U_4350,U_4351),fun(fun(product_prod(U_4350,U_4351),bool),bool),U_4351),member(product_prod(U_4350,U_4351)))),product_Pair(U_4350,U_4351)))),U_4349)),hAPP(fun(product_prod(U_4350,U_4351),bool),fun(U_4350,fun(U_4351,bool)),hAPP(fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4350,fun(U_4351,bool))),combc(U_4350,fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)),hAPP(fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),hAPP(fun(fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),fun(fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)))),combb(fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)),U_4350),combc(U_4351,fun(product_prod(U_4350,U_4351),bool),bool)),hAPP(fun(U_4350,fun(U_4351,product_prod(U_4350,U_4351))),fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),hAPP(fun(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(fun(U_4350,fun(U_4351,product_prod(U_4350,U_4351))),fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)))),combb(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),U_4350),hAPP(fun(product_prod(U_4350,U_4351),fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),combb(product_prod(U_4350,U_4351),fun(fun(product_prod(U_4350,U_4351),bool),bool),U_4351),member(product_prod(U_4350,U_4351)))),product_Pair(U_4350,U_4351)))),U_4348)),U_4347),U_4346))
        | ~ hBOOL(hAPP(fun(product_prod(U_4350,U_4351),bool),bool,hAPP(product_prod(U_4350,U_4351),fun(fun(product_prod(U_4350,U_4351),bool),bool),member(product_prod(U_4350,U_4351)),hAPP(U_4351,product_prod(U_4350,U_4351),hAPP(U_4350,fun(U_4351,product_prod(U_4350,U_4351)),product_Pair(U_4350,U_4351),U_4347),U_4346)),hAPP(fun(product_prod(U_4350,U_4351),bool),fun(product_prod(U_4350,U_4351),bool),hAPP(fun(product_prod(U_4350,U_4351),bool),fun(fun(product_prod(U_4350,U_4351),bool),fun(product_prod(U_4350,U_4351),bool)),semilattice_inf_inf(fun(product_prod(U_4350,U_4351),bool)),U_4349),U_4348))) )
      & ( hBOOL(hAPP(fun(product_prod(U_4350,U_4351),bool),bool,hAPP(product_prod(U_4350,U_4351),fun(fun(product_prod(U_4350,U_4351),bool),bool),member(product_prod(U_4350,U_4351)),hAPP(U_4351,product_prod(U_4350,U_4351),hAPP(U_4350,fun(U_4351,product_prod(U_4350,U_4351)),product_Pair(U_4350,U_4351),U_4347),U_4346)),hAPP(fun(product_prod(U_4350,U_4351),bool),fun(product_prod(U_4350,U_4351),bool),hAPP(fun(product_prod(U_4350,U_4351),bool),fun(fun(product_prod(U_4350,U_4351),bool),fun(product_prod(U_4350,U_4351),bool)),semilattice_inf_inf(fun(product_prod(U_4350,U_4351),bool)),U_4349),U_4348)))
        | ~ hBOOL(hAPP(U_4351,bool,hAPP(U_4350,fun(U_4351,bool),hAPP(fun(U_4350,fun(U_4351,bool)),fun(U_4350,fun(U_4351,bool)),hAPP(fun(U_4350,fun(U_4351,bool)),fun(fun(U_4350,fun(U_4351,bool)),fun(U_4350,fun(U_4351,bool))),semilattice_inf_inf(fun(U_4350,fun(U_4351,bool))),hAPP(fun(product_prod(U_4350,U_4351),bool),fun(U_4350,fun(U_4351,bool)),hAPP(fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4350,fun(U_4351,bool))),combc(U_4350,fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)),hAPP(fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),hAPP(fun(fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),fun(fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)))),combb(fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)),U_4350),combc(U_4351,fun(product_prod(U_4350,U_4351),bool),bool)),hAPP(fun(U_4350,fun(U_4351,product_prod(U_4350,U_4351))),fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),hAPP(fun(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(fun(U_4350,fun(U_4351,product_prod(U_4350,U_4351))),fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)))),combb(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),U_4350),hAPP(fun(product_prod(U_4350,U_4351),fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),combb(product_prod(U_4350,U_4351),fun(fun(product_prod(U_4350,U_4351),bool),bool),U_4351),member(product_prod(U_4350,U_4351)))),product_Pair(U_4350,U_4351)))),U_4349)),hAPP(fun(product_prod(U_4350,U_4351),bool),fun(U_4350,fun(U_4351,bool)),hAPP(fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4350,fun(U_4351,bool))),combc(U_4350,fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)),hAPP(fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),hAPP(fun(fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool))),fun(fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(U_4350,fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)))),combb(fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(product_prod(U_4350,U_4351),bool),fun(U_4351,bool)),U_4350),combc(U_4351,fun(product_prod(U_4350,U_4351),bool),bool)),hAPP(fun(U_4350,fun(U_4351,product_prod(U_4350,U_4351))),fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),hAPP(fun(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),fun(fun(U_4350,fun(U_4351,product_prod(U_4350,U_4351))),fun(U_4350,fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)))),combb(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool)),U_4350),hAPP(fun(product_prod(U_4350,U_4351),fun(fun(product_prod(U_4350,U_4351),bool),bool)),fun(fun(U_4351,product_prod(U_4350,U_4351)),fun(U_4351,fun(fun(product_prod(U_4350,U_4351),bool),bool))),combb(product_prod(U_4350,U_4351),fun(fun(product_prod(U_4350,U_4351),bool),bool),U_4351),member(product_prod(U_4350,U_4351)))),product_Pair(U_4350,U_4351)))),U_4348)),U_4347),U_4346)) ) ),
    inference(variable_rename,[status(thm)],[f_1059_1]) ).

fof(f_1059_3,plain,
    ( ! [U_4363,U_4361,U_4359,U_4357,U_4355,U_4353] :
        ( hBOOL(hAPP(U_4363,bool,hAPP(U_4361,fun(U_4363,bool),hAPP(fun(U_4361,fun(U_4363,bool)),fun(U_4361,fun(U_4363,bool)),hAPP(fun(U_4361,fun(U_4363,bool)),fun(fun(U_4361,fun(U_4363,bool)),fun(U_4361,fun(U_4363,bool))),semilattice_inf_inf(fun(U_4361,fun(U_4363,bool))),hAPP(fun(product_prod(U_4361,U_4363),bool),fun(U_4361,fun(U_4363,bool)),hAPP(fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4361,fun(U_4363,bool))),combc(U_4361,fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)),hAPP(fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),hAPP(fun(fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),fun(fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)))),combb(fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)),U_4361),combc(U_4363,fun(product_prod(U_4361,U_4363),bool),bool)),hAPP(fun(U_4361,fun(U_4363,product_prod(U_4361,U_4363))),fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),hAPP(fun(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(fun(U_4361,fun(U_4363,product_prod(U_4361,U_4363))),fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)))),combb(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),U_4361),hAPP(fun(product_prod(U_4361,U_4363),fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),combb(product_prod(U_4361,U_4363),fun(fun(product_prod(U_4361,U_4363),bool),bool),U_4363),member(product_prod(U_4361,U_4363)))),product_Pair(U_4361,U_4363)))),U_4359)),hAPP(fun(product_prod(U_4361,U_4363),bool),fun(U_4361,fun(U_4363,bool)),hAPP(fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4361,fun(U_4363,bool))),combc(U_4361,fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)),hAPP(fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),hAPP(fun(fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),fun(fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)))),combb(fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)),U_4361),combc(U_4363,fun(product_prod(U_4361,U_4363),bool),bool)),hAPP(fun(U_4361,fun(U_4363,product_prod(U_4361,U_4363))),fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),hAPP(fun(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(fun(U_4361,fun(U_4363,product_prod(U_4361,U_4363))),fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)))),combb(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),U_4361),hAPP(fun(product_prod(U_4361,U_4363),fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),combb(product_prod(U_4361,U_4363),fun(fun(product_prod(U_4361,U_4363),bool),bool),U_4363),member(product_prod(U_4361,U_4363)))),product_Pair(U_4361,U_4363)))),U_4357)),U_4355),U_4353))
        | ~ hBOOL(hAPP(fun(product_prod(U_4361,U_4363),bool),bool,hAPP(product_prod(U_4361,U_4363),fun(fun(product_prod(U_4361,U_4363),bool),bool),member(product_prod(U_4361,U_4363)),hAPP(U_4363,product_prod(U_4361,U_4363),hAPP(U_4361,fun(U_4363,product_prod(U_4361,U_4363)),product_Pair(U_4361,U_4363),U_4355),U_4353)),hAPP(fun(product_prod(U_4361,U_4363),bool),fun(product_prod(U_4361,U_4363),bool),hAPP(fun(product_prod(U_4361,U_4363),bool),fun(fun(product_prod(U_4361,U_4363),bool),fun(product_prod(U_4361,U_4363),bool)),semilattice_inf_inf(fun(product_prod(U_4361,U_4363),bool)),U_4359),U_4357))) )
    & ! [U_4362,U_4360,U_4358,U_4356,U_4354,U_4352] :
        ( hBOOL(hAPP(fun(product_prod(U_4360,U_4362),bool),bool,hAPP(product_prod(U_4360,U_4362),fun(fun(product_prod(U_4360,U_4362),bool),bool),member(product_prod(U_4360,U_4362)),hAPP(U_4362,product_prod(U_4360,U_4362),hAPP(U_4360,fun(U_4362,product_prod(U_4360,U_4362)),product_Pair(U_4360,U_4362),U_4354),U_4352)),hAPP(fun(product_prod(U_4360,U_4362),bool),fun(product_prod(U_4360,U_4362),bool),hAPP(fun(product_prod(U_4360,U_4362),bool),fun(fun(product_prod(U_4360,U_4362),bool),fun(product_prod(U_4360,U_4362),bool)),semilattice_inf_inf(fun(product_prod(U_4360,U_4362),bool)),U_4358),U_4356)))
        | ~ hBOOL(hAPP(U_4362,bool,hAPP(U_4360,fun(U_4362,bool),hAPP(fun(U_4360,fun(U_4362,bool)),fun(U_4360,fun(U_4362,bool)),hAPP(fun(U_4360,fun(U_4362,bool)),fun(fun(U_4360,fun(U_4362,bool)),fun(U_4360,fun(U_4362,bool))),semilattice_inf_inf(fun(U_4360,fun(U_4362,bool))),hAPP(fun(product_prod(U_4360,U_4362),bool),fun(U_4360,fun(U_4362,bool)),hAPP(fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4360,fun(U_4362,bool))),combc(U_4360,fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)),hAPP(fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),hAPP(fun(fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),fun(fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)))),combb(fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)),U_4360),combc(U_4362,fun(product_prod(U_4360,U_4362),bool),bool)),hAPP(fun(U_4360,fun(U_4362,product_prod(U_4360,U_4362))),fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),hAPP(fun(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(fun(U_4360,fun(U_4362,product_prod(U_4360,U_4362))),fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)))),combb(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),U_4360),hAPP(fun(product_prod(U_4360,U_4362),fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),combb(product_prod(U_4360,U_4362),fun(fun(product_prod(U_4360,U_4362),bool),bool),U_4362),member(product_prod(U_4360,U_4362)))),product_Pair(U_4360,U_4362)))),U_4358)),hAPP(fun(product_prod(U_4360,U_4362),bool),fun(U_4360,fun(U_4362,bool)),hAPP(fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4360,fun(U_4362,bool))),combc(U_4360,fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)),hAPP(fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),hAPP(fun(fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),fun(fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)))),combb(fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)),U_4360),combc(U_4362,fun(product_prod(U_4360,U_4362),bool),bool)),hAPP(fun(U_4360,fun(U_4362,product_prod(U_4360,U_4362))),fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),hAPP(fun(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(fun(U_4360,fun(U_4362,product_prod(U_4360,U_4362))),fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)))),combb(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),U_4360),hAPP(fun(product_prod(U_4360,U_4362),fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),combb(product_prod(U_4360,U_4362),fun(fun(product_prod(U_4360,U_4362),bool),bool),U_4362),member(product_prod(U_4360,U_4362)))),product_Pair(U_4360,U_4362)))),U_4356)),U_4354),U_4352)) ) ),
    inference(miniscope,[status(thm)],[f_1059_2]) ).

cnf(f_1059_4,plain,
    ( hBOOL(hAPP(fun(product_prod(U_4360,U_4362),bool),bool,hAPP(product_prod(U_4360,U_4362),fun(fun(product_prod(U_4360,U_4362),bool),bool),member(product_prod(U_4360,U_4362)),hAPP(U_4362,product_prod(U_4360,U_4362),hAPP(U_4360,fun(U_4362,product_prod(U_4360,U_4362)),product_Pair(U_4360,U_4362),U_4354),U_4352)),hAPP(fun(product_prod(U_4360,U_4362),bool),fun(product_prod(U_4360,U_4362),bool),hAPP(fun(product_prod(U_4360,U_4362),bool),fun(fun(product_prod(U_4360,U_4362),bool),fun(product_prod(U_4360,U_4362),bool)),semilattice_inf_inf(fun(product_prod(U_4360,U_4362),bool)),U_4358),U_4356)))
    | ~ hBOOL(hAPP(U_4362,bool,hAPP(U_4360,fun(U_4362,bool),hAPP(fun(U_4360,fun(U_4362,bool)),fun(U_4360,fun(U_4362,bool)),hAPP(fun(U_4360,fun(U_4362,bool)),fun(fun(U_4360,fun(U_4362,bool)),fun(U_4360,fun(U_4362,bool))),semilattice_inf_inf(fun(U_4360,fun(U_4362,bool))),hAPP(fun(product_prod(U_4360,U_4362),bool),fun(U_4360,fun(U_4362,bool)),hAPP(fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4360,fun(U_4362,bool))),combc(U_4360,fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)),hAPP(fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),hAPP(fun(fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),fun(fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)))),combb(fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)),U_4360),combc(U_4362,fun(product_prod(U_4360,U_4362),bool),bool)),hAPP(fun(U_4360,fun(U_4362,product_prod(U_4360,U_4362))),fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),hAPP(fun(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(fun(U_4360,fun(U_4362,product_prod(U_4360,U_4362))),fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)))),combb(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),U_4360),hAPP(fun(product_prod(U_4360,U_4362),fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),combb(product_prod(U_4360,U_4362),fun(fun(product_prod(U_4360,U_4362),bool),bool),U_4362),member(product_prod(U_4360,U_4362)))),product_Pair(U_4360,U_4362)))),U_4358)),hAPP(fun(product_prod(U_4360,U_4362),bool),fun(U_4360,fun(U_4362,bool)),hAPP(fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4360,fun(U_4362,bool))),combc(U_4360,fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)),hAPP(fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),hAPP(fun(fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool))),fun(fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(U_4360,fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)))),combb(fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(product_prod(U_4360,U_4362),bool),fun(U_4362,bool)),U_4360),combc(U_4362,fun(product_prod(U_4360,U_4362),bool),bool)),hAPP(fun(U_4360,fun(U_4362,product_prod(U_4360,U_4362))),fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),hAPP(fun(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),fun(fun(U_4360,fun(U_4362,product_prod(U_4360,U_4362))),fun(U_4360,fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)))),combb(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool)),U_4360),hAPP(fun(product_prod(U_4360,U_4362),fun(fun(product_prod(U_4360,U_4362),bool),bool)),fun(fun(U_4362,product_prod(U_4360,U_4362)),fun(U_4362,fun(fun(product_prod(U_4360,U_4362),bool),bool))),combb(product_prod(U_4360,U_4362),fun(fun(product_prod(U_4360,U_4362),bool),bool),U_4362),member(product_prod(U_4360,U_4362)))),product_Pair(U_4360,U_4362)))),U_4356)),U_4354),U_4352)) ),
    inference(clausify,[status(thm)],[f_1059_3]) ).

cnf(f_1059_5,plain,
    ( hBOOL(hAPP(U_4363,bool,hAPP(U_4361,fun(U_4363,bool),hAPP(fun(U_4361,fun(U_4363,bool)),fun(U_4361,fun(U_4363,bool)),hAPP(fun(U_4361,fun(U_4363,bool)),fun(fun(U_4361,fun(U_4363,bool)),fun(U_4361,fun(U_4363,bool))),semilattice_inf_inf(fun(U_4361,fun(U_4363,bool))),hAPP(fun(product_prod(U_4361,U_4363),bool),fun(U_4361,fun(U_4363,bool)),hAPP(fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4361,fun(U_4363,bool))),combc(U_4361,fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)),hAPP(fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),hAPP(fun(fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),fun(fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)))),combb(fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)),U_4361),combc(U_4363,fun(product_prod(U_4361,U_4363),bool),bool)),hAPP(fun(U_4361,fun(U_4363,product_prod(U_4361,U_4363))),fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),hAPP(fun(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(fun(U_4361,fun(U_4363,product_prod(U_4361,U_4363))),fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)))),combb(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),U_4361),hAPP(fun(product_prod(U_4361,U_4363),fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),combb(product_prod(U_4361,U_4363),fun(fun(product_prod(U_4361,U_4363),bool),bool),U_4363),member(product_prod(U_4361,U_4363)))),product_Pair(U_4361,U_4363)))),U_4359)),hAPP(fun(product_prod(U_4361,U_4363),bool),fun(U_4361,fun(U_4363,bool)),hAPP(fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4361,fun(U_4363,bool))),combc(U_4361,fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)),hAPP(fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),hAPP(fun(fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool))),fun(fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(U_4361,fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)))),combb(fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(product_prod(U_4361,U_4363),bool),fun(U_4363,bool)),U_4361),combc(U_4363,fun(product_prod(U_4361,U_4363),bool),bool)),hAPP(fun(U_4361,fun(U_4363,product_prod(U_4361,U_4363))),fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),hAPP(fun(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),fun(fun(U_4361,fun(U_4363,product_prod(U_4361,U_4363))),fun(U_4361,fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)))),combb(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool)),U_4361),hAPP(fun(product_prod(U_4361,U_4363),fun(fun(product_prod(U_4361,U_4363),bool),bool)),fun(fun(U_4363,product_prod(U_4361,U_4363)),fun(U_4363,fun(fun(product_prod(U_4361,U_4363),bool),bool))),combb(product_prod(U_4361,U_4363),fun(fun(product_prod(U_4361,U_4363),bool),bool),U_4363),member(product_prod(U_4361,U_4363)))),product_Pair(U_4361,U_4363)))),U_4357)),U_4355),U_4353))
    | ~ hBOOL(hAPP(fun(product_prod(U_4361,U_4363),bool),bool,hAPP(product_prod(U_4361,U_4363),fun(fun(product_prod(U_4361,U_4363),bool),bool),member(product_prod(U_4361,U_4363)),hAPP(U_4363,product_prod(U_4361,U_4363),hAPP(U_4361,fun(U_4363,product_prod(U_4361,U_4363)),product_Pair(U_4361,U_4363),U_4355),U_4353)),hAPP(fun(product_prod(U_4361,U_4363),bool),fun(product_prod(U_4361,U_4363),bool),hAPP(fun(product_prod(U_4361,U_4363),bool),fun(fun(product_prod(U_4361,U_4363),bool),fun(product_prod(U_4361,U_4363),bool)),semilattice_inf_inf(fun(product_prod(U_4361,U_4363),bool)),U_4359),U_4357))) ),
    inference(clausify,[status(thm)],[f_1059_3]) ).

fof(f_1060_1,plain,
    ! [X_a,X_b] :
      ( ! [G,A_1] :
          ( ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1) = zero_zero(X_b)
            | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
          & ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),plus_plus(X_b)),G),zero_zero(X_b)),A_1)
            | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_970_setsum_OF__eq]) ).

fof(f_1060_2,plain,
    ! [U_4367,U_4366] :
      ( ! [U_4365,U_4364] :
          ( ( hAPP(fun(U_4367,bool),U_4366,hAPP(fun(U_4367,U_4366),fun(fun(U_4367,bool),U_4366),big_co1399186613setsum(U_4367,U_4366),U_4365),U_4364) = zero_zero(U_4366)
            | hBOOL(hAPP(fun(U_4367,bool),bool,finite_finite_1(U_4367),U_4364)) )
          & ( hAPP(fun(U_4367,bool),U_4366,hAPP(fun(U_4367,U_4366),fun(fun(U_4367,bool),U_4366),big_co1399186613setsum(U_4367,U_4366),U_4365),U_4364) = hAPP(fun(U_4367,bool),U_4366,hAPP(U_4366,fun(fun(U_4367,bool),U_4366),hAPP(fun(U_4367,U_4366),fun(U_4366,fun(fun(U_4367,bool),U_4366)),hAPP(fun(U_4366,fun(U_4366,U_4366)),fun(fun(U_4367,U_4366),fun(U_4366,fun(fun(U_4367,bool),U_4366))),finite_fold_image(U_4366,U_4367),plus_plus(U_4366)),U_4365),zero_zero(U_4366)),U_4364)
            | ~ hBOOL(hAPP(fun(U_4367,bool),bool,finite_finite_1(U_4367),U_4364)) ) )
      | ~ comm_monoid_add(U_4366) ),
    inference(variable_rename,[status(thm)],[f_1060_1]) ).

fof(f_1060_3,plain,
    ! [U_4367,U_4366] :
      ( ( ! [U_4371,U_4369] :
            ( hAPP(fun(U_4367,bool),U_4366,hAPP(fun(U_4367,U_4366),fun(fun(U_4367,bool),U_4366),big_co1399186613setsum(U_4367,U_4366),U_4371),U_4369) = zero_zero(U_4366)
            | hBOOL(hAPP(fun(U_4367,bool),bool,finite_finite_1(U_4367),U_4369)) )
        & ! [U_4370,U_4368] :
            ( hAPP(fun(U_4367,bool),U_4366,hAPP(fun(U_4367,U_4366),fun(fun(U_4367,bool),U_4366),big_co1399186613setsum(U_4367,U_4366),U_4370),U_4368) = hAPP(fun(U_4367,bool),U_4366,hAPP(U_4366,fun(fun(U_4367,bool),U_4366),hAPP(fun(U_4367,U_4366),fun(U_4366,fun(fun(U_4367,bool),U_4366)),hAPP(fun(U_4366,fun(U_4366,U_4366)),fun(fun(U_4367,U_4366),fun(U_4366,fun(fun(U_4367,bool),U_4366))),finite_fold_image(U_4366,U_4367),plus_plus(U_4366)),U_4370),zero_zero(U_4366)),U_4368)
            | ~ hBOOL(hAPP(fun(U_4367,bool),bool,finite_finite_1(U_4367),U_4368)) ) )
      | ~ comm_monoid_add(U_4366) ),
    inference(miniscope,[status(thm)],[f_1060_2]) ).

cnf(f_1060_4,plain,
    ( hAPP(fun(U_4367,bool),U_4366,hAPP(fun(U_4367,U_4366),fun(fun(U_4367,bool),U_4366),big_co1399186613setsum(U_4367,U_4366),U_4370),U_4368) = hAPP(fun(U_4367,bool),U_4366,hAPP(U_4366,fun(fun(U_4367,bool),U_4366),hAPP(fun(U_4367,U_4366),fun(U_4366,fun(fun(U_4367,bool),U_4366)),hAPP(fun(U_4366,fun(U_4366,U_4366)),fun(fun(U_4367,U_4366),fun(U_4366,fun(fun(U_4367,bool),U_4366))),finite_fold_image(U_4366,U_4367),plus_plus(U_4366)),U_4370),zero_zero(U_4366)),U_4368)
    | ~ hBOOL(hAPP(fun(U_4367,bool),bool,finite_finite_1(U_4367),U_4368))
    | ~ comm_monoid_add(U_4366) ),
    inference(clausify,[status(thm)],[f_1060_3]) ).

cnf(f_1060_5,plain,
    ( hAPP(fun(U_4367,bool),U_4366,hAPP(fun(U_4367,U_4366),fun(fun(U_4367,bool),U_4366),big_co1399186613setsum(U_4367,U_4366),U_4371),U_4369) = zero_zero(U_4366)
    | hBOOL(hAPP(fun(U_4367,bool),bool,finite_finite_1(U_4367),U_4369))
    | ~ comm_monoid_add(U_4366) ),
    inference(clausify,[status(thm)],[f_1060_3]) ).

fof(f_1061_1,plain,
    ! [X_a,X_b] :
      ( ! [G,A_1] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1) = hAPP(fun(X_a,bool),X_b,hAPP(X_b,fun(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_b,fun(fun(X_a,bool),X_b))),finite_fold_image(X_b,X_a),plus_plus(X_b)),G),zero_zero(X_b)),A_1)
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_971_setsum_Oeq__fold]) ).

fof(f_1061_2,plain,
    ! [U_4375,U_4374] :
      ( ! [U_4373,U_4372] :
          ( hAPP(fun(U_4375,bool),U_4374,hAPP(fun(U_4375,U_4374),fun(fun(U_4375,bool),U_4374),big_co1399186613setsum(U_4375,U_4374),U_4373),U_4372) = hAPP(fun(U_4375,bool),U_4374,hAPP(U_4374,fun(fun(U_4375,bool),U_4374),hAPP(fun(U_4375,U_4374),fun(U_4374,fun(fun(U_4375,bool),U_4374)),hAPP(fun(U_4374,fun(U_4374,U_4374)),fun(fun(U_4375,U_4374),fun(U_4374,fun(fun(U_4375,bool),U_4374))),finite_fold_image(U_4374,U_4375),plus_plus(U_4374)),U_4373),zero_zero(U_4374)),U_4372)
          | ~ hBOOL(hAPP(fun(U_4375,bool),bool,finite_finite_1(U_4375),U_4372)) )
      | ~ comm_monoid_add(U_4374) ),
    inference(variable_rename,[status(thm)],[f_1061_1]) ).

cnf(f_1061_3,plain,
    ( hAPP(fun(U_4375,bool),U_4374,hAPP(fun(U_4375,U_4374),fun(fun(U_4375,bool),U_4374),big_co1399186613setsum(U_4375,U_4374),U_4373),U_4372) = hAPP(fun(U_4375,bool),U_4374,hAPP(U_4374,fun(fun(U_4375,bool),U_4374),hAPP(fun(U_4375,U_4374),fun(U_4374,fun(fun(U_4375,bool),U_4374)),hAPP(fun(U_4374,fun(U_4374,U_4374)),fun(fun(U_4375,U_4374),fun(U_4374,fun(fun(U_4375,bool),U_4374))),finite_fold_image(U_4374,U_4375),plus_plus(U_4374)),U_4373),zero_zero(U_4374)),U_4372)
    | ~ hBOOL(hAPP(fun(U_4375,bool),bool,finite_finite_1(U_4375),U_4372))
    | ~ comm_monoid_add(U_4374) ),
    inference(clausify,[status(thm)],[f_1061_2]) ).

fof(f_1062_1,plain,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1))
        & hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1)) )
      | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_972_inf2E]) ).

fof(f_1062_2,plain,
    ! [U_4381,U_4380,U_4379,U_4378,U_4377,U_4376] :
      ( ( hBOOL(hAPP(U_4381,bool,hAPP(U_4380,fun(U_4381,bool),U_4378,U_4377),U_4376))
        & hBOOL(hAPP(U_4381,bool,hAPP(U_4380,fun(U_4381,bool),U_4379,U_4377),U_4376)) )
      | ~ hBOOL(hAPP(U_4381,bool,hAPP(U_4380,fun(U_4381,bool),hAPP(fun(U_4380,fun(U_4381,bool)),fun(U_4380,fun(U_4381,bool)),hAPP(fun(U_4380,fun(U_4381,bool)),fun(fun(U_4380,fun(U_4381,bool)),fun(U_4380,fun(U_4381,bool))),semilattice_inf_inf(fun(U_4380,fun(U_4381,bool))),U_4379),U_4378),U_4377),U_4376)) ),
    inference(variable_rename,[status(thm)],[f_1062_1]) ).

cnf(f_1062_3,plain,
    ( hBOOL(hAPP(U_4381,bool,hAPP(U_4380,fun(U_4381,bool),U_4379,U_4377),U_4376))
    | ~ hBOOL(hAPP(U_4381,bool,hAPP(U_4380,fun(U_4381,bool),hAPP(fun(U_4380,fun(U_4381,bool)),fun(U_4380,fun(U_4381,bool)),hAPP(fun(U_4380,fun(U_4381,bool)),fun(fun(U_4380,fun(U_4381,bool)),fun(U_4380,fun(U_4381,bool))),semilattice_inf_inf(fun(U_4380,fun(U_4381,bool))),U_4379),U_4378),U_4377),U_4376)) ),
    inference(clausify,[status(thm)],[f_1062_2]) ).

cnf(f_1062_4,plain,
    ( hBOOL(hAPP(U_4381,bool,hAPP(U_4380,fun(U_4381,bool),U_4378,U_4377),U_4376))
    | ~ hBOOL(hAPP(U_4381,bool,hAPP(U_4380,fun(U_4381,bool),hAPP(fun(U_4380,fun(U_4381,bool)),fun(U_4380,fun(U_4381,bool)),hAPP(fun(U_4380,fun(U_4381,bool)),fun(fun(U_4380,fun(U_4381,bool)),fun(U_4380,fun(U_4381,bool))),semilattice_inf_inf(fun(U_4380,fun(U_4381,bool))),U_4379),U_4378),U_4377),U_4376)) ),
    inference(clausify,[status(thm)],[f_1062_2]) ).

fof(f_1063_1,plain,
    ! [X_b,X_a,B,A_1,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1))
      | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1))
      | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_973_inf2I]) ).

fof(f_1063_2,plain,
    ! [U_4387,U_4386,U_4385,U_4384,U_4383,U_4382] :
      ( hBOOL(hAPP(U_4387,bool,hAPP(U_4386,fun(U_4387,bool),hAPP(fun(U_4386,fun(U_4387,bool)),fun(U_4386,fun(U_4387,bool)),hAPP(fun(U_4386,fun(U_4387,bool)),fun(fun(U_4386,fun(U_4387,bool)),fun(U_4386,fun(U_4387,bool))),semilattice_inf_inf(fun(U_4386,fun(U_4387,bool))),U_4384),U_4385),U_4383),U_4382))
      | ~ hBOOL(hAPP(U_4387,bool,hAPP(U_4386,fun(U_4387,bool),U_4385,U_4383),U_4382))
      | ~ hBOOL(hAPP(U_4387,bool,hAPP(U_4386,fun(U_4387,bool),U_4384,U_4383),U_4382)) ),
    inference(variable_rename,[status(thm)],[f_1063_1]) ).

cnf(f_1063_3,plain,
    ( hBOOL(hAPP(U_4387,bool,hAPP(U_4386,fun(U_4387,bool),hAPP(fun(U_4386,fun(U_4387,bool)),fun(U_4386,fun(U_4387,bool)),hAPP(fun(U_4386,fun(U_4387,bool)),fun(fun(U_4386,fun(U_4387,bool)),fun(U_4386,fun(U_4387,bool))),semilattice_inf_inf(fun(U_4386,fun(U_4387,bool))),U_4384),U_4385),U_4383),U_4382))
    | ~ hBOOL(hAPP(U_4387,bool,hAPP(U_4386,fun(U_4387,bool),U_4385,U_4383),U_4382))
    | ~ hBOOL(hAPP(U_4387,bool,hAPP(U_4386,fun(U_4387,bool),U_4384,U_4383),U_4382)) ),
    inference(clausify,[status(thm)],[f_1063_2]) ).

fof(f_1064_1,plain,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),B,X_2),Y_1))
      | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_974_inf2D2]) ).

fof(f_1064_2,plain,
    ! [U_4393,U_4392,U_4391,U_4390,U_4389,U_4388] :
      ( hBOOL(hAPP(U_4393,bool,hAPP(U_4392,fun(U_4393,bool),U_4390,U_4389),U_4388))
      | ~ hBOOL(hAPP(U_4393,bool,hAPP(U_4392,fun(U_4393,bool),hAPP(fun(U_4392,fun(U_4393,bool)),fun(U_4392,fun(U_4393,bool)),hAPP(fun(U_4392,fun(U_4393,bool)),fun(fun(U_4392,fun(U_4393,bool)),fun(U_4392,fun(U_4393,bool))),semilattice_inf_inf(fun(U_4392,fun(U_4393,bool))),U_4391),U_4390),U_4389),U_4388)) ),
    inference(variable_rename,[status(thm)],[f_1064_1]) ).

cnf(f_1064_3,plain,
    ( hBOOL(hAPP(U_4393,bool,hAPP(U_4392,fun(U_4393,bool),U_4390,U_4389),U_4388))
    | ~ hBOOL(hAPP(U_4393,bool,hAPP(U_4392,fun(U_4393,bool),hAPP(fun(U_4392,fun(U_4393,bool)),fun(U_4392,fun(U_4393,bool)),hAPP(fun(U_4392,fun(U_4393,bool)),fun(fun(U_4392,fun(U_4393,bool)),fun(U_4392,fun(U_4393,bool))),semilattice_inf_inf(fun(U_4392,fun(U_4393,bool))),U_4391),U_4390),U_4389),U_4388)) ),
    inference(clausify,[status(thm)],[f_1064_2]) ).

fof(f_1065_1,plain,
    ! [X_b,X_a,A_1,B,X_2,Y_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),A_1,X_2),Y_1))
      | ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),semilattice_inf_inf(fun(X_a,fun(X_b,bool))),A_1),B),X_2),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_975_inf2D1]) ).

fof(f_1065_2,plain,
    ! [U_4399,U_4398,U_4397,U_4396,U_4395,U_4394] :
      ( hBOOL(hAPP(U_4399,bool,hAPP(U_4398,fun(U_4399,bool),U_4397,U_4395),U_4394))
      | ~ hBOOL(hAPP(U_4399,bool,hAPP(U_4398,fun(U_4399,bool),hAPP(fun(U_4398,fun(U_4399,bool)),fun(U_4398,fun(U_4399,bool)),hAPP(fun(U_4398,fun(U_4399,bool)),fun(fun(U_4398,fun(U_4399,bool)),fun(U_4398,fun(U_4399,bool))),semilattice_inf_inf(fun(U_4398,fun(U_4399,bool))),U_4397),U_4396),U_4395),U_4394)) ),
    inference(variable_rename,[status(thm)],[f_1065_1]) ).

cnf(f_1065_3,plain,
    ( hBOOL(hAPP(U_4399,bool,hAPP(U_4398,fun(U_4399,bool),U_4397,U_4395),U_4394))
    | ~ hBOOL(hAPP(U_4399,bool,hAPP(U_4398,fun(U_4399,bool),hAPP(fun(U_4398,fun(U_4399,bool)),fun(U_4398,fun(U_4399,bool)),hAPP(fun(U_4398,fun(U_4399,bool)),fun(fun(U_4398,fun(U_4399,bool)),fun(U_4398,fun(U_4399,bool))),semilattice_inf_inf(fun(U_4398,fun(U_4399,bool))),U_4397),U_4396),U_4395),U_4394)) ),
    inference(clausify,[status(thm)],[f_1065_2]) ).

fof(f_1066_1,plain,
    ! [X_a] :
      ( ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),X) = ti(X_a,X)
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_976_Sup__fin_Oidem]) ).

fof(f_1066_2,plain,
    ! [U_4401] :
      ( ! [U_4400] : hAPP(U_4401,U_4401,hAPP(U_4401,fun(U_4401,U_4401),semilattice_sup_sup(U_4401),U_4400),U_4400) = ti(U_4401,U_4400)
      | ~ lattice(U_4401) ),
    inference(variable_rename,[status(thm)],[f_1066_1]) ).

cnf(f_1066_3,plain,
    ( hAPP(U_4401,U_4401,hAPP(U_4401,fun(U_4401,U_4401),semilattice_sup_sup(U_4401),U_4400),U_4400) = ti(U_4401,U_4400)
    | ~ lattice(U_4401) ),
    inference(clausify,[status(thm)],[f_1066_2]) ).

fof(f_1067_1,plain,
    ! [X_a] :
      ( ! [X] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),X) = ti(X_a,X)
      | ~ lattice(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_977_Inf__fin_Oidem]) ).

fof(f_1067_2,plain,
    ! [U_4403] :
      ( ! [U_4402] : hAPP(U_4403,U_4403,hAPP(U_4403,fun(U_4403,U_4403),semilattice_inf_inf(U_4403),U_4402),U_4402) = ti(U_4403,U_4402)
      | ~ lattice(U_4403) ),
    inference(variable_rename,[status(thm)],[f_1067_1]) ).

cnf(f_1067_3,plain,
    ( hAPP(U_4403,U_4403,hAPP(U_4403,fun(U_4403,U_4403),semilattice_inf_inf(U_4403),U_4402),U_4402) = ti(U_4403,U_4402)
    | ~ lattice(U_4403) ),
    inference(clausify,[status(thm)],[f_1067_2]) ).

fof(f_1068_1,plain,
    ! [X_b,X_c,X_a] :
      ( ! [F,B,A_1] : hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),F)),B)),A_1) = hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),hAPP(fun(X_b,bool),fun(X_c,X_a),hAPP(fun(X_c,fun(fun(X_b,bool),X_a)),fun(fun(X_b,bool),fun(X_c,X_a)),combc(X_c,fun(X_b,bool),X_a),hAPP(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a)),hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),fun(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a))),combb(fun(X_b,X_a),fun(fun(X_b,bool),X_a),X_c),big_co1399186613setsum(X_b,X_a)),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_c,fun(X_b,X_a)),combc(X_b,X_c,X_a),F))),A_1)),B)
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_978_setsum__commute]) ).

fof(f_1068_2,plain,
    ! [U_4409,U_4408,U_4407] :
      ( ! [U_4406,U_4405,U_4404] : hAPP(fun(U_4409,bool),U_4407,hAPP(fun(U_4409,U_4407),fun(fun(U_4409,bool),U_4407),big_co1399186613setsum(U_4409,U_4407),hAPP(fun(U_4408,bool),fun(U_4409,U_4407),hAPP(fun(U_4409,fun(fun(U_4408,bool),U_4407)),fun(fun(U_4408,bool),fun(U_4409,U_4407)),combc(U_4409,fun(U_4408,bool),U_4407),hAPP(fun(U_4409,fun(U_4408,U_4407)),fun(U_4409,fun(fun(U_4408,bool),U_4407)),hAPP(fun(fun(U_4408,U_4407),fun(fun(U_4408,bool),U_4407)),fun(fun(U_4409,fun(U_4408,U_4407)),fun(U_4409,fun(fun(U_4408,bool),U_4407))),combb(fun(U_4408,U_4407),fun(fun(U_4408,bool),U_4407),U_4409),big_co1399186613setsum(U_4408,U_4407)),U_4406)),U_4405)),U_4404) = hAPP(fun(U_4408,bool),U_4407,hAPP(fun(U_4408,U_4407),fun(fun(U_4408,bool),U_4407),big_co1399186613setsum(U_4408,U_4407),hAPP(fun(U_4409,bool),fun(U_4408,U_4407),hAPP(fun(U_4408,fun(fun(U_4409,bool),U_4407)),fun(fun(U_4409,bool),fun(U_4408,U_4407)),combc(U_4408,fun(U_4409,bool),U_4407),hAPP(fun(U_4408,fun(U_4409,U_4407)),fun(U_4408,fun(fun(U_4409,bool),U_4407)),hAPP(fun(fun(U_4409,U_4407),fun(fun(U_4409,bool),U_4407)),fun(fun(U_4408,fun(U_4409,U_4407)),fun(U_4408,fun(fun(U_4409,bool),U_4407))),combb(fun(U_4409,U_4407),fun(fun(U_4409,bool),U_4407),U_4408),big_co1399186613setsum(U_4409,U_4407)),hAPP(fun(U_4409,fun(U_4408,U_4407)),fun(U_4408,fun(U_4409,U_4407)),combc(U_4409,U_4408,U_4407),U_4406))),U_4404)),U_4405)
      | ~ comm_monoid_add(U_4407) ),
    inference(variable_rename,[status(thm)],[f_1068_1]) ).

cnf(f_1068_3,plain,
    ( hAPP(fun(U_4409,bool),U_4407,hAPP(fun(U_4409,U_4407),fun(fun(U_4409,bool),U_4407),big_co1399186613setsum(U_4409,U_4407),hAPP(fun(U_4408,bool),fun(U_4409,U_4407),hAPP(fun(U_4409,fun(fun(U_4408,bool),U_4407)),fun(fun(U_4408,bool),fun(U_4409,U_4407)),combc(U_4409,fun(U_4408,bool),U_4407),hAPP(fun(U_4409,fun(U_4408,U_4407)),fun(U_4409,fun(fun(U_4408,bool),U_4407)),hAPP(fun(fun(U_4408,U_4407),fun(fun(U_4408,bool),U_4407)),fun(fun(U_4409,fun(U_4408,U_4407)),fun(U_4409,fun(fun(U_4408,bool),U_4407))),combb(fun(U_4408,U_4407),fun(fun(U_4408,bool),U_4407),U_4409),big_co1399186613setsum(U_4408,U_4407)),U_4406)),U_4405)),U_4404) = hAPP(fun(U_4408,bool),U_4407,hAPP(fun(U_4408,U_4407),fun(fun(U_4408,bool),U_4407),big_co1399186613setsum(U_4408,U_4407),hAPP(fun(U_4409,bool),fun(U_4408,U_4407),hAPP(fun(U_4408,fun(fun(U_4409,bool),U_4407)),fun(fun(U_4409,bool),fun(U_4408,U_4407)),combc(U_4408,fun(U_4409,bool),U_4407),hAPP(fun(U_4408,fun(U_4409,U_4407)),fun(U_4408,fun(fun(U_4409,bool),U_4407)),hAPP(fun(fun(U_4409,U_4407),fun(fun(U_4409,bool),U_4407)),fun(fun(U_4408,fun(U_4409,U_4407)),fun(U_4408,fun(fun(U_4409,bool),U_4407))),combb(fun(U_4409,U_4407),fun(fun(U_4409,bool),U_4407),U_4408),big_co1399186613setsum(U_4409,U_4407)),hAPP(fun(U_4409,fun(U_4408,U_4407)),fun(U_4408,fun(U_4409,U_4407)),combc(U_4409,U_4408,U_4407),U_4406))),U_4404)),U_4405)
    | ~ comm_monoid_add(U_4407) ),
    inference(clausify,[status(thm)],[f_1068_2]) ).

fof(f_1069_1,plain,
    ! [X_b,X_a] :
      ( ! [A_1] : hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),zero_zero(X_a))),A_1) = zero_zero(X_a)
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_979_setsum__0]) ).

fof(f_1069_2,plain,
    ! [U_4412,U_4411] :
      ( ! [U_4410] : hAPP(fun(U_4412,bool),U_4411,hAPP(fun(U_4412,U_4411),fun(fun(U_4412,bool),U_4411),big_co1399186613setsum(U_4412,U_4411),hAPP(U_4411,fun(U_4412,U_4411),combk(U_4411,U_4412),zero_zero(U_4411))),U_4410) = zero_zero(U_4411)
      | ~ comm_monoid_add(U_4411) ),
    inference(variable_rename,[status(thm)],[f_1069_1]) ).

cnf(f_1069_3,plain,
    ( hAPP(fun(U_4412,bool),U_4411,hAPP(fun(U_4412,U_4411),fun(fun(U_4412,bool),U_4411),big_co1399186613setsum(U_4412,U_4411),hAPP(U_4411,fun(U_4412,U_4411),combk(U_4411,U_4412),zero_zero(U_4411))),U_4410) = zero_zero(U_4411)
    | ~ comm_monoid_add(U_4411) ),
    inference(clausify,[status(thm)],[f_1069_2]) ).

fof(f_1070_1,plain,
    ! [X_b,X_a] :
      ( ! [F,G,A_1] : hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),plus_plus(X_a)),F)),G)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_1))
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_980_setsum__addf]) ).

fof(f_1070_2,plain,
    ! [U_4417,U_4416] :
      ( ! [U_4415,U_4414,U_4413] : hAPP(fun(U_4417,bool),U_4416,hAPP(fun(U_4417,U_4416),fun(fun(U_4417,bool),U_4416),big_co1399186613setsum(U_4417,U_4416),hAPP(fun(U_4417,U_4416),fun(U_4417,U_4416),hAPP(fun(U_4417,fun(U_4416,U_4416)),fun(fun(U_4417,U_4416),fun(U_4417,U_4416)),combs(U_4417,U_4416,U_4416),hAPP(fun(U_4417,U_4416),fun(U_4417,fun(U_4416,U_4416)),hAPP(fun(U_4416,fun(U_4416,U_4416)),fun(fun(U_4417,U_4416),fun(U_4417,fun(U_4416,U_4416))),combb(U_4416,fun(U_4416,U_4416),U_4417),plus_plus(U_4416)),U_4415)),U_4414)),U_4413) = hAPP(U_4416,U_4416,hAPP(U_4416,fun(U_4416,U_4416),plus_plus(U_4416),hAPP(fun(U_4417,bool),U_4416,hAPP(fun(U_4417,U_4416),fun(fun(U_4417,bool),U_4416),big_co1399186613setsum(U_4417,U_4416),U_4415),U_4413)),hAPP(fun(U_4417,bool),U_4416,hAPP(fun(U_4417,U_4416),fun(fun(U_4417,bool),U_4416),big_co1399186613setsum(U_4417,U_4416),U_4414),U_4413))
      | ~ comm_monoid_add(U_4416) ),
    inference(variable_rename,[status(thm)],[f_1070_1]) ).

cnf(f_1070_3,plain,
    ( hAPP(fun(U_4417,bool),U_4416,hAPP(fun(U_4417,U_4416),fun(fun(U_4417,bool),U_4416),big_co1399186613setsum(U_4417,U_4416),hAPP(fun(U_4417,U_4416),fun(U_4417,U_4416),hAPP(fun(U_4417,fun(U_4416,U_4416)),fun(fun(U_4417,U_4416),fun(U_4417,U_4416)),combs(U_4417,U_4416,U_4416),hAPP(fun(U_4417,U_4416),fun(U_4417,fun(U_4416,U_4416)),hAPP(fun(U_4416,fun(U_4416,U_4416)),fun(fun(U_4417,U_4416),fun(U_4417,fun(U_4416,U_4416))),combb(U_4416,fun(U_4416,U_4416),U_4417),plus_plus(U_4416)),U_4415)),U_4414)),U_4413) = hAPP(U_4416,U_4416,hAPP(U_4416,fun(U_4416,U_4416),plus_plus(U_4416),hAPP(fun(U_4417,bool),U_4416,hAPP(fun(U_4417,U_4416),fun(fun(U_4417,bool),U_4416),big_co1399186613setsum(U_4417,U_4416),U_4415),U_4413)),hAPP(fun(U_4417,bool),U_4416,hAPP(fun(U_4417,U_4416),fun(fun(U_4417,bool),U_4416),big_co1399186613setsum(U_4417,U_4416),U_4414),U_4413))
    | ~ comm_monoid_add(U_4416) ),
    inference(clausify,[status(thm)],[f_1070_2]) ).

fof(f_1071_1,plain,
    ! [X_b,X_a] :
      ( ! [R_1,F,A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_1)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1)),F)),A_1)
      | ~ semiring_0(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_981_setsum__right__distrib]) ).

fof(f_1071_2,plain,
    ! [U_4422,U_4421] :
      ( ! [U_4420,U_4419,U_4418] : hAPP(U_4421,U_4421,hAPP(U_4421,fun(U_4421,U_4421),times_times(U_4421),U_4420),hAPP(fun(U_4422,bool),U_4421,hAPP(fun(U_4422,U_4421),fun(fun(U_4422,bool),U_4421),big_co1399186613setsum(U_4422,U_4421),U_4419),U_4418)) = hAPP(fun(U_4422,bool),U_4421,hAPP(fun(U_4422,U_4421),fun(fun(U_4422,bool),U_4421),big_co1399186613setsum(U_4422,U_4421),hAPP(fun(U_4422,U_4421),fun(U_4422,U_4421),hAPP(fun(U_4421,U_4421),fun(fun(U_4422,U_4421),fun(U_4422,U_4421)),combb(U_4421,U_4421,U_4422),hAPP(U_4421,fun(U_4421,U_4421),times_times(U_4421),U_4420)),U_4419)),U_4418)
      | ~ semiring_0(U_4421) ),
    inference(variable_rename,[status(thm)],[f_1071_1]) ).

cnf(f_1071_3,plain,
    ( hAPP(U_4421,U_4421,hAPP(U_4421,fun(U_4421,U_4421),times_times(U_4421),U_4420),hAPP(fun(U_4422,bool),U_4421,hAPP(fun(U_4422,U_4421),fun(fun(U_4422,bool),U_4421),big_co1399186613setsum(U_4422,U_4421),U_4419),U_4418)) = hAPP(fun(U_4422,bool),U_4421,hAPP(fun(U_4422,U_4421),fun(fun(U_4422,bool),U_4421),big_co1399186613setsum(U_4422,U_4421),hAPP(fun(U_4422,U_4421),fun(U_4422,U_4421),hAPP(fun(U_4421,U_4421),fun(fun(U_4422,U_4421),fun(U_4422,U_4421)),combb(U_4421,U_4421,U_4422),hAPP(U_4421,fun(U_4421,U_4421),times_times(U_4421),U_4420)),U_4419)),U_4418)
    | ~ semiring_0(U_4421) ),
    inference(clausify,[status(thm)],[f_1071_2]) ).

fof(f_1072_1,plain,
    ! [X_b,X_a] :
      ( ! [F,A_1,R_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_1)),R_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F)),R_1)),A_1)
      | ~ semiring_0(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_982_setsum__left__distrib]) ).

fof(f_1072_2,plain,
    ! [U_4427,U_4426] :
      ( ! [U_4425,U_4424,U_4423] : hAPP(U_4426,U_4426,hAPP(U_4426,fun(U_4426,U_4426),times_times(U_4426),hAPP(fun(U_4427,bool),U_4426,hAPP(fun(U_4427,U_4426),fun(fun(U_4427,bool),U_4426),big_co1399186613setsum(U_4427,U_4426),U_4425),U_4424)),U_4423) = hAPP(fun(U_4427,bool),U_4426,hAPP(fun(U_4427,U_4426),fun(fun(U_4427,bool),U_4426),big_co1399186613setsum(U_4427,U_4426),hAPP(U_4426,fun(U_4427,U_4426),hAPP(fun(U_4427,fun(U_4426,U_4426)),fun(U_4426,fun(U_4427,U_4426)),combc(U_4427,U_4426,U_4426),hAPP(fun(U_4427,U_4426),fun(U_4427,fun(U_4426,U_4426)),hAPP(fun(U_4426,fun(U_4426,U_4426)),fun(fun(U_4427,U_4426),fun(U_4427,fun(U_4426,U_4426))),combb(U_4426,fun(U_4426,U_4426),U_4427),times_times(U_4426)),U_4425)),U_4423)),U_4424)
      | ~ semiring_0(U_4426) ),
    inference(variable_rename,[status(thm)],[f_1072_1]) ).

cnf(f_1072_3,plain,
    ( hAPP(U_4426,U_4426,hAPP(U_4426,fun(U_4426,U_4426),times_times(U_4426),hAPP(fun(U_4427,bool),U_4426,hAPP(fun(U_4427,U_4426),fun(fun(U_4427,bool),U_4426),big_co1399186613setsum(U_4427,U_4426),U_4425),U_4424)),U_4423) = hAPP(fun(U_4427,bool),U_4426,hAPP(fun(U_4427,U_4426),fun(fun(U_4427,bool),U_4426),big_co1399186613setsum(U_4427,U_4426),hAPP(U_4426,fun(U_4427,U_4426),hAPP(fun(U_4427,fun(U_4426,U_4426)),fun(U_4426,fun(U_4427,U_4426)),combc(U_4427,U_4426,U_4426),hAPP(fun(U_4427,U_4426),fun(U_4427,fun(U_4426,U_4426)),hAPP(fun(U_4426,fun(U_4426,U_4426)),fun(fun(U_4427,U_4426),fun(U_4427,fun(U_4426,U_4426))),combb(U_4426,fun(U_4426,U_4426),U_4427),times_times(U_4426)),U_4425)),U_4423)),U_4424)
    | ~ semiring_0(U_4426) ),
    inference(clausify,[status(thm)],[f_1072_2]) ).

fof(f_1073_1,plain,
    ! [X_b,X_c,X_a] :
      ( ! [F,A_1,G,B] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_1)),hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),G),B)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),hAPP(fun(X_c,X_a),fun(X_b,fun(X_c,X_a)),hAPP(fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_c,X_a),fun(X_b,fun(X_c,X_a))),combc(X_b,fun(X_c,X_a),fun(X_c,X_a)),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),hAPP(fun(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a)))),combb(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a)),X_b),combb(X_a,X_a,X_c)),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F))),G))),B)),A_1)
      | ~ semiring_0(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_983_setsum__product]) ).

fof(f_1073_2,plain,
    ! [U_4434,U_4433,U_4432] :
      ( ! [U_4431,U_4430,U_4429,U_4428] : hAPP(U_4432,U_4432,hAPP(U_4432,fun(U_4432,U_4432),times_times(U_4432),hAPP(fun(U_4434,bool),U_4432,hAPP(fun(U_4434,U_4432),fun(fun(U_4434,bool),U_4432),big_co1399186613setsum(U_4434,U_4432),U_4431),U_4430)),hAPP(fun(U_4433,bool),U_4432,hAPP(fun(U_4433,U_4432),fun(fun(U_4433,bool),U_4432),big_co1399186613setsum(U_4433,U_4432),U_4429),U_4428)) = hAPP(fun(U_4434,bool),U_4432,hAPP(fun(U_4434,U_4432),fun(fun(U_4434,bool),U_4432),big_co1399186613setsum(U_4434,U_4432),hAPP(fun(U_4433,bool),fun(U_4434,U_4432),hAPP(fun(U_4434,fun(fun(U_4433,bool),U_4432)),fun(fun(U_4433,bool),fun(U_4434,U_4432)),combc(U_4434,fun(U_4433,bool),U_4432),hAPP(fun(U_4434,fun(U_4433,U_4432)),fun(U_4434,fun(fun(U_4433,bool),U_4432)),hAPP(fun(fun(U_4433,U_4432),fun(fun(U_4433,bool),U_4432)),fun(fun(U_4434,fun(U_4433,U_4432)),fun(U_4434,fun(fun(U_4433,bool),U_4432))),combb(fun(U_4433,U_4432),fun(fun(U_4433,bool),U_4432),U_4434),big_co1399186613setsum(U_4433,U_4432)),hAPP(fun(U_4433,U_4432),fun(U_4434,fun(U_4433,U_4432)),hAPP(fun(U_4434,fun(fun(U_4433,U_4432),fun(U_4433,U_4432))),fun(fun(U_4433,U_4432),fun(U_4434,fun(U_4433,U_4432))),combc(U_4434,fun(U_4433,U_4432),fun(U_4433,U_4432)),hAPP(fun(U_4434,fun(U_4432,U_4432)),fun(U_4434,fun(fun(U_4433,U_4432),fun(U_4433,U_4432))),hAPP(fun(fun(U_4432,U_4432),fun(fun(U_4433,U_4432),fun(U_4433,U_4432))),fun(fun(U_4434,fun(U_4432,U_4432)),fun(U_4434,fun(fun(U_4433,U_4432),fun(U_4433,U_4432)))),combb(fun(U_4432,U_4432),fun(fun(U_4433,U_4432),fun(U_4433,U_4432)),U_4434),combb(U_4432,U_4432,U_4433)),hAPP(fun(U_4434,U_4432),fun(U_4434,fun(U_4432,U_4432)),hAPP(fun(U_4432,fun(U_4432,U_4432)),fun(fun(U_4434,U_4432),fun(U_4434,fun(U_4432,U_4432))),combb(U_4432,fun(U_4432,U_4432),U_4434),times_times(U_4432)),U_4431))),U_4429))),U_4428)),U_4430)
      | ~ semiring_0(U_4432) ),
    inference(variable_rename,[status(thm)],[f_1073_1]) ).

cnf(f_1073_3,plain,
    ( hAPP(U_4432,U_4432,hAPP(U_4432,fun(U_4432,U_4432),times_times(U_4432),hAPP(fun(U_4434,bool),U_4432,hAPP(fun(U_4434,U_4432),fun(fun(U_4434,bool),U_4432),big_co1399186613setsum(U_4434,U_4432),U_4431),U_4430)),hAPP(fun(U_4433,bool),U_4432,hAPP(fun(U_4433,U_4432),fun(fun(U_4433,bool),U_4432),big_co1399186613setsum(U_4433,U_4432),U_4429),U_4428)) = hAPP(fun(U_4434,bool),U_4432,hAPP(fun(U_4434,U_4432),fun(fun(U_4434,bool),U_4432),big_co1399186613setsum(U_4434,U_4432),hAPP(fun(U_4433,bool),fun(U_4434,U_4432),hAPP(fun(U_4434,fun(fun(U_4433,bool),U_4432)),fun(fun(U_4433,bool),fun(U_4434,U_4432)),combc(U_4434,fun(U_4433,bool),U_4432),hAPP(fun(U_4434,fun(U_4433,U_4432)),fun(U_4434,fun(fun(U_4433,bool),U_4432)),hAPP(fun(fun(U_4433,U_4432),fun(fun(U_4433,bool),U_4432)),fun(fun(U_4434,fun(U_4433,U_4432)),fun(U_4434,fun(fun(U_4433,bool),U_4432))),combb(fun(U_4433,U_4432),fun(fun(U_4433,bool),U_4432),U_4434),big_co1399186613setsum(U_4433,U_4432)),hAPP(fun(U_4433,U_4432),fun(U_4434,fun(U_4433,U_4432)),hAPP(fun(U_4434,fun(fun(U_4433,U_4432),fun(U_4433,U_4432))),fun(fun(U_4433,U_4432),fun(U_4434,fun(U_4433,U_4432))),combc(U_4434,fun(U_4433,U_4432),fun(U_4433,U_4432)),hAPP(fun(U_4434,fun(U_4432,U_4432)),fun(U_4434,fun(fun(U_4433,U_4432),fun(U_4433,U_4432))),hAPP(fun(fun(U_4432,U_4432),fun(fun(U_4433,U_4432),fun(U_4433,U_4432))),fun(fun(U_4434,fun(U_4432,U_4432)),fun(U_4434,fun(fun(U_4433,U_4432),fun(U_4433,U_4432)))),combb(fun(U_4432,U_4432),fun(fun(U_4433,U_4432),fun(U_4433,U_4432)),U_4434),combb(U_4432,U_4432,U_4433)),hAPP(fun(U_4434,U_4432),fun(U_4434,fun(U_4432,U_4432)),hAPP(fun(U_4432,fun(U_4432,U_4432)),fun(fun(U_4434,U_4432),fun(U_4434,fun(U_4432,U_4432))),combb(U_4432,fun(U_4432,U_4432),U_4434),times_times(U_4432)),U_4431))),U_4429))),U_4428)),U_4430)
    | ~ semiring_0(U_4432) ),
    inference(clausify,[status(thm)],[f_1073_2]) ).

fof(f_1074_1,plain,
    ! [X_a,X_b] :
      ( ! [F,A_1] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_1) = zero_zero(X_b)
          | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_984_setsum__infinite]) ).

fof(f_1074_2,plain,
    ! [U_4438,U_4437] :
      ( ! [U_4436,U_4435] :
          ( hAPP(fun(U_4438,bool),U_4437,hAPP(fun(U_4438,U_4437),fun(fun(U_4438,bool),U_4437),big_co1399186613setsum(U_4438,U_4437),U_4436),U_4435) = zero_zero(U_4437)
          | hBOOL(hAPP(fun(U_4438,bool),bool,finite_finite_1(U_4438),U_4435)) )
      | ~ comm_monoid_add(U_4437) ),
    inference(variable_rename,[status(thm)],[f_1074_1]) ).

cnf(f_1074_3,plain,
    ( hAPP(fun(U_4438,bool),U_4437,hAPP(fun(U_4438,U_4437),fun(fun(U_4438,bool),U_4437),big_co1399186613setsum(U_4438,U_4437),U_4436),U_4435) = zero_zero(U_4437)
    | hBOOL(hAPP(fun(U_4438,bool),bool,finite_finite_1(U_4438),U_4435))
    | ~ comm_monoid_add(U_4437) ),
    inference(clausify,[status(thm)],[f_1074_2]) ).

fof(f_1075_1,plain,
    ! [X_a,X_b] :
      ( ! [G,A_1] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1) = zero_zero(X_b)
          | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_985_setsum_Oinfinite]) ).

fof(f_1075_2,plain,
    ! [U_4442,U_4441] :
      ( ! [U_4440,U_4439] :
          ( hAPP(fun(U_4442,bool),U_4441,hAPP(fun(U_4442,U_4441),fun(fun(U_4442,bool),U_4441),big_co1399186613setsum(U_4442,U_4441),U_4440),U_4439) = zero_zero(U_4441)
          | hBOOL(hAPP(fun(U_4442,bool),bool,finite_finite_1(U_4442),U_4439)) )
      | ~ comm_monoid_add(U_4441) ),
    inference(variable_rename,[status(thm)],[f_1075_1]) ).

cnf(f_1075_3,plain,
    ( hAPP(fun(U_4442,bool),U_4441,hAPP(fun(U_4442,U_4441),fun(fun(U_4442,bool),U_4441),big_co1399186613setsum(U_4442,U_4441),U_4440),U_4439) = zero_zero(U_4441)
    | hBOOL(hAPP(fun(U_4442,bool),bool,finite_finite_1(U_4442),U_4439))
    | ~ comm_monoid_add(U_4441) ),
    inference(clausify,[status(thm)],[f_1075_2]) ).

fof(f_1076_1,plain,
    ! [X_a,F,Fa] :
      ( ( ( hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),Fa) = zero_zero(nat)
          | ? [X_1] :
              ( hAPP(X_a,nat,F,X_1) != zero_zero(nat)
              & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),Fa)) ) )
        & ( ! [X_1] :
              ( hAPP(X_a,nat,F,X_1) = zero_zero(nat)
              | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),Fa)) )
          | hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),Fa) != zero_zero(nat) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_986_setsum__eq__0__iff]) ).

fof(f_1076_2,plain,
    ! [U_4447,U_4446,U_4445] :
      ( ( ( hAPP(fun(U_4447,bool),nat,hAPP(fun(U_4447,nat),fun(fun(U_4447,bool),nat),big_co1399186613setsum(U_4447,nat),U_4446),U_4445) = zero_zero(nat)
          | ? [U_4444] :
              ( hAPP(U_4447,nat,U_4446,U_4444) != zero_zero(nat)
              & hBOOL(hAPP(fun(U_4447,bool),bool,hAPP(U_4447,fun(fun(U_4447,bool),bool),member(U_4447),U_4444),U_4445)) ) )
        & ( ! [U_4443] :
              ( hAPP(U_4447,nat,U_4446,U_4443) = zero_zero(nat)
              | ~ hBOOL(hAPP(fun(U_4447,bool),bool,hAPP(U_4447,fun(fun(U_4447,bool),bool),member(U_4447),U_4443),U_4445)) )
          | hAPP(fun(U_4447,bool),nat,hAPP(fun(U_4447,nat),fun(fun(U_4447,bool),nat),big_co1399186613setsum(U_4447,nat),U_4446),U_4445) != zero_zero(nat) ) )
      | ~ hBOOL(hAPP(fun(U_4447,bool),bool,finite_finite_1(U_4447),U_4445)) ),
    inference(variable_rename,[status(thm)],[f_1076_1]) ).

fof(f_1076_3,plain,
    ! [U_4447,U_4446,U_4445] :
      ( ( ( hAPP(fun(U_4447,bool),nat,hAPP(fun(U_4447,nat),fun(fun(U_4447,bool),nat),big_co1399186613setsum(U_4447,nat),U_4446),U_4445) = zero_zero(nat)
          | ( hAPP(U_4447,nat,U_4446,sK182(U_4447,U_4446,U_4445)) != zero_zero(nat)
            & hBOOL(hAPP(fun(U_4447,bool),bool,hAPP(U_4447,fun(fun(U_4447,bool),bool),member(U_4447),sK182(U_4447,U_4446,U_4445)),U_4445)) ) )
        & ( ! [U_4443] :
              ( hAPP(U_4447,nat,U_4446,U_4443) = zero_zero(nat)
              | ~ hBOOL(hAPP(fun(U_4447,bool),bool,hAPP(U_4447,fun(fun(U_4447,bool),bool),member(U_4447),U_4443),U_4445)) )
          | hAPP(fun(U_4447,bool),nat,hAPP(fun(U_4447,nat),fun(fun(U_4447,bool),nat),big_co1399186613setsum(U_4447,nat),U_4446),U_4445) != zero_zero(nat) ) )
      | ~ hBOOL(hAPP(fun(U_4447,bool),bool,finite_finite_1(U_4447),U_4445)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_4444,sK182(U_4447,U_4446,U_4445))],[f_1076_2]) ).

cnf(f_1076_4,plain,
    ( hAPP(U_4447,nat,U_4446,U_4443) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(U_4447,bool),bool,hAPP(U_4447,fun(fun(U_4447,bool),bool),member(U_4447),U_4443),U_4445))
    | hAPP(fun(U_4447,bool),nat,hAPP(fun(U_4447,nat),fun(fun(U_4447,bool),nat),big_co1399186613setsum(U_4447,nat),U_4446),U_4445) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(U_4447,bool),bool,finite_finite_1(U_4447),U_4445)) ),
    inference(clausify,[status(thm)],[f_1076_3]) ).

cnf(f_1076_5,plain,
    ( hBOOL(hAPP(fun(U_4447,bool),bool,hAPP(U_4447,fun(fun(U_4447,bool),bool),member(U_4447),sK182(U_4447,U_4446,U_4445)),U_4445))
    | hAPP(fun(U_4447,bool),nat,hAPP(fun(U_4447,nat),fun(fun(U_4447,bool),nat),big_co1399186613setsum(U_4447,nat),U_4446),U_4445) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(U_4447,bool),bool,finite_finite_1(U_4447),U_4445)) ),
    inference(clausify,[status(thm)],[f_1076_3]) ).

cnf(f_1076_6,plain,
    ( hAPP(U_4447,nat,U_4446,sK182(U_4447,U_4446,U_4445)) != zero_zero(nat)
    | hAPP(fun(U_4447,bool),nat,hAPP(fun(U_4447,nat),fun(fun(U_4447,bool),nat),big_co1399186613setsum(U_4447,nat),U_4446),U_4445) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(U_4447,bool),bool,finite_finite_1(U_4447),U_4445)) ),
    inference(clausify,[status(thm)],[f_1076_3]) ).

fof(f_1077_1,plain,
    ! [X_a,X_b] :
      ( ! [Ba,Aa,S] :
          ( ( ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),Aa))),Ba)),zero_zero(X_b))),S) = zero_zero(X_b)
              | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) )
            & ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),Aa))),Ba)),zero_zero(X_b))),S) = hAPP(X_a,X_b,Ba,Aa)
              | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) ) )
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_987_setsum__delta_H]) ).

fof(f_1077_2,plain,
    ! [U_4452,U_4451] :
      ( ! [U_4450,U_4449,U_4448] :
          ( ( ( hAPP(fun(U_4452,bool),U_4451,hAPP(fun(U_4452,U_4451),fun(fun(U_4452,bool),U_4451),big_co1399186613setsum(U_4452,U_4451),hAPP(U_4451,fun(U_4452,U_4451),hAPP(fun(U_4452,fun(U_4451,U_4451)),fun(U_4451,fun(U_4452,U_4451)),combc(U_4452,U_4451,U_4451),hAPP(fun(U_4452,U_4451),fun(U_4452,fun(U_4451,U_4451)),hAPP(fun(U_4452,fun(U_4451,fun(U_4451,U_4451))),fun(fun(U_4452,U_4451),fun(U_4452,fun(U_4451,U_4451))),combs(U_4452,U_4451,fun(U_4451,U_4451)),hAPP(fun(U_4452,bool),fun(U_4452,fun(U_4451,fun(U_4451,U_4451))),hAPP(fun(bool,fun(U_4451,fun(U_4451,U_4451))),fun(fun(U_4452,bool),fun(U_4452,fun(U_4451,fun(U_4451,U_4451)))),combb(bool,fun(U_4451,fun(U_4451,U_4451)),U_4452),if(U_4451)),hAPP(U_4452,fun(U_4452,bool),fequal(U_4452),U_4449))),U_4450)),zero_zero(U_4451))),U_4448) = zero_zero(U_4451)
              | hBOOL(hAPP(fun(U_4452,bool),bool,hAPP(U_4452,fun(fun(U_4452,bool),bool),member(U_4452),U_4449),U_4448)) )
            & ( hAPP(fun(U_4452,bool),U_4451,hAPP(fun(U_4452,U_4451),fun(fun(U_4452,bool),U_4451),big_co1399186613setsum(U_4452,U_4451),hAPP(U_4451,fun(U_4452,U_4451),hAPP(fun(U_4452,fun(U_4451,U_4451)),fun(U_4451,fun(U_4452,U_4451)),combc(U_4452,U_4451,U_4451),hAPP(fun(U_4452,U_4451),fun(U_4452,fun(U_4451,U_4451)),hAPP(fun(U_4452,fun(U_4451,fun(U_4451,U_4451))),fun(fun(U_4452,U_4451),fun(U_4452,fun(U_4451,U_4451))),combs(U_4452,U_4451,fun(U_4451,U_4451)),hAPP(fun(U_4452,bool),fun(U_4452,fun(U_4451,fun(U_4451,U_4451))),hAPP(fun(bool,fun(U_4451,fun(U_4451,U_4451))),fun(fun(U_4452,bool),fun(U_4452,fun(U_4451,fun(U_4451,U_4451)))),combb(bool,fun(U_4451,fun(U_4451,U_4451)),U_4452),if(U_4451)),hAPP(U_4452,fun(U_4452,bool),fequal(U_4452),U_4449))),U_4450)),zero_zero(U_4451))),U_4448) = hAPP(U_4452,U_4451,U_4450,U_4449)
              | ~ hBOOL(hAPP(fun(U_4452,bool),bool,hAPP(U_4452,fun(fun(U_4452,bool),bool),member(U_4452),U_4449),U_4448)) ) )
          | ~ hBOOL(hAPP(fun(U_4452,bool),bool,finite_finite_1(U_4452),U_4448)) )
      | ~ comm_monoid_add(U_4451) ),
    inference(variable_rename,[status(thm)],[f_1077_1]) ).

cnf(f_1077_3,plain,
    ( hAPP(fun(U_4452,bool),U_4451,hAPP(fun(U_4452,U_4451),fun(fun(U_4452,bool),U_4451),big_co1399186613setsum(U_4452,U_4451),hAPP(U_4451,fun(U_4452,U_4451),hAPP(fun(U_4452,fun(U_4451,U_4451)),fun(U_4451,fun(U_4452,U_4451)),combc(U_4452,U_4451,U_4451),hAPP(fun(U_4452,U_4451),fun(U_4452,fun(U_4451,U_4451)),hAPP(fun(U_4452,fun(U_4451,fun(U_4451,U_4451))),fun(fun(U_4452,U_4451),fun(U_4452,fun(U_4451,U_4451))),combs(U_4452,U_4451,fun(U_4451,U_4451)),hAPP(fun(U_4452,bool),fun(U_4452,fun(U_4451,fun(U_4451,U_4451))),hAPP(fun(bool,fun(U_4451,fun(U_4451,U_4451))),fun(fun(U_4452,bool),fun(U_4452,fun(U_4451,fun(U_4451,U_4451)))),combb(bool,fun(U_4451,fun(U_4451,U_4451)),U_4452),if(U_4451)),hAPP(U_4452,fun(U_4452,bool),fequal(U_4452),U_4449))),U_4450)),zero_zero(U_4451))),U_4448) = hAPP(U_4452,U_4451,U_4450,U_4449)
    | ~ hBOOL(hAPP(fun(U_4452,bool),bool,hAPP(U_4452,fun(fun(U_4452,bool),bool),member(U_4452),U_4449),U_4448))
    | ~ hBOOL(hAPP(fun(U_4452,bool),bool,finite_finite_1(U_4452),U_4448))
    | ~ comm_monoid_add(U_4451) ),
    inference(clausify,[status(thm)],[f_1077_2]) ).

cnf(f_1077_4,plain,
    ( hAPP(fun(U_4452,bool),U_4451,hAPP(fun(U_4452,U_4451),fun(fun(U_4452,bool),U_4451),big_co1399186613setsum(U_4452,U_4451),hAPP(U_4451,fun(U_4452,U_4451),hAPP(fun(U_4452,fun(U_4451,U_4451)),fun(U_4451,fun(U_4452,U_4451)),combc(U_4452,U_4451,U_4451),hAPP(fun(U_4452,U_4451),fun(U_4452,fun(U_4451,U_4451)),hAPP(fun(U_4452,fun(U_4451,fun(U_4451,U_4451))),fun(fun(U_4452,U_4451),fun(U_4452,fun(U_4451,U_4451))),combs(U_4452,U_4451,fun(U_4451,U_4451)),hAPP(fun(U_4452,bool),fun(U_4452,fun(U_4451,fun(U_4451,U_4451))),hAPP(fun(bool,fun(U_4451,fun(U_4451,U_4451))),fun(fun(U_4452,bool),fun(U_4452,fun(U_4451,fun(U_4451,U_4451)))),combb(bool,fun(U_4451,fun(U_4451,U_4451)),U_4452),if(U_4451)),hAPP(U_4452,fun(U_4452,bool),fequal(U_4452),U_4449))),U_4450)),zero_zero(U_4451))),U_4448) = zero_zero(U_4451)
    | hBOOL(hAPP(fun(U_4452,bool),bool,hAPP(U_4452,fun(fun(U_4452,bool),bool),member(U_4452),U_4449),U_4448))
    | ~ hBOOL(hAPP(fun(U_4452,bool),bool,finite_finite_1(U_4452),U_4448))
    | ~ comm_monoid_add(U_4451) ),
    inference(clausify,[status(thm)],[f_1077_2]) ).

fof(f_1078_1,plain,
    ! [X_a,X_b] :
      ( ! [Ba,Aa,S] :
          ( ( ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Aa))),Ba)),zero_zero(X_b))),S) = zero_zero(X_b)
              | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) )
            & ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Aa))),Ba)),zero_zero(X_b))),S) = hAPP(X_a,X_b,Ba,Aa)
              | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) ) )
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_988_setsum__delta]) ).

fof(f_1078_2,plain,
    ! [U_4457,U_4456] :
      ( ! [U_4455,U_4454,U_4453] :
          ( ( ( hAPP(fun(U_4457,bool),U_4456,hAPP(fun(U_4457,U_4456),fun(fun(U_4457,bool),U_4456),big_co1399186613setsum(U_4457,U_4456),hAPP(U_4456,fun(U_4457,U_4456),hAPP(fun(U_4457,fun(U_4456,U_4456)),fun(U_4456,fun(U_4457,U_4456)),combc(U_4457,U_4456,U_4456),hAPP(fun(U_4457,U_4456),fun(U_4457,fun(U_4456,U_4456)),hAPP(fun(U_4457,fun(U_4456,fun(U_4456,U_4456))),fun(fun(U_4457,U_4456),fun(U_4457,fun(U_4456,U_4456))),combs(U_4457,U_4456,fun(U_4456,U_4456)),hAPP(fun(U_4457,bool),fun(U_4457,fun(U_4456,fun(U_4456,U_4456))),hAPP(fun(bool,fun(U_4456,fun(U_4456,U_4456))),fun(fun(U_4457,bool),fun(U_4457,fun(U_4456,fun(U_4456,U_4456)))),combb(bool,fun(U_4456,fun(U_4456,U_4456)),U_4457),if(U_4456)),hAPP(U_4457,fun(U_4457,bool),hAPP(fun(U_4457,fun(U_4457,bool)),fun(U_4457,fun(U_4457,bool)),combc(U_4457,U_4457,bool),fequal(U_4457)),U_4454))),U_4455)),zero_zero(U_4456))),U_4453) = zero_zero(U_4456)
              | hBOOL(hAPP(fun(U_4457,bool),bool,hAPP(U_4457,fun(fun(U_4457,bool),bool),member(U_4457),U_4454),U_4453)) )
            & ( hAPP(fun(U_4457,bool),U_4456,hAPP(fun(U_4457,U_4456),fun(fun(U_4457,bool),U_4456),big_co1399186613setsum(U_4457,U_4456),hAPP(U_4456,fun(U_4457,U_4456),hAPP(fun(U_4457,fun(U_4456,U_4456)),fun(U_4456,fun(U_4457,U_4456)),combc(U_4457,U_4456,U_4456),hAPP(fun(U_4457,U_4456),fun(U_4457,fun(U_4456,U_4456)),hAPP(fun(U_4457,fun(U_4456,fun(U_4456,U_4456))),fun(fun(U_4457,U_4456),fun(U_4457,fun(U_4456,U_4456))),combs(U_4457,U_4456,fun(U_4456,U_4456)),hAPP(fun(U_4457,bool),fun(U_4457,fun(U_4456,fun(U_4456,U_4456))),hAPP(fun(bool,fun(U_4456,fun(U_4456,U_4456))),fun(fun(U_4457,bool),fun(U_4457,fun(U_4456,fun(U_4456,U_4456)))),combb(bool,fun(U_4456,fun(U_4456,U_4456)),U_4457),if(U_4456)),hAPP(U_4457,fun(U_4457,bool),hAPP(fun(U_4457,fun(U_4457,bool)),fun(U_4457,fun(U_4457,bool)),combc(U_4457,U_4457,bool),fequal(U_4457)),U_4454))),U_4455)),zero_zero(U_4456))),U_4453) = hAPP(U_4457,U_4456,U_4455,U_4454)
              | ~ hBOOL(hAPP(fun(U_4457,bool),bool,hAPP(U_4457,fun(fun(U_4457,bool),bool),member(U_4457),U_4454),U_4453)) ) )
          | ~ hBOOL(hAPP(fun(U_4457,bool),bool,finite_finite_1(U_4457),U_4453)) )
      | ~ comm_monoid_add(U_4456) ),
    inference(variable_rename,[status(thm)],[f_1078_1]) ).

cnf(f_1078_3,plain,
    ( hAPP(fun(U_4457,bool),U_4456,hAPP(fun(U_4457,U_4456),fun(fun(U_4457,bool),U_4456),big_co1399186613setsum(U_4457,U_4456),hAPP(U_4456,fun(U_4457,U_4456),hAPP(fun(U_4457,fun(U_4456,U_4456)),fun(U_4456,fun(U_4457,U_4456)),combc(U_4457,U_4456,U_4456),hAPP(fun(U_4457,U_4456),fun(U_4457,fun(U_4456,U_4456)),hAPP(fun(U_4457,fun(U_4456,fun(U_4456,U_4456))),fun(fun(U_4457,U_4456),fun(U_4457,fun(U_4456,U_4456))),combs(U_4457,U_4456,fun(U_4456,U_4456)),hAPP(fun(U_4457,bool),fun(U_4457,fun(U_4456,fun(U_4456,U_4456))),hAPP(fun(bool,fun(U_4456,fun(U_4456,U_4456))),fun(fun(U_4457,bool),fun(U_4457,fun(U_4456,fun(U_4456,U_4456)))),combb(bool,fun(U_4456,fun(U_4456,U_4456)),U_4457),if(U_4456)),hAPP(U_4457,fun(U_4457,bool),hAPP(fun(U_4457,fun(U_4457,bool)),fun(U_4457,fun(U_4457,bool)),combc(U_4457,U_4457,bool),fequal(U_4457)),U_4454))),U_4455)),zero_zero(U_4456))),U_4453) = hAPP(U_4457,U_4456,U_4455,U_4454)
    | ~ hBOOL(hAPP(fun(U_4457,bool),bool,hAPP(U_4457,fun(fun(U_4457,bool),bool),member(U_4457),U_4454),U_4453))
    | ~ hBOOL(hAPP(fun(U_4457,bool),bool,finite_finite_1(U_4457),U_4453))
    | ~ comm_monoid_add(U_4456) ),
    inference(clausify,[status(thm)],[f_1078_2]) ).

cnf(f_1078_4,plain,
    ( hAPP(fun(U_4457,bool),U_4456,hAPP(fun(U_4457,U_4456),fun(fun(U_4457,bool),U_4456),big_co1399186613setsum(U_4457,U_4456),hAPP(U_4456,fun(U_4457,U_4456),hAPP(fun(U_4457,fun(U_4456,U_4456)),fun(U_4456,fun(U_4457,U_4456)),combc(U_4457,U_4456,U_4456),hAPP(fun(U_4457,U_4456),fun(U_4457,fun(U_4456,U_4456)),hAPP(fun(U_4457,fun(U_4456,fun(U_4456,U_4456))),fun(fun(U_4457,U_4456),fun(U_4457,fun(U_4456,U_4456))),combs(U_4457,U_4456,fun(U_4456,U_4456)),hAPP(fun(U_4457,bool),fun(U_4457,fun(U_4456,fun(U_4456,U_4456))),hAPP(fun(bool,fun(U_4456,fun(U_4456,U_4456))),fun(fun(U_4457,bool),fun(U_4457,fun(U_4456,fun(U_4456,U_4456)))),combb(bool,fun(U_4456,fun(U_4456,U_4456)),U_4457),if(U_4456)),hAPP(U_4457,fun(U_4457,bool),hAPP(fun(U_4457,fun(U_4457,bool)),fun(U_4457,fun(U_4457,bool)),combc(U_4457,U_4457,bool),fequal(U_4457)),U_4454))),U_4455)),zero_zero(U_4456))),U_4453) = zero_zero(U_4456)
    | hBOOL(hAPP(fun(U_4457,bool),bool,hAPP(U_4457,fun(fun(U_4457,bool),bool),member(U_4457),U_4454),U_4453))
    | ~ hBOOL(hAPP(fun(U_4457,bool),bool,finite_finite_1(U_4457),U_4453))
    | ~ comm_monoid_add(U_4456) ),
    inference(clausify,[status(thm)],[f_1078_2]) ).

fof(f_1079_1,plain,
    ! [X_a,X_b] :
      ( ! [G,Ha,A_1] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),G)),Ha)),A_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),Ha),A_1))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_989_setsum_Odistrib]) ).

fof(f_1079_2,plain,
    ! [U_4462,U_4461] :
      ( ! [U_4460,U_4459,U_4458] :
          ( hAPP(fun(U_4462,bool),U_4461,hAPP(fun(U_4462,U_4461),fun(fun(U_4462,bool),U_4461),big_co1399186613setsum(U_4462,U_4461),hAPP(fun(U_4462,U_4461),fun(U_4462,U_4461),hAPP(fun(U_4462,fun(U_4461,U_4461)),fun(fun(U_4462,U_4461),fun(U_4462,U_4461)),combs(U_4462,U_4461,U_4461),hAPP(fun(U_4462,U_4461),fun(U_4462,fun(U_4461,U_4461)),hAPP(fun(U_4461,fun(U_4461,U_4461)),fun(fun(U_4462,U_4461),fun(U_4462,fun(U_4461,U_4461))),combb(U_4461,fun(U_4461,U_4461),U_4462),plus_plus(U_4461)),U_4460)),U_4459)),U_4458) = hAPP(U_4461,U_4461,hAPP(U_4461,fun(U_4461,U_4461),plus_plus(U_4461),hAPP(fun(U_4462,bool),U_4461,hAPP(fun(U_4462,U_4461),fun(fun(U_4462,bool),U_4461),big_co1399186613setsum(U_4462,U_4461),U_4460),U_4458)),hAPP(fun(U_4462,bool),U_4461,hAPP(fun(U_4462,U_4461),fun(fun(U_4462,bool),U_4461),big_co1399186613setsum(U_4462,U_4461),U_4459),U_4458))
          | ~ hBOOL(hAPP(fun(U_4462,bool),bool,finite_finite_1(U_4462),U_4458)) )
      | ~ comm_monoid_add(U_4461) ),
    inference(variable_rename,[status(thm)],[f_1079_1]) ).

cnf(f_1079_3,plain,
    ( hAPP(fun(U_4462,bool),U_4461,hAPP(fun(U_4462,U_4461),fun(fun(U_4462,bool),U_4461),big_co1399186613setsum(U_4462,U_4461),hAPP(fun(U_4462,U_4461),fun(U_4462,U_4461),hAPP(fun(U_4462,fun(U_4461,U_4461)),fun(fun(U_4462,U_4461),fun(U_4462,U_4461)),combs(U_4462,U_4461,U_4461),hAPP(fun(U_4462,U_4461),fun(U_4462,fun(U_4461,U_4461)),hAPP(fun(U_4461,fun(U_4461,U_4461)),fun(fun(U_4462,U_4461),fun(U_4462,fun(U_4461,U_4461))),combb(U_4461,fun(U_4461,U_4461),U_4462),plus_plus(U_4461)),U_4460)),U_4459)),U_4458) = hAPP(U_4461,U_4461,hAPP(U_4461,fun(U_4461,U_4461),plus_plus(U_4461),hAPP(fun(U_4462,bool),U_4461,hAPP(fun(U_4462,U_4461),fun(fun(U_4462,bool),U_4461),big_co1399186613setsum(U_4462,U_4461),U_4460),U_4458)),hAPP(fun(U_4462,bool),U_4461,hAPP(fun(U_4462,U_4461),fun(fun(U_4462,bool),U_4461),big_co1399186613setsum(U_4462,U_4461),U_4459),U_4458))
    | ~ hBOOL(hAPP(fun(U_4462,bool),bool,finite_finite_1(U_4462),U_4458))
    | ~ comm_monoid_add(U_4461) ),
    inference(clausify,[status(thm)],[f_1079_2]) ).

fof(f_1080_1,plain,
    ! [X_a,A_1] : hAPP(fun(X_a,bool),nat,finite_card(X_a),A_1) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),A_1),
    inference(fof_nnf,[status(thm)],[fact_990_card__eq__setsum]) ).

fof(f_1080_2,plain,
    ! [U_4464,U_4463] : hAPP(fun(U_4464,bool),nat,finite_card(U_4464),U_4463) = hAPP(fun(U_4464,bool),nat,hAPP(fun(U_4464,nat),fun(fun(U_4464,bool),nat),big_co1399186613setsum(U_4464,nat),hAPP(nat,fun(U_4464,nat),combk(nat,U_4464),one_one(nat))),U_4463),
    inference(variable_rename,[status(thm)],[f_1080_1]) ).

cnf(f_1080_3,plain,
    hAPP(fun(U_4464,bool),nat,finite_card(U_4464),U_4463) = hAPP(fun(U_4464,bool),nat,hAPP(fun(U_4464,nat),fun(fun(U_4464,bool),nat),big_co1399186613setsum(U_4464,nat),hAPP(nat,fun(U_4464,nat),combk(nat,U_4464),one_one(nat))),U_4463),
    inference(clausify,[status(thm)],[f_1080_2]) ).

fof(f_1081_1,plain,
    ! [X_a,X_b,X_c] :
      ( ! [Ha,F,B] :
          ( hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),Ha),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)) = hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),comp(X_b,X_c,X_a),Ha),F)),B)
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B)) )
      | ~ comm_monoid_add(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_991_setsum__reindex]) ).

fof(f_1081_2,plain,
    ! [U_4470,U_4469,U_4468] :
      ( ! [U_4467,U_4466,U_4465] :
          ( hAPP(fun(U_4469,bool),U_4468,hAPP(fun(U_4469,U_4468),fun(fun(U_4469,bool),U_4468),big_co1399186613setsum(U_4469,U_4468),U_4467),hAPP(fun(U_4470,bool),fun(U_4469,bool),hAPP(fun(U_4470,U_4469),fun(fun(U_4470,bool),fun(U_4469,bool)),image(U_4470,U_4469),U_4466),U_4465)) = hAPP(fun(U_4470,bool),U_4468,hAPP(fun(U_4470,U_4468),fun(fun(U_4470,bool),U_4468),big_co1399186613setsum(U_4470,U_4468),hAPP(fun(U_4470,U_4469),fun(U_4470,U_4468),hAPP(fun(U_4469,U_4468),fun(fun(U_4470,U_4469),fun(U_4470,U_4468)),comp(U_4469,U_4468,U_4470),U_4467),U_4466)),U_4465)
          | ~ hBOOL(hAPP(fun(U_4470,bool),bool,hAPP(fun(U_4470,U_4469),fun(fun(U_4470,bool),bool),inj_on(U_4470,U_4469),U_4466),U_4465)) )
      | ~ comm_monoid_add(U_4468) ),
    inference(variable_rename,[status(thm)],[f_1081_1]) ).

cnf(f_1081_3,plain,
    ( hAPP(fun(U_4469,bool),U_4468,hAPP(fun(U_4469,U_4468),fun(fun(U_4469,bool),U_4468),big_co1399186613setsum(U_4469,U_4468),U_4467),hAPP(fun(U_4470,bool),fun(U_4469,bool),hAPP(fun(U_4470,U_4469),fun(fun(U_4470,bool),fun(U_4469,bool)),image(U_4470,U_4469),U_4466),U_4465)) = hAPP(fun(U_4470,bool),U_4468,hAPP(fun(U_4470,U_4468),fun(fun(U_4470,bool),U_4468),big_co1399186613setsum(U_4470,U_4468),hAPP(fun(U_4470,U_4469),fun(U_4470,U_4468),hAPP(fun(U_4469,U_4468),fun(fun(U_4470,U_4469),fun(U_4470,U_4468)),comp(U_4469,U_4468,U_4470),U_4467),U_4466)),U_4465)
    | ~ hBOOL(hAPP(fun(U_4470,bool),bool,hAPP(fun(U_4470,U_4469),fun(fun(U_4470,bool),bool),inj_on(U_4470,U_4469),U_4466),U_4465))
    | ~ comm_monoid_add(U_4468) ),
    inference(clausify,[status(thm)],[f_1081_2]) ).

fof(f_1082_1,plain,
    ! [X_a,F,A_1] :
      ( ( ( hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_1) = hAPP(nat,nat,suc,zero_zero(nat))
          | ! [X_1] :
              ( ? [Xa] :
                  ( hAPP(X_a,nat,F,Xa) != zero_zero(nat)
                  & ti(X_a,X_1) != ti(X_a,Xa)
                  & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) )
              | hAPP(X_a,nat,F,X_1) != hAPP(nat,nat,suc,zero_zero(nat))
              | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) )
        & ( ? [X_1] :
              ( ! [Xa] :
                  ( hAPP(X_a,nat,F,Xa) = zero_zero(nat)
                  | ti(X_a,X_1) = ti(X_a,Xa)
                  | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) )
              & hAPP(X_a,nat,F,X_1) = hAPP(nat,nat,suc,zero_zero(nat))
              & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) )
          | hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_1) != hAPP(nat,nat,suc,zero_zero(nat)) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_992_setsum__eq__Suc0__iff]) ).

fof(f_1082_2,plain,
    ! [U_4477,U_4476,U_4475] :
      ( ( ( hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) = hAPP(nat,nat,suc,zero_zero(nat))
          | ! [U_4474] :
              ( ? [U_4473] :
                  ( hAPP(U_4477,nat,U_4476,U_4473) != zero_zero(nat)
                  & ti(U_4477,U_4474) != ti(U_4477,U_4473)
                  & hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4473),U_4475)) )
              | hAPP(U_4477,nat,U_4476,U_4474) != hAPP(nat,nat,suc,zero_zero(nat))
              | ~ hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4474),U_4475)) ) )
        & ( ? [U_4472] :
              ( ! [U_4471] :
                  ( hAPP(U_4477,nat,U_4476,U_4471) = zero_zero(nat)
                  | ti(U_4477,U_4472) = ti(U_4477,U_4471)
                  | ~ hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4471),U_4475)) )
              & hAPP(U_4477,nat,U_4476,U_4472) = hAPP(nat,nat,suc,zero_zero(nat))
              & hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4472),U_4475)) )
          | hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) != hAPP(nat,nat,suc,zero_zero(nat)) ) )
      | ~ hBOOL(hAPP(fun(U_4477,bool),bool,finite_finite_1(U_4477),U_4475)) ),
    inference(variable_rename,[status(thm)],[f_1082_1]) ).

fof(f_1082_3,plain,
    ! [U_4477,U_4476,U_4475] :
      ( ( ( hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) = hAPP(nat,nat,suc,zero_zero(nat))
          | ! [U_4474] :
              ( ? [U_4473] :
                  ( hAPP(U_4477,nat,U_4476,U_4473) != zero_zero(nat)
                  & ti(U_4477,U_4474) != ti(U_4477,U_4473)
                  & hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4473),U_4475)) )
              | hAPP(U_4477,nat,U_4476,U_4474) != hAPP(nat,nat,suc,zero_zero(nat))
              | ~ hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4474),U_4475)) ) )
        & ( ( ! [U_4471] :
                ( hAPP(U_4477,nat,U_4476,U_4471) = zero_zero(nat)
                | ti(U_4477,sK183(U_4477,U_4476,U_4475)) = ti(U_4477,U_4471)
                | ~ hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4471),U_4475)) )
            & hAPP(U_4477,nat,U_4476,sK183(U_4477,U_4476,U_4475)) = hAPP(nat,nat,suc,zero_zero(nat))
            & hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),sK183(U_4477,U_4476,U_4475)),U_4475)) )
          | hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) != hAPP(nat,nat,suc,zero_zero(nat)) ) )
      | ~ hBOOL(hAPP(fun(U_4477,bool),bool,finite_finite_1(U_4477),U_4475)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_4472,sK183(U_4477,U_4476,U_4475))],[f_1082_2]) ).

fof(f_1082_4,plain,
    ! [U_4477,U_4476,U_4475] :
      ( ( ( hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) = hAPP(nat,nat,suc,zero_zero(nat))
          | ! [U_4474] :
              ( ( hAPP(U_4477,nat,U_4476,sK184(U_4477,U_4476,U_4475,U_4474)) != zero_zero(nat)
                & ti(U_4477,U_4474) != ti(U_4477,sK184(U_4477,U_4476,U_4475,U_4474))
                & hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),sK184(U_4477,U_4476,U_4475,U_4474)),U_4475)) )
              | hAPP(U_4477,nat,U_4476,U_4474) != hAPP(nat,nat,suc,zero_zero(nat))
              | ~ hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4474),U_4475)) ) )
        & ( ( ! [U_4471] :
                ( hAPP(U_4477,nat,U_4476,U_4471) = zero_zero(nat)
                | ti(U_4477,sK183(U_4477,U_4476,U_4475)) = ti(U_4477,U_4471)
                | ~ hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4471),U_4475)) )
            & hAPP(U_4477,nat,U_4476,sK183(U_4477,U_4476,U_4475)) = hAPP(nat,nat,suc,zero_zero(nat))
            & hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),sK183(U_4477,U_4476,U_4475)),U_4475)) )
          | hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) != hAPP(nat,nat,suc,zero_zero(nat)) ) )
      | ~ hBOOL(hAPP(fun(U_4477,bool),bool,finite_finite_1(U_4477),U_4475)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_4473,sK184(U_4477,U_4476,U_4475,U_4474))],[f_1082_3]) ).

cnf(f_1082_5,plain,
    ( hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),sK183(U_4477,U_4476,U_4475)),U_4475))
    | hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(U_4477,bool),bool,finite_finite_1(U_4477),U_4475)) ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

cnf(f_1082_6,plain,
    ( hAPP(U_4477,nat,U_4476,sK183(U_4477,U_4476,U_4475)) = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(U_4477,bool),bool,finite_finite_1(U_4477),U_4475)) ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

cnf(f_1082_7,plain,
    ( hAPP(U_4477,nat,U_4476,U_4471) = zero_zero(nat)
    | ti(U_4477,sK183(U_4477,U_4476,U_4475)) = ti(U_4477,U_4471)
    | ~ hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4471),U_4475))
    | hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(U_4477,bool),bool,finite_finite_1(U_4477),U_4475)) ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

cnf(f_1082_8,plain,
    ( hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),sK184(U_4477,U_4476,U_4475,U_4474)),U_4475))
    | hAPP(U_4477,nat,U_4476,U_4474) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4474),U_4475))
    | hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(U_4477,bool),bool,finite_finite_1(U_4477),U_4475)) ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

cnf(f_1082_9,plain,
    ( ti(U_4477,U_4474) != ti(U_4477,sK184(U_4477,U_4476,U_4475,U_4474))
    | hAPP(U_4477,nat,U_4476,U_4474) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4474),U_4475))
    | hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(U_4477,bool),bool,finite_finite_1(U_4477),U_4475)) ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

cnf(f_1082_10,plain,
    ( hAPP(U_4477,nat,U_4476,sK184(U_4477,U_4476,U_4475,U_4474)) != zero_zero(nat)
    | hAPP(U_4477,nat,U_4476,U_4474) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(U_4477,bool),bool,hAPP(U_4477,fun(fun(U_4477,bool),bool),member(U_4477),U_4474),U_4475))
    | hAPP(fun(U_4477,bool),nat,hAPP(fun(U_4477,nat),fun(fun(U_4477,bool),nat),big_co1399186613setsum(U_4477,nat),U_4476),U_4475) = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(U_4477,bool),bool,finite_finite_1(U_4477),U_4475)) ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

fof(f_1083_1,plain,
    ! [X_a,F,A_1] :
      ( ( ( hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_1) = one_one(nat)
          | ! [X_1] :
              ( ? [Xa] :
                  ( hAPP(X_a,nat,F,Xa) != zero_zero(nat)
                  & ti(X_a,X_1) != ti(X_a,Xa)
                  & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) )
              | hAPP(X_a,nat,F,X_1) != one_one(nat)
              | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) )
        & ( ? [X_1] :
              ( ! [Xa] :
                  ( hAPP(X_a,nat,F,Xa) = zero_zero(nat)
                  | ti(X_a,X_1) = ti(X_a,Xa)
                  | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) )
              & hAPP(X_a,nat,F,X_1) = one_one(nat)
              & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) )
          | hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_1) != one_one(nat) ) )
      | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_993_setsum__eq__1__iff]) ).

fof(f_1083_2,plain,
    ! [U_4484,U_4483,U_4482] :
      ( ( ( hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) = one_one(nat)
          | ! [U_4481] :
              ( ? [U_4480] :
                  ( hAPP(U_4484,nat,U_4483,U_4480) != zero_zero(nat)
                  & ti(U_4484,U_4481) != ti(U_4484,U_4480)
                  & hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4480),U_4482)) )
              | hAPP(U_4484,nat,U_4483,U_4481) != one_one(nat)
              | ~ hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4481),U_4482)) ) )
        & ( ? [U_4479] :
              ( ! [U_4478] :
                  ( hAPP(U_4484,nat,U_4483,U_4478) = zero_zero(nat)
                  | ti(U_4484,U_4479) = ti(U_4484,U_4478)
                  | ~ hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4478),U_4482)) )
              & hAPP(U_4484,nat,U_4483,U_4479) = one_one(nat)
              & hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4479),U_4482)) )
          | hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) != one_one(nat) ) )
      | ~ hBOOL(hAPP(fun(U_4484,bool),bool,finite_finite_1(U_4484),U_4482)) ),
    inference(variable_rename,[status(thm)],[f_1083_1]) ).

fof(f_1083_3,plain,
    ! [U_4484,U_4483,U_4482] :
      ( ( ( hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) = one_one(nat)
          | ! [U_4481] :
              ( ? [U_4480] :
                  ( hAPP(U_4484,nat,U_4483,U_4480) != zero_zero(nat)
                  & ti(U_4484,U_4481) != ti(U_4484,U_4480)
                  & hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4480),U_4482)) )
              | hAPP(U_4484,nat,U_4483,U_4481) != one_one(nat)
              | ~ hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4481),U_4482)) ) )
        & ( ( ! [U_4478] :
                ( hAPP(U_4484,nat,U_4483,U_4478) = zero_zero(nat)
                | ti(U_4484,sK185(U_4484,U_4483,U_4482)) = ti(U_4484,U_4478)
                | ~ hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4478),U_4482)) )
            & hAPP(U_4484,nat,U_4483,sK185(U_4484,U_4483,U_4482)) = one_one(nat)
            & hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),sK185(U_4484,U_4483,U_4482)),U_4482)) )
          | hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) != one_one(nat) ) )
      | ~ hBOOL(hAPP(fun(U_4484,bool),bool,finite_finite_1(U_4484),U_4482)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_4479,sK185(U_4484,U_4483,U_4482))],[f_1083_2]) ).

fof(f_1083_4,plain,
    ! [U_4484,U_4483,U_4482] :
      ( ( ( hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) = one_one(nat)
          | ! [U_4481] :
              ( ( hAPP(U_4484,nat,U_4483,sK186(U_4484,U_4483,U_4482,U_4481)) != zero_zero(nat)
                & ti(U_4484,U_4481) != ti(U_4484,sK186(U_4484,U_4483,U_4482,U_4481))
                & hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),sK186(U_4484,U_4483,U_4482,U_4481)),U_4482)) )
              | hAPP(U_4484,nat,U_4483,U_4481) != one_one(nat)
              | ~ hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4481),U_4482)) ) )
        & ( ( ! [U_4478] :
                ( hAPP(U_4484,nat,U_4483,U_4478) = zero_zero(nat)
                | ti(U_4484,sK185(U_4484,U_4483,U_4482)) = ti(U_4484,U_4478)
                | ~ hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4478),U_4482)) )
            & hAPP(U_4484,nat,U_4483,sK185(U_4484,U_4483,U_4482)) = one_one(nat)
            & hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),sK185(U_4484,U_4483,U_4482)),U_4482)) )
          | hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) != one_one(nat) ) )
      | ~ hBOOL(hAPP(fun(U_4484,bool),bool,finite_finite_1(U_4484),U_4482)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_4480,sK186(U_4484,U_4483,U_4482,U_4481))],[f_1083_3]) ).

cnf(f_1083_5,plain,
    ( hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),sK185(U_4484,U_4483,U_4482)),U_4482))
    | hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) != one_one(nat)
    | ~ hBOOL(hAPP(fun(U_4484,bool),bool,finite_finite_1(U_4484),U_4482)) ),
    inference(clausify,[status(thm)],[f_1083_4]) ).

cnf(f_1083_6,plain,
    ( hAPP(U_4484,nat,U_4483,sK185(U_4484,U_4483,U_4482)) = one_one(nat)
    | hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) != one_one(nat)
    | ~ hBOOL(hAPP(fun(U_4484,bool),bool,finite_finite_1(U_4484),U_4482)) ),
    inference(clausify,[status(thm)],[f_1083_4]) ).

cnf(f_1083_7,plain,
    ( hAPP(U_4484,nat,U_4483,U_4478) = zero_zero(nat)
    | ti(U_4484,sK185(U_4484,U_4483,U_4482)) = ti(U_4484,U_4478)
    | ~ hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4478),U_4482))
    | hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) != one_one(nat)
    | ~ hBOOL(hAPP(fun(U_4484,bool),bool,finite_finite_1(U_4484),U_4482)) ),
    inference(clausify,[status(thm)],[f_1083_4]) ).

cnf(f_1083_8,plain,
    ( hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),sK186(U_4484,U_4483,U_4482,U_4481)),U_4482))
    | hAPP(U_4484,nat,U_4483,U_4481) != one_one(nat)
    | ~ hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4481),U_4482))
    | hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) = one_one(nat)
    | ~ hBOOL(hAPP(fun(U_4484,bool),bool,finite_finite_1(U_4484),U_4482)) ),
    inference(clausify,[status(thm)],[f_1083_4]) ).

cnf(f_1083_9,plain,
    ( ti(U_4484,U_4481) != ti(U_4484,sK186(U_4484,U_4483,U_4482,U_4481))
    | hAPP(U_4484,nat,U_4483,U_4481) != one_one(nat)
    | ~ hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4481),U_4482))
    | hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) = one_one(nat)
    | ~ hBOOL(hAPP(fun(U_4484,bool),bool,finite_finite_1(U_4484),U_4482)) ),
    inference(clausify,[status(thm)],[f_1083_4]) ).

cnf(f_1083_10,plain,
    ( hAPP(U_4484,nat,U_4483,sK186(U_4484,U_4483,U_4482,U_4481)) != zero_zero(nat)
    | hAPP(U_4484,nat,U_4483,U_4481) != one_one(nat)
    | ~ hBOOL(hAPP(fun(U_4484,bool),bool,hAPP(U_4484,fun(fun(U_4484,bool),bool),member(U_4484),U_4481),U_4482))
    | hAPP(fun(U_4484,bool),nat,hAPP(fun(U_4484,nat),fun(fun(U_4484,bool),nat),big_co1399186613setsum(U_4484,nat),U_4483),U_4482) = one_one(nat)
    | ~ hBOOL(hAPP(fun(U_4484,bool),bool,finite_finite_1(U_4484),U_4482)) ),
    inference(clausify,[status(thm)],[f_1083_4]) ).

fof(f_1084_1,plain,
    ! [X_a,X_b] :
      ( ! [F,B,A_1] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))),F)),zero_zero(X_b))),A_1)
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_994_setsum__restrict__set]) ).

fof(f_1084_2,plain,
    ! [U_4489,U_4488] :
      ( ! [U_4487,U_4486,U_4485] :
          ( hAPP(fun(U_4489,bool),U_4488,hAPP(fun(U_4489,U_4488),fun(fun(U_4489,bool),U_4488),big_co1399186613setsum(U_4489,U_4488),U_4487),hAPP(fun(U_4489,bool),fun(U_4489,bool),hAPP(fun(U_4489,bool),fun(fun(U_4489,bool),fun(U_4489,bool)),semilattice_inf_inf(fun(U_4489,bool)),U_4485),U_4486)) = hAPP(fun(U_4489,bool),U_4488,hAPP(fun(U_4489,U_4488),fun(fun(U_4489,bool),U_4488),big_co1399186613setsum(U_4489,U_4488),hAPP(U_4488,fun(U_4489,U_4488),hAPP(fun(U_4489,fun(U_4488,U_4488)),fun(U_4488,fun(U_4489,U_4488)),combc(U_4489,U_4488,U_4488),hAPP(fun(U_4489,U_4488),fun(U_4489,fun(U_4488,U_4488)),hAPP(fun(U_4489,fun(U_4488,fun(U_4488,U_4488))),fun(fun(U_4489,U_4488),fun(U_4489,fun(U_4488,U_4488))),combs(U_4489,U_4488,fun(U_4488,U_4488)),hAPP(fun(U_4489,bool),fun(U_4489,fun(U_4488,fun(U_4488,U_4488))),hAPP(fun(bool,fun(U_4488,fun(U_4488,U_4488))),fun(fun(U_4489,bool),fun(U_4489,fun(U_4488,fun(U_4488,U_4488)))),combb(bool,fun(U_4488,fun(U_4488,U_4488)),U_4489),if(U_4488)),hAPP(fun(U_4489,bool),fun(U_4489,bool),hAPP(fun(U_4489,fun(fun(U_4489,bool),bool)),fun(fun(U_4489,bool),fun(U_4489,bool)),combc(U_4489,fun(U_4489,bool),bool),member(U_4489)),U_4486))),U_4487)),zero_zero(U_4488))),U_4485)
          | ~ hBOOL(hAPP(fun(U_4489,bool),bool,finite_finite_1(U_4489),U_4485)) )
      | ~ comm_monoid_add(U_4488) ),
    inference(variable_rename,[status(thm)],[f_1084_1]) ).

cnf(f_1084_3,plain,
    ( hAPP(fun(U_4489,bool),U_4488,hAPP(fun(U_4489,U_4488),fun(fun(U_4489,bool),U_4488),big_co1399186613setsum(U_4489,U_4488),U_4487),hAPP(fun(U_4489,bool),fun(U_4489,bool),hAPP(fun(U_4489,bool),fun(fun(U_4489,bool),fun(U_4489,bool)),semilattice_inf_inf(fun(U_4489,bool)),U_4485),U_4486)) = hAPP(fun(U_4489,bool),U_4488,hAPP(fun(U_4489,U_4488),fun(fun(U_4489,bool),U_4488),big_co1399186613setsum(U_4489,U_4488),hAPP(U_4488,fun(U_4489,U_4488),hAPP(fun(U_4489,fun(U_4488,U_4488)),fun(U_4488,fun(U_4489,U_4488)),combc(U_4489,U_4488,U_4488),hAPP(fun(U_4489,U_4488),fun(U_4489,fun(U_4488,U_4488)),hAPP(fun(U_4489,fun(U_4488,fun(U_4488,U_4488))),fun(fun(U_4489,U_4488),fun(U_4489,fun(U_4488,U_4488))),combs(U_4489,U_4488,fun(U_4488,U_4488)),hAPP(fun(U_4489,bool),fun(U_4489,fun(U_4488,fun(U_4488,U_4488))),hAPP(fun(bool,fun(U_4488,fun(U_4488,U_4488))),fun(fun(U_4489,bool),fun(U_4489,fun(U_4488,fun(U_4488,U_4488)))),combb(bool,fun(U_4488,fun(U_4488,U_4488)),U_4489),if(U_4488)),hAPP(fun(U_4489,bool),fun(U_4489,bool),hAPP(fun(U_4489,fun(fun(U_4489,bool),bool)),fun(fun(U_4489,bool),fun(U_4489,bool)),combc(U_4489,fun(U_4489,bool),bool),member(U_4489)),U_4486))),U_4487)),zero_zero(U_4488))),U_4485)
    | ~ hBOOL(hAPP(fun(U_4489,bool),bool,finite_finite_1(U_4489),U_4485))
    | ~ comm_monoid_add(U_4488) ),
    inference(clausify,[status(thm)],[f_1084_2]) ).

fof(f_1085_1,plain,
    ! [X_a,X_b] :
      ( ! [G,B,A_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_1)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),B))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_995_setsum__Un__Int]) ).

fof(f_1085_2,plain,
    ! [U_4494,U_4493] :
      ( ! [U_4492,U_4491,U_4490] :
          ( hAPP(U_4493,U_4493,hAPP(U_4493,fun(U_4493,U_4493),plus_plus(U_4493),hAPP(fun(U_4494,bool),U_4493,hAPP(fun(U_4494,U_4493),fun(fun(U_4494,bool),U_4493),big_co1399186613setsum(U_4494,U_4493),U_4492),hAPP(fun(U_4494,bool),fun(U_4494,bool),hAPP(fun(U_4494,bool),fun(fun(U_4494,bool),fun(U_4494,bool)),semilattice_sup_sup(fun(U_4494,bool)),U_4490),U_4491))),hAPP(fun(U_4494,bool),U_4493,hAPP(fun(U_4494,U_4493),fun(fun(U_4494,bool),U_4493),big_co1399186613setsum(U_4494,U_4493),U_4492),hAPP(fun(U_4494,bool),fun(U_4494,bool),hAPP(fun(U_4494,bool),fun(fun(U_4494,bool),fun(U_4494,bool)),semilattice_inf_inf(fun(U_4494,bool)),U_4490),U_4491))) = hAPP(U_4493,U_4493,hAPP(U_4493,fun(U_4493,U_4493),plus_plus(U_4493),hAPP(fun(U_4494,bool),U_4493,hAPP(fun(U_4494,U_4493),fun(fun(U_4494,bool),U_4493),big_co1399186613setsum(U_4494,U_4493),U_4492),U_4490)),hAPP(fun(U_4494,bool),U_4493,hAPP(fun(U_4494,U_4493),fun(fun(U_4494,bool),U_4493),big_co1399186613setsum(U_4494,U_4493),U_4492),U_4491))
          | ~ hBOOL(hAPP(fun(U_4494,bool),bool,finite_finite_1(U_4494),U_4491))
          | ~ hBOOL(hAPP(fun(U_4494,bool),bool,finite_finite_1(U_4494),U_4490)) )
      | ~ comm_monoid_add(U_4493) ),
    inference(variable_rename,[status(thm)],[f_1085_1]) ).

cnf(f_1085_3,plain,
    ( hAPP(U_4493,U_4493,hAPP(U_4493,fun(U_4493,U_4493),plus_plus(U_4493),hAPP(fun(U_4494,bool),U_4493,hAPP(fun(U_4494,U_4493),fun(fun(U_4494,bool),U_4493),big_co1399186613setsum(U_4494,U_4493),U_4492),hAPP(fun(U_4494,bool),fun(U_4494,bool),hAPP(fun(U_4494,bool),fun(fun(U_4494,bool),fun(U_4494,bool)),semilattice_sup_sup(fun(U_4494,bool)),U_4490),U_4491))),hAPP(fun(U_4494,bool),U_4493,hAPP(fun(U_4494,U_4493),fun(fun(U_4494,bool),U_4493),big_co1399186613setsum(U_4494,U_4493),U_4492),hAPP(fun(U_4494,bool),fun(U_4494,bool),hAPP(fun(U_4494,bool),fun(fun(U_4494,bool),fun(U_4494,bool)),semilattice_inf_inf(fun(U_4494,bool)),U_4490),U_4491))) = hAPP(U_4493,U_4493,hAPP(U_4493,fun(U_4493,U_4493),plus_plus(U_4493),hAPP(fun(U_4494,bool),U_4493,hAPP(fun(U_4494,U_4493),fun(fun(U_4494,bool),U_4493),big_co1399186613setsum(U_4494,U_4493),U_4492),U_4490)),hAPP(fun(U_4494,bool),U_4493,hAPP(fun(U_4494,U_4493),fun(fun(U_4494,bool),U_4493),big_co1399186613setsum(U_4494,U_4493),U_4492),U_4491))
    | ~ hBOOL(hAPP(fun(U_4494,bool),bool,finite_finite_1(U_4494),U_4491))
    | ~ hBOOL(hAPP(fun(U_4494,bool),bool,finite_finite_1(U_4494),U_4490))
    | ~ comm_monoid_add(U_4493) ),
    inference(clausify,[status(thm)],[f_1085_2]) ).

fof(f_1086_1,plain,
    ! [X_a,X_b] :
      ( ! [G,Ha,A_1] :
          ( hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),Ha),A_1)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),comp(X_a,X_b,X_a),G),Ha)),A_1)
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),Ha),A_1))
          | ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) )
      | ~ comm_monoid_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_996_setsum_Oreindex]) ).

fof(f_1086_2,plain,
    ! [U_4499,U_4498] :
      ( ! [U_4497,U_4496,U_4495] :
          ( hAPP(fun(U_4499,bool),U_4498,hAPP(fun(U_4499,U_4498),fun(fun(U_4499,bool),U_4498),big_co1399186613setsum(U_4499,U_4498),U_4497),hAPP(fun(U_4499,bool),fun(U_4499,bool),hAPP(fun(U_4499,U_4499),fun(fun(U_4499,bool),fun(U_4499,bool)),image(U_4499,U_4499),U_4496),U_4495)) = hAPP(fun(U_4499,bool),U_4498,hAPP(fun(U_4499,U_4498),fun(fun(U_4499,bool),U_4498),big_co1399186613setsum(U_4499,U_4498),hAPP(fun(U_4499,U_4499),fun(U_4499,U_4498),hAPP(fun(U_4499,U_4498),fun(fun(U_4499,U_4499),fun(U_4499,U_4498)),comp(U_4499,U_4498,U_4499),U_4497),U_4496)),U_4495)
          | ~ hBOOL(hAPP(fun(U_4499,bool),bool,hAPP(fun(U_4499,U_4499),fun(fun(U_4499,bool),bool),inj_on(U_4499,U_4499),U_4496),U_4495))
          | ~ hBOOL(hAPP(fun(U_4499,bool),bool,finite_finite_1(U_4499),U_4495)) )
      | ~ comm_monoid_add(U_4498) ),
    inference(variable_rename,[status(thm)],[f_1086_1]) ).

cnf(f_1086_3,plain,
    ( hAPP(fun(U_4499,bool),U_4498,hAPP(fun(U_4499,U_4498),fun(fun(U_4499,bool),U_4498),big_co1399186613setsum(U_4499,U_4498),U_4497),hAPP(fun(U_4499,bool),fun(U_4499,bool),hAPP(fun(U_4499,U_4499),fun(fun(U_4499,bool),fun(U_4499,bool)),image(U_4499,U_4499),U_4496),U_4495)) = hAPP(fun(U_4499,bool),U_4498,hAPP(fun(U_4499,U_4498),fun(fun(U_4499,bool),U_4498),big_co1399186613setsum(U_4499,U_4498),hAPP(fun(U_4499,U_4499),fun(U_4499,U_4498),hAPP(fun(U_4499,U_4498),fun(fun(U_4499,U_4499),fun(U_4499,U_4498)),comp(U_4499,U_4498,U_4499),U_4497),U_4496)),U_4495)
    | ~ hBOOL(hAPP(fun(U_4499,bool),bool,hAPP(fun(U_4499,U_4499),fun(fun(U_4499,bool),bool),inj_on(U_4499,U_4499),U_4496),U_4495))
    | ~ hBOOL(hAPP(fun(U_4499,bool),bool,finite_finite_1(U_4499),U_4495))
    | ~ comm_monoid_add(U_4498) ),
    inference(clausify,[status(thm)],[f_1086_2]) ).

fof(f_1087_1,plain,
    bounded_lattice(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Lattices_Obounded__lattice]) ).

cnf(f_1087_2,plain,
    bounded_lattice(bool),
    inference(clausify,[status(thm)],[f_1087_1]) ).

fof(f_1088_1,plain,
    ! [T_2,T_1] :
      ( bounded_lattice(fun(T_2,T_1))
      | ~ bounded_lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Obounded__lattice]) ).

fof(f_1088_2,plain,
    ! [U_4501,U_4500] :
      ( bounded_lattice(fun(U_4501,U_4500))
      | ~ bounded_lattice(U_4500) ),
    inference(variable_rename,[status(thm)],[f_1088_1]) ).

cnf(f_1088_3,plain,
    ( bounded_lattice(fun(U_4501,U_4500))
    | ~ bounded_lattice(U_4500) ),
    inference(clausify,[status(thm)],[f_1088_2]) ).

fof(f_1089_1,plain,
    ! [T_2,T_1] :
      ( bounded_lattice_top(fun(T_2,T_1))
      | ~ bounded_lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Obounded__lattice__top]) ).

fof(f_1089_2,plain,
    ! [U_4503,U_4502] :
      ( bounded_lattice_top(fun(U_4503,U_4502))
      | ~ bounded_lattice(U_4502) ),
    inference(variable_rename,[status(thm)],[f_1089_1]) ).

cnf(f_1089_3,plain,
    ( bounded_lattice_top(fun(U_4503,U_4502))
    | ~ bounded_lattice(U_4502) ),
    inference(clausify,[status(thm)],[f_1089_2]) ).

fof(f_1090_1,plain,
    ! [T_2,T_1] :
      ( semilattice_sup(fun(T_2,T_1))
      | ~ lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Osemilattice__sup]) ).

fof(f_1090_2,plain,
    ! [U_4505,U_4504] :
      ( semilattice_sup(fun(U_4505,U_4504))
      | ~ lattice(U_4504) ),
    inference(variable_rename,[status(thm)],[f_1090_1]) ).

cnf(f_1090_3,plain,
    ( semilattice_sup(fun(U_4505,U_4504))
    | ~ lattice(U_4504) ),
    inference(clausify,[status(thm)],[f_1090_2]) ).

fof(f_1091_1,plain,
    ! [T_2,T_1] :
      ( semilattice_inf(fun(T_2,T_1))
      | ~ lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Osemilattice__inf]) ).

fof(f_1091_2,plain,
    ! [U_4507,U_4506] :
      ( semilattice_inf(fun(U_4507,U_4506))
      | ~ lattice(U_4506) ),
    inference(variable_rename,[status(thm)],[f_1091_1]) ).

cnf(f_1091_3,plain,
    ( semilattice_inf(fun(U_4507,U_4506))
    | ~ lattice(U_4506) ),
    inference(clausify,[status(thm)],[f_1091_2]) ).

fof(f_1092_1,plain,
    ! [T_2,T_1] :
      ( distrib_lattice(fun(T_2,T_1))
      | ~ distrib_lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Odistrib__lattice]) ).

fof(f_1092_2,plain,
    ! [U_4509,U_4508] :
      ( distrib_lattice(fun(U_4509,U_4508))
      | ~ distrib_lattice(U_4508) ),
    inference(variable_rename,[status(thm)],[f_1092_1]) ).

cnf(f_1092_3,plain,
    ( distrib_lattice(fun(U_4509,U_4508))
    | ~ distrib_lattice(U_4508) ),
    inference(clausify,[status(thm)],[f_1092_2]) ).

fof(f_1093_1,plain,
    ! [T_2,T_1] :
      ( preorder(fun(T_2,T_1))
      | ~ preorder(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Opreorder]) ).

fof(f_1093_2,plain,
    ! [U_4511,U_4510] :
      ( preorder(fun(U_4511,U_4510))
      | ~ preorder(U_4510) ),
    inference(variable_rename,[status(thm)],[f_1093_1]) ).

cnf(f_1093_3,plain,
    ( preorder(fun(U_4511,U_4510))
    | ~ preorder(U_4510) ),
    inference(clausify,[status(thm)],[f_1093_2]) ).

fof(f_1094_1,plain,
    ! [T_2,T_1] :
      ( finite_finite(fun(T_2,T_1))
      | ~ finite_finite(T_2)
      | ~ finite_finite(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Finite__Set_Ofinite]) ).

fof(f_1094_2,plain,
    ! [U_4513,U_4512] :
      ( finite_finite(fun(U_4513,U_4512))
      | ~ finite_finite(U_4513)
      | ~ finite_finite(U_4512) ),
    inference(variable_rename,[status(thm)],[f_1094_1]) ).

cnf(f_1094_3,plain,
    ( finite_finite(fun(U_4513,U_4512))
    | ~ finite_finite(U_4513)
    | ~ finite_finite(U_4512) ),
    inference(clausify,[status(thm)],[f_1094_2]) ).

fof(f_1095_1,plain,
    ! [T_2,T_1] :
      ( lattice(fun(T_2,T_1))
      | ~ lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Olattice]) ).

fof(f_1095_2,plain,
    ! [U_4515,U_4514] :
      ( lattice(fun(U_4515,U_4514))
      | ~ lattice(U_4514) ),
    inference(variable_rename,[status(thm)],[f_1095_1]) ).

cnf(f_1095_3,plain,
    ( lattice(fun(U_4515,U_4514))
    | ~ lattice(U_4514) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

fof(f_1096_1,plain,
    ! [T_2,T_1] :
      ( order(fun(T_2,T_1))
      | ~ order(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oorder]) ).

fof(f_1096_2,plain,
    ! [U_4517,U_4516] :
      ( order(fun(U_4517,U_4516))
      | ~ order(U_4516) ),
    inference(variable_rename,[status(thm)],[f_1096_1]) ).

cnf(f_1096_3,plain,
    ( order(fun(U_4517,U_4516))
    | ~ order(U_4516) ),
    inference(clausify,[status(thm)],[f_1096_2]) ).

fof(f_1097_1,plain,
    ! [T_2,T_1] :
      ( top(fun(T_2,T_1))
      | ~ top(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Otop]) ).

fof(f_1097_2,plain,
    ! [U_4519,U_4518] :
      ( top(fun(U_4519,U_4518))
      | ~ top(U_4518) ),
    inference(variable_rename,[status(thm)],[f_1097_1]) ).

cnf(f_1097_3,plain,
    ( top(fun(U_4519,U_4518))
    | ~ top(U_4518) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

fof(f_1098_1,plain,
    ! [T_2,T_1] :
      ( ord(fun(T_2,T_1))
      | ~ ord(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oord]) ).

fof(f_1098_2,plain,
    ! [U_4521,U_4520] :
      ( ord(fun(U_4521,U_4520))
      | ~ ord(U_4520) ),
    inference(variable_rename,[status(thm)],[f_1098_1]) ).

cnf(f_1098_3,plain,
    ( ord(fun(U_4521,U_4520))
    | ~ ord(U_4520) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

fof(f_1099_1,plain,
    semiri456707255roduct(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc]) ).

cnf(f_1099_2,plain,
    semiri456707255roduct(nat),
    inference(clausify,[status(thm)],[f_1099_1]) ).

fof(f_1100_1,plain,
    ordere223160158up_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add]) ).

cnf(f_1100_2,plain,
    ordere223160158up_add(nat),
    inference(clausify,[status(thm)],[f_1100_1]) ).

fof(f_1101_1,plain,
    ordere236663937imp_le(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le]) ).

cnf(f_1101_2,plain,
    ordere236663937imp_le(nat),
    inference(clausify,[status(thm)],[f_1101_1]) ).

fof(f_1102_1,plain,
    linord893533164strict(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict]) ).

cnf(f_1102_2,plain,
    linord893533164strict(nat),
    inference(clausify,[status(thm)],[f_1102_1]) ).

fof(f_1103_1,plain,
    linord20386208strict(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semiring__strict]) ).

cnf(f_1103_2,plain,
    linord20386208strict(nat),
    inference(clausify,[status(thm)],[f_1103_1]) ).

fof(f_1104_1,plain,
    ordere779506340up_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add]) ).

cnf(f_1104_2,plain,
    ordere779506340up_add(nat),
    inference(clausify,[status(thm)],[f_1104_1]) ).

fof(f_1105_1,plain,
    ordere216010020id_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__comm__monoid__add]) ).

cnf(f_1105_2,plain,
    ordere216010020id_add(nat),
    inference(clausify,[status(thm)],[f_1105_1]) ).

fof(f_1106_1,plain,
    cancel146912293up_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add]) ).

cnf(f_1106_2,plain,
    cancel146912293up_add(nat),
    inference(clausify,[status(thm)],[f_1106_1]) ).

fof(f_1107_1,plain,
    ordere453448008miring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Oordered__cancel__semiring]) ).

cnf(f_1107_2,plain,
    ordere453448008miring(nat),
    inference(clausify,[status(thm)],[f_1107_1]) ).

fof(f_1108_1,plain,
    ordere1490568538miring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Oordered__comm__semiring]) ).

cnf(f_1108_2,plain,
    ordere1490568538miring(nat),
    inference(clausify,[status(thm)],[f_1108_1]) ).

fof(f_1109_1,plain,
    cancel_semigroup_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__semigroup__add]) ).

cnf(f_1109_2,plain,
    cancel_semigroup_add(nat),
    inference(clausify,[status(thm)],[f_1109_1]) ).

fof(f_1110_1,plain,
    linordered_semiring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semiring]) ).

cnf(f_1110_2,plain,
    linordered_semiring(nat),
    inference(clausify,[status(thm)],[f_1110_1]) ).

fof(f_1111_1,plain,
    linordered_semidom(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semidom]) ).

cnf(f_1111_2,plain,
    linordered_semidom(nat),
    inference(clausify,[status(thm)],[f_1111_1]) ).

fof(f_1112_1,plain,
    semilattice_sup(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Lattices_Osemilattice__sup]) ).

cnf(f_1112_2,plain,
    semilattice_sup(nat),
    inference(clausify,[status(thm)],[f_1112_1]) ).

fof(f_1113_1,plain,
    semilattice_inf(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Lattices_Osemilattice__inf]) ).

cnf(f_1113_2,plain,
    semilattice_inf(nat),
    inference(clausify,[status(thm)],[f_1113_1]) ).

fof(f_1114_1,plain,
    distrib_lattice(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Lattices_Odistrib__lattice]) ).

cnf(f_1114_2,plain,
    distrib_lattice(nat),
    inference(clausify,[status(thm)],[f_1114_1]) ).

fof(f_1115_1,plain,
    ab_semigroup_mult(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__mult]) ).

cnf(f_1115_2,plain,
    ab_semigroup_mult(nat),
    inference(clausify,[status(thm)],[f_1115_1]) ).

fof(f_1116_1,plain,
    comm_monoid_mult(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__mult]) ).

cnf(f_1116_2,plain,
    comm_monoid_mult(nat),
    inference(clausify,[status(thm)],[f_1116_1]) ).

fof(f_1117_1,plain,
    ab_semigroup_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__add]) ).

cnf(f_1117_2,plain,
    ab_semigroup_add(nat),
    inference(clausify,[status(thm)],[f_1117_1]) ).

fof(f_1118_1,plain,
    ordered_semiring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Oordered__semiring]) ).

cnf(f_1118_2,plain,
    ordered_semiring(nat),
    inference(clausify,[status(thm)],[f_1118_1]) ).

fof(f_1119_1,plain,
    no_zero_divisors(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ono__zero__divisors]) ).

cnf(f_1119_2,plain,
    no_zero_divisors(nat),
    inference(clausify,[status(thm)],[f_1119_1]) ).

fof(f_1120_1,plain,
    comm_monoid_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__add]) ).

cnf(f_1120_2,plain,
    comm_monoid_add(nat),
    inference(clausify,[status(thm)],[f_1120_1]) ).

fof(f_1121_1,plain,
    comm_semiring_1(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring__1]) ).

cnf(f_1121_2,plain,
    comm_semiring_1(nat),
    inference(clausify,[status(thm)],[f_1121_1]) ).

fof(f_1122_1,plain,
    comm_semiring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring]) ).

cnf(f_1122_2,plain,
    comm_semiring(nat),
    inference(clausify,[status(thm)],[f_1122_1]) ).

fof(f_1123_1,plain,
    zero_neq_one(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ozero__neq__one]) ).

cnf(f_1123_2,plain,
    zero_neq_one(nat),
    inference(clausify,[status(thm)],[f_1123_1]) ).

fof(f_1124_1,plain,
    preorder(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]) ).

cnf(f_1124_2,plain,
    preorder(nat),
    inference(clausify,[status(thm)],[f_1124_1]) ).

fof(f_1125_1,plain,
    linorder(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Olinorder]) ).

cnf(f_1125_2,plain,
    linorder(nat),
    inference(clausify,[status(thm)],[f_1125_1]) ).

fof(f_1126_1,plain,
    monoid_mult(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__mult]) ).

cnf(f_1126_2,plain,
    monoid_mult(nat),
    inference(clausify,[status(thm)],[f_1126_1]) ).

fof(f_1127_1,plain,
    monoid_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__add]) ).

cnf(f_1127_2,plain,
    monoid_add(nat),
    inference(clausify,[status(thm)],[f_1127_1]) ).

fof(f_1128_1,plain,
    semiring_0(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Osemiring__0]) ).

cnf(f_1128_2,plain,
    semiring_0(nat),
    inference(clausify,[status(thm)],[f_1128_1]) ).

fof(f_1129_1,plain,
    lattice(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Lattices_Olattice]) ).

cnf(f_1129_2,plain,
    lattice(nat),
    inference(clausify,[status(thm)],[f_1129_1]) ).

fof(f_1130_1,plain,
    mult_zero(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Omult__zero]) ).

cnf(f_1130_2,plain,
    mult_zero(nat),
    inference(clausify,[status(thm)],[f_1130_1]) ).

fof(f_1131_1,plain,
    order(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]) ).

cnf(f_1131_2,plain,
    order(nat),
    inference(clausify,[status(thm)],[f_1131_1]) ).

fof(f_1132_1,plain,
    semiring(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Osemiring]) ).

cnf(f_1132_2,plain,
    semiring(nat),
    inference(clausify,[status(thm)],[f_1132_1]) ).

fof(f_1133_1,plain,
    ord(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oord]) ).

cnf(f_1133_2,plain,
    ord(nat),
    inference(clausify,[status(thm)],[f_1133_1]) ).

fof(f_1134_1,plain,
    zero(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ozero]) ).

cnf(f_1134_2,plain,
    zero(nat),
    inference(clausify,[status(thm)],[f_1134_1]) ).

fof(f_1135_1,plain,
    one(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oone]) ).

cnf(f_1135_2,plain,
    one(nat),
    inference(clausify,[status(thm)],[f_1135_1]) ).

fof(f_1136_1,plain,
    bounded_lattice_top(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Lattices_Obounded__lattice__top]) ).

cnf(f_1136_2,plain,
    bounded_lattice_top(bool),
    inference(clausify,[status(thm)],[f_1136_1]) ).

fof(f_1137_1,plain,
    semilattice_sup(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Lattices_Osemilattice__sup]) ).

cnf(f_1137_2,plain,
    semilattice_sup(bool),
    inference(clausify,[status(thm)],[f_1137_1]) ).

fof(f_1138_1,plain,
    semilattice_inf(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Lattices_Osemilattice__inf]) ).

cnf(f_1138_2,plain,
    semilattice_inf(bool),
    inference(clausify,[status(thm)],[f_1138_1]) ).

fof(f_1139_1,plain,
    distrib_lattice(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Lattices_Odistrib__lattice]) ).

cnf(f_1139_2,plain,
    distrib_lattice(bool),
    inference(clausify,[status(thm)],[f_1139_1]) ).

fof(f_1140_1,plain,
    preorder(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]) ).

cnf(f_1140_2,plain,
    preorder(bool),
    inference(clausify,[status(thm)],[f_1140_1]) ).

fof(f_1141_1,plain,
    finite_finite(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]) ).

cnf(f_1141_2,plain,
    finite_finite(bool),
    inference(clausify,[status(thm)],[f_1141_1]) ).

fof(f_1142_1,plain,
    lattice(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Lattices_Olattice]) ).

cnf(f_1142_2,plain,
    lattice(bool),
    inference(clausify,[status(thm)],[f_1142_1]) ).

fof(f_1143_1,plain,
    order(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]) ).

cnf(f_1143_2,plain,
    order(bool),
    inference(clausify,[status(thm)],[f_1143_1]) ).

fof(f_1144_1,plain,
    top(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Otop]) ).

cnf(f_1144_2,plain,
    top(bool),
    inference(clausify,[status(thm)],[f_1144_1]) ).

fof(f_1145_1,plain,
    ord(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oord]) ).

cnf(f_1145_2,plain,
    ord(bool),
    inference(clausify,[status(thm)],[f_1145_1]) ).

fof(f_1146_1,plain,
    ! [T_2,T_1] :
      ( finite_finite(sum_sum(T_2,T_1))
      | ~ finite_finite(T_2)
      | ~ finite_finite(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_sum___Finite__Set_Ofinite]) ).

fof(f_1146_2,plain,
    ! [U_4523,U_4522] :
      ( finite_finite(sum_sum(U_4523,U_4522))
      | ~ finite_finite(U_4523)
      | ~ finite_finite(U_4522) ),
    inference(variable_rename,[status(thm)],[f_1146_1]) ).

cnf(f_1146_3,plain,
    ( finite_finite(sum_sum(U_4523,U_4522))
    | ~ finite_finite(U_4523)
    | ~ finite_finite(U_4522) ),
    inference(clausify,[status(thm)],[f_1146_2]) ).

fof(f_1147_1,plain,
    ! [T_1] :
      ( finite_finite(option(T_1))
      | ~ finite_finite(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Option_Ooption___Finite__Set_Ofinite]) ).

fof(f_1147_2,plain,
    ! [U_4524] :
      ( finite_finite(option(U_4524))
      | ~ finite_finite(U_4524) ),
    inference(variable_rename,[status(thm)],[f_1147_1]) ).

cnf(f_1147_3,plain,
    ( finite_finite(option(U_4524))
    | ~ finite_finite(U_4524) ),
    inference(clausify,[status(thm)],[f_1147_2]) ).

fof(f_1148_1,plain,
    ! [T_2,T_1] :
      ( finite_finite(product_prod(T_2,T_1))
      | ~ finite_finite(T_2)
      | ~ finite_finite(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_prod___Finite__Set_Ofinite]) ).

fof(f_1148_2,plain,
    ! [U_4526,U_4525] :
      ( finite_finite(product_prod(U_4526,U_4525))
      | ~ finite_finite(U_4526)
      | ~ finite_finite(U_4525) ),
    inference(variable_rename,[status(thm)],[f_1148_1]) ).

cnf(f_1148_3,plain,
    ( finite_finite(product_prod(U_4526,U_4525))
    | ~ finite_finite(U_4526)
    | ~ finite_finite(U_4525) ),
    inference(clausify,[status(thm)],[f_1148_2]) ).

fof(f_1149_1,plain,
    finite_finite(product_unit),
    inference(fof_nnf,[status(thm)],[arity_Product__Type_Ounit___Finite__Set_Ofinite]) ).

cnf(f_1149_2,plain,
    finite_finite(product_unit),
    inference(clausify,[status(thm)],[f_1149_1]) ).

fof(f_1150_1,plain,
    ! [T,A] : ti(T,ti(T,A)) = ti(T,A),
    inference(fof_nnf,[status(thm)],[help_ti_idem]) ).

fof(f_1150_2,plain,
    ! [U_4528,U_4527] : ti(U_4528,ti(U_4528,U_4527)) = ti(U_4528,U_4527),
    inference(variable_rename,[status(thm)],[f_1150_1]) ).

cnf(f_1150_3,plain,
    ti(U_4528,ti(U_4528,U_4527)) = ti(U_4528,U_4527),
    inference(clausify,[status(thm)],[f_1150_2]) ).

fof(f_1151_1,plain,
    ! [X_a,X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X),
    inference(fof_nnf,[status(thm)],[help_If_1_1_T]) ).

fof(f_1151_2,plain,
    ! [U_4531,U_4530,U_4529] : hAPP(U_4531,U_4531,hAPP(U_4531,fun(U_4531,U_4531),hAPP(bool,fun(U_4531,fun(U_4531,U_4531)),if(U_4531),fTrue),U_4530),U_4529) = ti(U_4531,U_4530),
    inference(variable_rename,[status(thm)],[f_1151_1]) ).

cnf(f_1151_3,plain,
    hAPP(U_4531,U_4531,hAPP(U_4531,fun(U_4531,U_4531),hAPP(bool,fun(U_4531,fun(U_4531,U_4531)),if(U_4531),fTrue),U_4530),U_4529) = ti(U_4531,U_4530),
    inference(clausify,[status(thm)],[f_1151_2]) ).

fof(f_1152_1,plain,
    ! [X_a,X,Y] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y),
    inference(fof_nnf,[status(thm)],[help_If_2_1_T]) ).

fof(f_1152_2,plain,
    ! [U_4534,U_4533,U_4532] : hAPP(U_4534,U_4534,hAPP(U_4534,fun(U_4534,U_4534),hAPP(bool,fun(U_4534,fun(U_4534,U_4534)),if(U_4534),fFalse),U_4533),U_4532) = ti(U_4534,U_4532),
    inference(variable_rename,[status(thm)],[f_1152_1]) ).

cnf(f_1152_3,plain,
    hAPP(U_4534,U_4534,hAPP(U_4534,fun(U_4534,U_4534),hAPP(bool,fun(U_4534,fun(U_4534,U_4534)),if(U_4534),fFalse),U_4533),U_4532) = ti(U_4534,U_4532),
    inference(clausify,[status(thm)],[f_1152_2]) ).

fof(f_1153_1,plain,
    ! [P] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    inference(fof_nnf,[status(thm)],[help_If_3_1_T]) ).

fof(f_1153_2,plain,
    ! [U_4535] :
      ( ti(bool,U_4535) = fFalse
      | ti(bool,U_4535) = fTrue ),
    inference(variable_rename,[status(thm)],[f_1153_1]) ).

cnf(f_1153_3,plain,
    ( ti(bool,U_4535) = fFalse
    | ti(bool,U_4535) = fTrue ),
    inference(clausify,[status(thm)],[f_1153_2]) ).

fof(f_1154_1,plain,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,fNot,P)) ),
    inference(fof_nnf,[status(thm)],[help_fNot_1_1_U]) ).

fof(f_1154_2,plain,
    ! [U_4536] :
      ( ~ hBOOL(U_4536)
      | ~ hBOOL(hAPP(bool,bool,fNot,U_4536)) ),
    inference(variable_rename,[status(thm)],[f_1154_1]) ).

cnf(f_1154_3,plain,
    ( ~ hBOOL(U_4536)
    | ~ hBOOL(hAPP(bool,bool,fNot,U_4536)) ),
    inference(clausify,[status(thm)],[f_1154_2]) ).

fof(f_1155_1,plain,
    ! [P] :
      ( hBOOL(hAPP(bool,bool,fNot,P))
      | hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fNot_2_1_U]) ).

fof(f_1155_2,plain,
    ! [U_4537] :
      ( hBOOL(hAPP(bool,bool,fNot,U_4537))
      | hBOOL(U_4537) ),
    inference(variable_rename,[status(thm)],[f_1155_1]) ).

cnf(f_1155_3,plain,
    ( hBOOL(hAPP(bool,bool,fNot,U_4537))
    | hBOOL(U_4537) ),
    inference(clausify,[status(thm)],[f_1155_2]) ).

fof(f_1156_1,plain,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_U]) ).

fof(f_1156_2,plain,
    ! [U_4543,U_4542,U_4541,U_4540,U_4539,U_4538] : hAPP(U_4543,U_4542,hAPP(fun(U_4543,U_4541),fun(U_4543,U_4542),hAPP(fun(U_4541,U_4542),fun(fun(U_4543,U_4541),fun(U_4543,U_4542)),combb(U_4541,U_4542,U_4543),U_4540),U_4539),U_4538) = hAPP(U_4541,U_4542,U_4540,hAPP(U_4543,U_4541,U_4539,U_4538)),
    inference(variable_rename,[status(thm)],[f_1156_1]) ).

cnf(f_1156_3,plain,
    hAPP(U_4543,U_4542,hAPP(fun(U_4543,U_4541),fun(U_4543,U_4542),hAPP(fun(U_4541,U_4542),fun(fun(U_4543,U_4541),fun(U_4543,U_4542)),combb(U_4541,U_4542,U_4543),U_4540),U_4539),U_4538) = hAPP(U_4541,U_4542,U_4540,hAPP(U_4543,U_4541,U_4539,U_4538)),
    inference(clausify,[status(thm)],[f_1156_2]) ).

fof(f_1157_1,plain,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_U]) ).

fof(f_1157_2,plain,
    ! [U_4549,U_4548,U_4547,U_4546,U_4545,U_4544] : hAPP(U_4549,U_4548,hAPP(U_4547,fun(U_4549,U_4548),hAPP(fun(U_4549,fun(U_4547,U_4548)),fun(U_4547,fun(U_4549,U_4548)),combc(U_4549,U_4547,U_4548),U_4546),U_4545),U_4544) = hAPP(U_4547,U_4548,hAPP(U_4549,fun(U_4547,U_4548),U_4546,U_4544),U_4545),
    inference(variable_rename,[status(thm)],[f_1157_1]) ).

cnf(f_1157_3,plain,
    hAPP(U_4549,U_4548,hAPP(U_4547,fun(U_4549,U_4548),hAPP(fun(U_4549,fun(U_4547,U_4548)),fun(U_4547,fun(U_4549,U_4548)),combc(U_4549,U_4547,U_4548),U_4546),U_4545),U_4544) = hAPP(U_4547,U_4548,hAPP(U_4549,fun(U_4547,U_4548),U_4546,U_4544),U_4545),
    inference(clausify,[status(thm)],[f_1157_2]) ).

fof(f_1158_1,plain,
    ! [X_a,P] : hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P),
    inference(fof_nnf,[status(thm)],[help_COMBI_1_1_U]) ).

fof(f_1158_2,plain,
    ! [U_4551,U_4550] : hAPP(U_4551,U_4551,combi(U_4551),U_4550) = ti(U_4551,U_4550),
    inference(variable_rename,[status(thm)],[f_1158_1]) ).

cnf(f_1158_3,plain,
    hAPP(U_4551,U_4551,combi(U_4551),U_4550) = ti(U_4551,U_4550),
    inference(clausify,[status(thm)],[f_1158_2]) ).

fof(f_1159_1,plain,
    ! [X_b,X_a,P,Q] : hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_U]) ).

fof(f_1159_2,plain,
    ! [U_4555,U_4554,U_4553,U_4552] : hAPP(U_4555,U_4554,hAPP(U_4554,fun(U_4555,U_4554),combk(U_4554,U_4555),U_4553),U_4552) = ti(U_4554,U_4553),
    inference(variable_rename,[status(thm)],[f_1159_1]) ).

cnf(f_1159_3,plain,
    hAPP(U_4555,U_4554,hAPP(U_4554,fun(U_4555,U_4554),combk(U_4554,U_4555),U_4553),U_4552) = ti(U_4554,U_4553),
    inference(clausify,[status(thm)],[f_1159_2]) ).

fof(f_1160_1,plain,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_U]) ).

fof(f_1160_2,plain,
    ! [U_4561,U_4560,U_4559,U_4558,U_4557,U_4556] : hAPP(U_4561,U_4560,hAPP(fun(U_4561,U_4559),fun(U_4561,U_4560),hAPP(fun(U_4561,fun(U_4559,U_4560)),fun(fun(U_4561,U_4559),fun(U_4561,U_4560)),combs(U_4561,U_4559,U_4560),U_4558),U_4557),U_4556) = hAPP(U_4559,U_4560,hAPP(U_4561,fun(U_4559,U_4560),U_4558,U_4556),hAPP(U_4561,U_4559,U_4557,U_4556)),
    inference(variable_rename,[status(thm)],[f_1160_1]) ).

cnf(f_1160_3,plain,
    hAPP(U_4561,U_4560,hAPP(fun(U_4561,U_4559),fun(U_4561,U_4560),hAPP(fun(U_4561,fun(U_4559,U_4560)),fun(fun(U_4561,U_4559),fun(U_4561,U_4560)),combs(U_4561,U_4559,U_4560),U_4558),U_4557),U_4556) = hAPP(U_4559,U_4560,hAPP(U_4561,fun(U_4559,U_4560),U_4558,U_4556),hAPP(U_4561,U_4559,U_4557,U_4556)),
    inference(clausify,[status(thm)],[f_1160_2]) ).

fof(f_1161_1,plain,
    hBOOL(fTrue),
    inference(fof_nnf,[status(thm)],[help_fTrue_1_1_U]) ).

cnf(f_1161_2,plain,
    hBOOL(fTrue),
    inference(clausify,[status(thm)],[f_1161_1]) ).

fof(f_1162_1,plain,
    ! [P] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    inference(fof_nnf,[status(thm)],[help_fTrue_1_1_T]) ).

fof(f_1162_2,plain,
    ! [U_4562] :
      ( ti(bool,U_4562) = fFalse
      | ti(bool,U_4562) = fTrue ),
    inference(variable_rename,[status(thm)],[f_1162_1]) ).

cnf(f_1162_3,plain,
    ( ti(bool,U_4562) = fFalse
    | ti(bool,U_4562) = fTrue ),
    inference(clausify,[status(thm)],[f_1162_2]) ).

fof(f_1163_1,plain,
    ! [Q,P] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))
      | ~ hBOOL(Q)
      | ~ hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fconj_1_1_U]) ).

fof(f_1163_2,plain,
    ! [U_4564,U_4563] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4563),U_4564))
      | ~ hBOOL(U_4564)
      | ~ hBOOL(U_4563) ),
    inference(variable_rename,[status(thm)],[f_1163_1]) ).

fof(f_1163_3,plain,
    ! [U_4564] :
      ( ! [U_4563] :
          ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4563),U_4564))
          | ~ hBOOL(U_4563) )
      | ~ hBOOL(U_4564) ),
    inference(miniscope,[status(thm)],[f_1163_2]) ).

cnf(f_1163_4,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4563),U_4564))
    | ~ hBOOL(U_4563)
    | ~ hBOOL(U_4564) ),
    inference(clausify,[status(thm)],[f_1163_3]) ).

fof(f_1164_1,plain,
    ! [P,Q] :
      ( hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fconj_2_1_U]) ).

fof(f_1164_2,plain,
    ! [U_4566,U_4565] :
      ( hBOOL(U_4566)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4566),U_4565)) ),
    inference(variable_rename,[status(thm)],[f_1164_1]) ).

fof(f_1164_3,plain,
    ! [U_4566] :
      ( ! [U_4565] : ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4566),U_4565))
      | hBOOL(U_4566) ),
    inference(miniscope,[status(thm)],[f_1164_2]) ).

cnf(f_1164_4,plain,
    ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4566),U_4565))
    | hBOOL(U_4566) ),
    inference(clausify,[status(thm)],[f_1164_3]) ).

fof(f_1165_1,plain,
    ! [P,Q] :
      ( hBOOL(Q)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fconj_3_1_U]) ).

fof(f_1165_2,plain,
    ! [U_4568,U_4567] :
      ( hBOOL(U_4567)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4568),U_4567)) ),
    inference(variable_rename,[status(thm)],[f_1165_1]) ).

cnf(f_1165_3,plain,
    ( hBOOL(U_4567)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_4568),U_4567)) ),
    inference(clausify,[status(thm)],[f_1165_2]) ).

fof(f_1166_1,plain,
    ! [Q,P] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
      | ~ hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fdisj_1_1_U]) ).

fof(f_1166_2,plain,
    ! [U_4570,U_4569] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4569),U_4570))
      | ~ hBOOL(U_4569) ),
    inference(variable_rename,[status(thm)],[f_1166_1]) ).

cnf(f_1166_3,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4569),U_4570))
    | ~ hBOOL(U_4569) ),
    inference(clausify,[status(thm)],[f_1166_2]) ).

fof(f_1167_1,plain,
    ! [P,Q] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
      | ~ hBOOL(Q) ),
    inference(fof_nnf,[status(thm)],[help_fdisj_2_1_U]) ).

fof(f_1167_2,plain,
    ! [U_4572,U_4571] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4572),U_4571))
      | ~ hBOOL(U_4571) ),
    inference(variable_rename,[status(thm)],[f_1167_1]) ).

cnf(f_1167_3,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4572),U_4571))
    | ~ hBOOL(U_4571) ),
    inference(clausify,[status(thm)],[f_1167_2]) ).

fof(f_1168_1,plain,
    ! [P,Q] :
      ( hBOOL(Q)
      | hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fdisj_3_1_U]) ).

fof(f_1168_2,plain,
    ! [U_4574,U_4573] :
      ( hBOOL(U_4573)
      | hBOOL(U_4574)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4574),U_4573)) ),
    inference(variable_rename,[status(thm)],[f_1168_1]) ).

fof(f_1168_3,plain,
    ! [U_4574] :
      ( ! [U_4573] :
          ( hBOOL(U_4573)
          | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4574),U_4573)) )
      | hBOOL(U_4574) ),
    inference(miniscope,[status(thm)],[f_1168_2]) ).

cnf(f_1168_4,plain,
    ( hBOOL(U_4573)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_4574),U_4573))
    | hBOOL(U_4574) ),
    inference(clausify,[status(thm)],[f_1168_3]) ).

fof(f_1169_1,plain,
    ~ hBOOL(fFalse),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_U]) ).

cnf(f_1169_2,plain,
    ~ hBOOL(fFalse),
    inference(clausify,[status(thm)],[f_1169_1]) ).

fof(f_1170_1,plain,
    ! [P] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T]) ).

fof(f_1170_2,plain,
    ! [U_4575] :
      ( ti(bool,U_4575) = fFalse
      | ti(bool,U_4575) = fTrue ),
    inference(variable_rename,[status(thm)],[f_1170_1]) ).

cnf(f_1170_3,plain,
    ( ti(bool,U_4575) = fFalse
    | ti(bool,U_4575) = fTrue ),
    inference(clausify,[status(thm)],[f_1170_2]) ).

fof(f_1171_1,plain,
    ! [X_a,X,Y] :
      ( ti(X_a,X) = ti(X_a,Y)
      | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_T]) ).

fof(f_1171_2,plain,
    ! [U_4578,U_4577,U_4576] :
      ( ti(U_4578,U_4577) = ti(U_4578,U_4576)
      | ~ hBOOL(hAPP(U_4578,bool,hAPP(U_4578,fun(U_4578,bool),fequal(U_4578),U_4577),U_4576)) ),
    inference(variable_rename,[status(thm)],[f_1171_1]) ).

cnf(f_1171_3,plain,
    ( ti(U_4578,U_4577) = ti(U_4578,U_4576)
    | ~ hBOOL(hAPP(U_4578,bool,hAPP(U_4578,fun(U_4578,bool),fequal(U_4578),U_4577),U_4576)) ),
    inference(clausify,[status(thm)],[f_1171_2]) ).

fof(f_1172_1,plain,
    ! [X_a,X,Y] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y))
      | ti(X_a,X) != ti(X_a,Y) ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_T]) ).

fof(f_1172_2,plain,
    ! [U_4581,U_4580,U_4579] :
      ( hBOOL(hAPP(U_4581,bool,hAPP(U_4581,fun(U_4581,bool),fequal(U_4581),U_4580),U_4579))
      | ti(U_4581,U_4580) != ti(U_4581,U_4579) ),
    inference(variable_rename,[status(thm)],[f_1172_1]) ).

cnf(f_1172_3,plain,
    ( hBOOL(hAPP(U_4581,bool,hAPP(U_4581,fun(U_4581,bool),fequal(U_4581),U_4580),U_4579))
    | ti(U_4581,U_4580) != ti(U_4581,U_4579) ),
    inference(clausify,[status(thm)],[f_1172_2]) ).

fof(f_1173_1,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
    inference(negate,[status(cth)],[conj_0]) ).

fof(f_1173_2,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
    inference(definitional_conversion,[status(esa)],[f_1173_1]) ).

cnf(f_1173_3,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
    inference(clausify,[status(thm)],[f_1173_2]) ).

cnf(f_94_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_94_7]) ).

cnf(f_95_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_95_7]) ).

cnf(f_101_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_101_7]) ).

cnf(f_101_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_101_8]) ).

cnf(f_101_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_101_13]) ).

cnf(f_113_23_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_113_23]) ).

cnf(f_113_24_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_113_24]) ).

cnf(f_135_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_4]) ).

cnf(f_135_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_5]) ).

cnf(f_135_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_6]) ).

cnf(f_135_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_7]) ).

cnf(f_135_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_8]) ).

cnf(f_135_9_simplified,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ),
    inference(simplify_clause,[status(thm)],[f_135_9]) ).

cnf(f_135_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_10]) ).

cnf(f_135_14_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_14]) ).

cnf(f_135_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_15]) ).

cnf(f_135_16_simplified,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_268) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
    inference(simplify_clause,[status(thm)],[f_135_16]) ).

cnf(f_135_17_simplified,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,U_268) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
    inference(simplify_clause,[status(thm)],[f_135_17]) ).

cnf(f_135_18_simplified,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_268)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_268)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
    inference(simplify_clause,[status(thm)],[f_135_18]) ).

cnf(f_135_19_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_19]) ).

cnf(f_135_20_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_20]) ).

cnf(f_135_24_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_24]) ).

cnf(f_135_25_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_25]) ).

cnf(f_135_26_simplified,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e))) ),
    inference(simplify_clause,[status(thm)],[f_135_26]) ).

cnf(f_135_28_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_28]) ).

cnf(f_135_29_simplified,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_269) != n ),
    inference(simplify_clause,[status(thm)],[f_135_29]) ).

cnf(f_135_30_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_30]) ).

cnf(f_135_31_simplified,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,U_269)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,U_269)),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,U_269) = n ),
    inference(simplify_clause,[status(thm)],[f_135_31]) ).

cnf(f_135_32_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_32]) ).

cnf(f_135_34_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_34]) ).

cnf(f_169_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_169_7]) ).

cnf(f_169_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_169_8]) ).

cnf(f_169_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_169_15]) ).

cnf(f_174_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_174_4]) ).

cnf(f_174_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_174_5]) ).

cnf(f_174_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_174_10]) ).

cnf(f_174_14_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_174_14]) ).

cnf(f_174_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_174_15]) ).

cnf(f_174_20_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_174_20]) ).

cnf(f_174_24_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_174_24]) ).

cnf(f_174_28_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_174_28]) ).

cnf(f_174_30_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_174_30]) ).

cnf(f_181_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_181_7]) ).

cnf(f_181_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_181_8]) ).

cnf(f_181_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_181_15]) ).

cnf(f_311_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_4]) ).

cnf(f_311_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_5]) ).

cnf(f_311_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_6]) ).

cnf(f_311_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_7]) ).

cnf(f_311_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_8]) ).

cnf(f_311_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_9]) ).

cnf(f_311_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_10]) ).

cnf(f_615_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_615_10]) ).

cnf(f_615_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_615_11]) ).

cnf(f_615_14_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_615_14]) ).

cnf(f_615_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_615_15]) ).

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,
    ( 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_5,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_6,axiom,
    ( ti(Eq_x_0,Eq_x_1) = ti(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,
    ( big_co1399186613setsum(Eq_x_0,Eq_x_1) = big_co1399186613setsum(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,
    ( combb(Eq_x_0,Eq_x_1,Eq_x_2) = combb(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_9,axiom,
    ( combc(Eq_x_0,Eq_x_1,Eq_x_2) = combc(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_10,axiom,
    ( combi(Eq_x_0) = combi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,axiom,
    ( combk(Eq_x_0,Eq_x_1) = combk(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,
    ( combs(Eq_x_0,Eq_x_1,Eq_x_2) = combs(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_13,axiom,
    ( finite_card(Eq_x_0) = finite_card(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( finite_finite_1(Eq_x_0) = finite_finite_1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,axiom,
    ( finite_fold_image(Eq_x_0,Eq_x_1) = finite_fold_image(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,
    ( finite_folding_idem(Eq_x_0,Eq_x_1) = finite_folding_idem(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( finite_folding_image(Eq_x_0,Eq_x_1) = finite_folding_image(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( finite908156982e_idem(Eq_x_0,Eq_x_1) = finite908156982e_idem(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( in_rel(Eq_x_0,Eq_x_1) = in_rel(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( comp(Eq_x_0,Eq_x_1,Eq_x_2) = comp(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_21,axiom,
    ( inj_on(Eq_x_0,Eq_x_1) = inj_on(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,
    ( the_inv_into(Eq_x_0,Eq_x_1) = the_inv_into(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,
    ( pi(Eq_x_0,Eq_x_1) = pi(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,
    ( compose(Eq_x_0,Eq_x_1,Eq_x_2) = compose(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_25,axiom,
    ( extensional(Eq_x_0,Eq_x_1) = extensional(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,
    ( restrict(Eq_x_0,Eq_x_1) = restrict(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,
    ( one_one(Eq_x_0) = one_one(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,axiom,
    ( plus_plus(Eq_x_0) = plus_plus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( times_times(Eq_x_0) = times_times(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( zero_zero(Eq_x_0) = zero_zero(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( undefined(Eq_x_0) = undefined(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_32,axiom,
    ( hilbert_inv_into(Eq_x_0,Eq_x_1) = hilbert_inv_into(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,
    ( if(Eq_x_0) = if(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_34,axiom,
    ( ring_1_Ints(Eq_x_0) = ring_1_Ints(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_35,axiom,
    ( semilattice_inf_inf(Eq_x_0) = semilattice_inf_inf(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_36,axiom,
    ( semilattice_sup_sup(Eq_x_0) = semilattice_sup_sup(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_37,axiom,
    ( nat_case(Eq_x_0) = nat_case(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_38,axiom,
    ( size_size(Eq_x_0) = size_size(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_39,axiom,
    ( ord_less(Eq_x_0) = ord_less(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_40,axiom,
    ( ord_less_eq(Eq_x_0) = ord_less_eq(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_41,axiom,
    ( top_top(Eq_x_0) = top_top(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_42,axiom,
    ( product_Pair(Eq_x_0,Eq_x_1) = product_Pair(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,
    ( product_prod_rec(Eq_x_0,Eq_x_1,Eq_x_2) = product_prod_rec(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_44,axiom,
    ( ord_atLeast(Eq_x_0) = ord_atLeast(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_45,axiom,
    ( ord_atLeastAtMost(Eq_x_0) = ord_atLeastAtMost(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_46,axiom,
    ( ord_atLeastLessThan(Eq_x_0) = ord_atLeastLessThan(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_47,axiom,
    ( ord_greaterThan(Eq_x_0) = ord_greaterThan(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_48,axiom,
    ( ord_gr1471790799AtMost(Eq_x_0) = ord_gr1471790799AtMost(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,axiom,
    ( ord_gr676655987ssThan(Eq_x_0) = ord_gr676655987ssThan(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_50,axiom,
    ( collect(Eq_x_0) = collect(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_51,axiom,
    ( image(Eq_x_0,Eq_x_1) = image(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,
    ( sum_sum(Eq_x_0,Eq_x_1) = sum_sum(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,
    ( sum_Plus(Eq_x_0,Eq_x_1) = sum_Plus(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,
    ( finite_psubset(Eq_x_0) = finite_psubset(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_55,axiom,
    ( measure(Eq_x_0) = measure(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_56,axiom,
    ( mlex_prod(Eq_x_0) = mlex_prod(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_57,axiom,
    ( fequal(Eq_x_0) = fequal(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_58,axiom,
    ( hAPP(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = hAPP(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_59,axiom,
    ( member(Eq_x_0) = member(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_60,axiom,
    ( option(Eq_x_0) = option(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_61,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_62,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_63,axiom,
    ( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK3(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_64,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_65,axiom,
    ( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK5(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_66,axiom,
    ( sK6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK6(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_67,axiom,
    ( sK7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK7(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_68,axiom,
    ( sK8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK8(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_69,axiom,
    ( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_70,axiom,
    ( sK10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_71,axiom,
    ( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(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_72,axiom,
    ( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(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_73,axiom,
    ( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(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_74,axiom,
    ( sK14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK14(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_75,axiom,
    ( sK15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK15(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_76,axiom,
    ( sK16(Eq_x_0) = sK16(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_77,axiom,
    ( sK17(Eq_x_0) = sK17(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_78,axiom,
    ( sK18(Eq_x_0) = sK18(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_79,axiom,
    ( sK19(Eq_x_0) = sK19(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_80,axiom,
    ( sK20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_81,axiom,
    ( sK21(Eq_x_0) = sK21(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_82,axiom,
    ( sK22(Eq_x_0) = sK22(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_83,axiom,
    ( sK23(Eq_x_0) = sK23(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_84,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_85,axiom,
    ( sK27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_86,axiom,
    ( sK28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_87,axiom,
    ( sK29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_88,axiom,
    ( sK30(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK30(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_89,axiom,
    ( sK31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_90,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_91,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_92,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_93,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_94,axiom,
    ( sK38(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_95,axiom,
    ( sK39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK39(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_96,axiom,
    ( sK40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_97,axiom,
    ( sK41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK41(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_98,axiom,
    ( sK42(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,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_100,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_101,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_102,axiom,
    ( sK46(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK46(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_103,axiom,
    ( sK47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK47(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_104,axiom,
    ( sK48(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK48(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_105,axiom,
    ( sK49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK49(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_106,axiom,
    ( sK50(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK50(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_107,axiom,
    ( sK51(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK51(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_108,axiom,
    ( sK52(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK52(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_109,axiom,
    ( sK53(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK53(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_110,axiom,
    ( sK54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK54(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_111,axiom,
    ( sK55(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK55(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_112,axiom,
    ( sK56(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK56(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_113,axiom,
    ( sK57(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK57(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_114,axiom,
    ( sK58(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK58(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_115,axiom,
    ( sK59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK59(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_116,axiom,
    ( sK60(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK60(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_117,axiom,
    ( sK61(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK61(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_118,axiom,
    ( sK62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK62(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_119,axiom,
    ( sK63(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK63(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_120,axiom,
    ( sK64(Eq_x_0,Eq_x_1) = sK64(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,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_122,axiom,
    ( sK66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK66(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_123,axiom,
    ( sK67(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK67(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_124,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_125,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_126,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_127,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_128,axiom,
    ( sK72(Eq_x_0,Eq_x_1,Eq_x_2) = sK72(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_129,axiom,
    ( sK73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK73(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_130,axiom,
    ( sK75(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK75(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_131,axiom,
    ( sK76(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK76(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_132,axiom,
    ( sK77(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK77(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_133,axiom,
    ( sK78(Eq_x_0,Eq_x_1) = sK78(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,
    ( sK79(Eq_x_0) = sK79(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_135,axiom,
    ( sK80(Eq_x_0,Eq_x_1) = sK80(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_136,axiom,
    ( sK81(Eq_x_0) = sK81(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_137,axiom,
    ( sK82(Eq_x_0,Eq_x_1) = sK82(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_138,axiom,
    ( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_139,axiom,
    ( sK84(Eq_x_0,Eq_x_1) = sK84(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_140,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_141,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_142,axiom,
    ( sK87(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK87(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_143,axiom,
    ( sK88(Eq_x_0,Eq_x_1) = sK88(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,
    ( sK89(Eq_x_0,Eq_x_1) = sK89(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_145,axiom,
    ( sK90(Eq_x_0,Eq_x_1) = sK90(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,
    ( sK91(Eq_x_0,Eq_x_1) = sK91(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_147,axiom,
    ( sK92(Eq_x_0) = sK92(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_148,axiom,
    ( sK93(Eq_x_0,Eq_x_1) = sK93(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_149,axiom,
    ( sK94(Eq_x_0,Eq_x_1) = sK94(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,
    ( sK95(Eq_x_0,Eq_x_1,Eq_x_2) = sK95(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_151,axiom,
    ( sK96(Eq_x_0,Eq_x_1) = sK96(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,
    ( sK97(Eq_x_0) = sK97(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_153,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_154,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_155,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_156,axiom,
    ( sK101(Eq_x_0,Eq_x_1) = sK101(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,
    ( sK102(Eq_x_0,Eq_x_1) = sK102(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,
    ( sK103(Eq_x_0,Eq_x_1) = sK103(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,
    ( sK104(Eq_x_0) = sK104(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_160,axiom,
    ( sK105(Eq_x_0) = sK105(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_161,axiom,
    ( sK106(Eq_x_0) = sK106(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_162,axiom,
    ( sK107(Eq_x_0,Eq_x_1) = sK107(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,
    ( sK108(Eq_x_0,Eq_x_1,Eq_x_2) = sK108(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_164,axiom,
    ( sK110(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK110(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_165,axiom,
    ( sK111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK111(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_166,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_167,axiom,
    ( sK113(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK113(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_168,axiom,
    ( sK114(Eq_x_0,Eq_x_1,Eq_x_2) = sK114(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_169,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_170,axiom,
    ( sK116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK116(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_171,axiom,
    ( sK117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK117(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_172,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_173,axiom,
    ( sK119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK119(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_174,axiom,
    ( sK120(Eq_x_0,Eq_x_1) = sK120(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,
    ( sK121(Eq_x_0,Eq_x_1) = sK121(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,
    ( sK122(Eq_x_0,Eq_x_1) = sK122(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,
    ( sK123(Eq_x_0,Eq_x_1) = sK123(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,
    ( 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_179,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_180,axiom,
    ( sK126(Eq_x_0,Eq_x_1) = sK126(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,
    ( sK127(Eq_x_0,Eq_x_1) = sK127(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,
    ( sK128(Eq_x_0,Eq_x_1) = sK128(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,
    ( sK129(Eq_x_0,Eq_x_1) = sK129(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,
    ( sK130(Eq_x_0,Eq_x_1) = sK130(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,
    ( sK131(Eq_x_0,Eq_x_1) = sK131(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,
    ( sK132(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK132(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_187,axiom,
    ( sK133(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK133(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_188,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_189,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_190,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_191,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_192,axiom,
    ( sK138(Eq_x_0,Eq_x_1,Eq_x_2) = sK138(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_193,axiom,
    ( sK139(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK139(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_194,axiom,
    ( sK140(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK140(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_195,axiom,
    ( sK141(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK141(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_196,axiom,
    ( sK142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK142(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_197,axiom,
    ( sK143(Eq_x_0,Eq_x_1,Eq_x_2) = sK143(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_198,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_199,axiom,
    ( sK145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK145(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_200,axiom,
    ( sK146(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | 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_201,axiom,
    ( sK147(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK147(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | 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_202,axiom,
    ( sK148(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK148(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | 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_203,axiom,
    ( sK149(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK149(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | 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_204,axiom,
    ( sK150(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK150(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | 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_205,axiom,
    ( sK151(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9) = sK151(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9)
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | 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_206,axiom,
    ( sK152(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9) = sK152(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9)
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | 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_207,axiom,
    ( sK153(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK153(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_208,axiom,
    ( sK154(Eq_x_0,Eq_x_1,Eq_x_2) = sK154(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_209,axiom,
    ( sK155(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK155(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_210,axiom,
    ( sK156(Eq_x_0) = sK156(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_211,axiom,
    ( sK157(Eq_x_0,Eq_x_1) = sK157(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,
    ( sK158(Eq_x_0,Eq_x_1,Eq_x_2) = sK158(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_213,axiom,
    ( sK159(Eq_x_0,Eq_x_1,Eq_x_2) = sK159(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_214,axiom,
    ( sK160(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK160(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | 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_215,axiom,
    ( sK161(Eq_x_0) = sK161(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_216,axiom,
    ( sK162(Eq_x_0) = sK162(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_217,axiom,
    ( sK163(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10) = sK163(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | 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_218,axiom,
    ( sK164(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10) = sK164(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | 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_219,axiom,
    ( sK165(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8) = sK165(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | 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_220,axiom,
    ( sK166(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8) = sK166(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | 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_221,axiom,
    ( sK167(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8) = sK167(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | 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_222,axiom,
    ( sK168(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8) = sK168(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | 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_223,axiom,
    ( sK169(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8) = sK169(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | 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_224,axiom,
    ( sK170(Eq_x_0,Eq_x_1) = sK170(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,
    ( sK171(Eq_x_0,Eq_x_1) = sK171(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,
    ( sK172(Eq_x_0,Eq_x_1) = sK172(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,
    ( sK173(Eq_x_0,Eq_x_1) = sK173(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,
    ( 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_229,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_230,axiom,
    ( sK176(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK176(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_231,axiom,
    ( sK177(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK177(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_232,axiom,
    ( sK178(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK178(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_233,axiom,
    ( sK179(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK179(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_234,axiom,
    ( sK180(Eq_x_0,Eq_x_1,Eq_x_2) = sK180(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_235,axiom,
    ( sK181(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK181(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_236,axiom,
    ( sK182(Eq_x_0,Eq_x_1,Eq_x_2) = sK182(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_237,axiom,
    ( sK183(Eq_x_0,Eq_x_1,Eq_x_2) = sK183(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_238,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_239,axiom,
    ( sK185(Eq_x_0,Eq_x_1,Eq_x_2) = sK185(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_240,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_241,axiom,
    ( comm_monoid_add(Eq_y_0)
    | ~ comm_monoid_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_242,axiom,
    ( one(Eq_y_0)
    | ~ one(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_243,axiom,
    ( monoid_add(Eq_y_0)
    | ~ monoid_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_244,axiom,
    ( ab_semigroup_add(Eq_y_0)
    | ~ ab_semigroup_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_245,axiom,
    ( cancel_semigroup_add(Eq_y_0)
    | ~ cancel_semigroup_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_246,axiom,
    ( semiring(Eq_y_0)
    | ~ semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_247,axiom,
    ( monoid_mult(Eq_y_0)
    | ~ monoid_mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_248,axiom,
    ( ab_semigroup_mult(Eq_y_0)
    | ~ ab_semigroup_mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_249,axiom,
    ( mult_zero(Eq_y_0)
    | ~ mult_zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_250,axiom,
    ( no_zero_divisors(Eq_y_0)
    | ~ no_zero_divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_251,axiom,
    ( zero(Eq_y_0)
    | ~ zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_252,axiom,
    ( ring_1(Eq_y_0)
    | ~ ring_1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_253,axiom,
    ( semilattice_inf(Eq_y_0)
    | ~ semilattice_inf(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_254,axiom,
    ( semilattice_sup(Eq_y_0)
    | ~ semilattice_sup(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_255,axiom,
    ( ord(Eq_y_0)
    | ~ ord(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_256,axiom,
    ( top(Eq_y_0)
    | ~ top(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_257,axiom,
    ( order(Eq_y_0)
    | ~ order(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_258,axiom,
    ( linorder(Eq_y_0)
    | ~ linorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_259,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_260,axiom,
    ( preorder(Eq_y_0)
    | ~ preorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_261,axiom,
    ( linordered_semidom(Eq_y_0)
    | ~ linordered_semidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_262,axiom,
    ( ordere223160158up_add(Eq_y_0)
    | ~ ordere223160158up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_263,axiom,
    ( dense_linorder(Eq_y_0)
    | ~ dense_linorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_264,axiom,
    ( linordered_idom(Eq_y_0)
    | ~ linordered_idom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_265,axiom,
    ( cancel146912293up_add(Eq_y_0)
    | ~ cancel146912293up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_266,axiom,
    ( ordere236663937imp_le(Eq_y_0)
    | ~ ordere236663937imp_le(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_267,axiom,
    ( ordere779506340up_add(Eq_y_0)
    | ~ ordere779506340up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_268,axiom,
    ( finite_finite(Eq_y_0)
    | ~ finite_finite(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_269,axiom,
    ( linord219039673up_add(Eq_y_0)
    | ~ linord219039673up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_270,axiom,
    ( zero_neq_one(Eq_y_0)
    | ~ zero_neq_one(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_271,axiom,
    ( ordere216010020id_add(Eq_y_0)
    | ~ ordere216010020id_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_272,axiom,
    ( comm_semiring_1(Eq_y_0)
    | ~ comm_semiring_1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_273,axiom,
    ( semiri456707255roduct(Eq_y_0)
    | ~ semiri456707255roduct(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_274,axiom,
    ( linordered_field(Eq_y_0)
    | ~ linordered_field(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_275,axiom,
    ( ring_char_0(Eq_y_0)
    | ~ ring_char_0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_276,axiom,
    ( linord626643107strict(Eq_y_0)
    | ~ linord626643107strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_277,axiom,
    ( ring_n68954251visors(Eq_y_0)
    | ~ ring_n68954251visors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_278,axiom,
    ( comm_monoid_mult(Eq_y_0)
    | ~ comm_monoid_mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_279,axiom,
    ( comm_semiring(Eq_y_0)
    | ~ comm_semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_280,axiom,
    ( linordered_ring(Eq_y_0)
    | ~ linordered_ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_281,axiom,
    ( linord581940658strict(Eq_y_0)
    | ~ linord581940658strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_282,axiom,
    ( ordere453448008miring(Eq_y_0)
    | ~ ordere453448008miring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_283,axiom,
    ( ordered_ring(Eq_y_0)
    | ~ ordered_ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_284,axiom,
    ( ordered_semiring(Eq_y_0)
    | ~ ordered_semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_285,axiom,
    ( ordere1490568538miring(Eq_y_0)
    | ~ ordere1490568538miring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_286,axiom,
    ( linord20386208strict(Eq_y_0)
    | ~ linord20386208strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_287,axiom,
    ( linord893533164strict(Eq_y_0)
    | ~ linord893533164strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_288,axiom,
    ( linordered_semiring(Eq_y_0)
    | ~ linordered_semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_289,axiom,
    ( linord1278240602ring_1(Eq_y_0)
    | ~ linord1278240602ring_1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_290,axiom,
    ( linord1117847801e_zero(Eq_y_0)
    | ~ linord1117847801e_zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_291,axiom,
    ( lattice(Eq_y_0)
    | ~ lattice(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_292,axiom,
    ( ab_sem1668676832m_mult(Eq_y_0)
    | ~ ab_sem1668676832m_mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_293,axiom,
    ( bounded_lattice_top(Eq_y_0)
    | ~ bounded_lattice_top(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_294,axiom,
    ( distrib_lattice(Eq_y_0)
    | ~ distrib_lattice(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_295,axiom,
    ( semiring_0(Eq_y_0)
    | ~ semiring_0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_296,axiom,
    ( bounded_lattice(Eq_y_0)
    | ~ bounded_lattice(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
% 0.00/0.02  % Problem  : SCT171+7 : 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 : n009.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 21:24:26 UTC 2026
% 0.08/0.35  % CPUTime  : 
% 8.47/8.75  % SZS status Theorem for theBenchmark
% 8.47/8.75  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------