%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SCT171+6 : 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 : n002.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 08:55:41 AM UTC 2026
% Result : Theorem 5.35s 5.66s
% Output : Proof 5.46s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OIIA_res,axiom,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OIIA_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OLin_res,axiom,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OLin_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OProf_res,axiom,
ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OProf_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Oabove_res,axiom,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Oabove_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Obelow_res,axiom,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Obelow_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Odictator_res,axiom,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Odictator_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omkbot_res,axiom,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omkbot_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omktop_res,axiom,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omktop_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Ounanimity_res,axiom,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Ounanimity_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] : ti(fun(fun(nat,fun(nat,nat)),fun(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat)))),finite_fold_image(nat,X_a)) = finite_fold_image(nat,X_a),
file('theBenchmark.p',tsy_c_Finite__Set_Ofold__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_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_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_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_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_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_Nat_OSuc_res,axiom,
ti(fun(nat,nat),suc) = suc,
file('theBenchmark.p',tsy_c_Nat_OSuc_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_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_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_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_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f,
file('theBenchmark.p',tsy_v_F_res) ).
fof(tsy_v_Lab_____res,axiom,
ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
file('theBenchmark.p',tsy_v_Lab_____res) ).
fof(tsy_v_Lba_____res,axiom,
ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
file('theBenchmark.p',tsy_v_Lba_____res) ).
fof(tsy_v_P_____res,hypothesis,
ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p,
file('theBenchmark.p',tsy_v_P_____res) ).
fof(tsy_v_a_____res,axiom,
ti(arrow_490897120le_alt,a) = a,
file('theBenchmark.p',tsy_v_a_____res) ).
fof(tsy_v_b_____res,axiom,
ti(arrow_490897120le_alt,b) = b,
file('theBenchmark.p',tsy_v_b_____res) ).
fof(tsy_v_c_____res,hypothesis,
ti(arrow_490897120le_alt,c) = c,
file('theBenchmark.p',tsy_v_c_____res) ).
fof(tsy_v_d_____res,hypothesis,
ti(arrow_490897120le_alt,d) = d,
file('theBenchmark.p',tsy_v_d_____res) ).
fof(tsy_v_e_____res,axiom,
ti(arrow_490897120le_alt,e) = e,
file('theBenchmark.p',tsy_v_e_____res) ).
fof(tsy_v_h_____res,axiom,
ti(fun(arrow_660593299e_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_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
file('theBenchmark.p',fact_0_assms_I3_J) ).
fof(fact_1_u,axiom,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,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_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
file('theBenchmark.p',fact_3__096P_A_058_AProf_096) ).
fof(fact_4_in__mkbot,axiom,
! [X_1,Y_2,L_3,Z] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_3),Z)))
<=> ( ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Z)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3)) )
& ( ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Z)
=> ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2) )
& ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Z) ) ),
file('theBenchmark.p',fact_4_in__mkbot) ).
fof(fact_5_in__mktop,axiom,
! [X_1,Y_2,L_3,Z] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_3),Z)))
<=> ( ( ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Z)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3)) )
& ( ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Z)
=> ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2) )
& ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Z) ) ),
file('theBenchmark.p',fact_5_in__mktop) ).
fof(fact_6__C2_C,axiom,
! [P_1,Pa,A_5,B_3,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( ti(arrow_490897120le_alt,A_5) != ti(arrow_490897120le_alt,B_3)
=> ( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,B_3)
=> ( ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,A_5)
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
=> ( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) ) ) ) ) ) ) ) ),
file('theBenchmark.p',fact_6__C2_C) ).
fof(fact_7__C1_C,axiom,
! [P_1,Pa,A_5,B_3,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( ti(arrow_490897120le_alt,A_5) != ti(arrow_490897120le_alt,B_3)
=> ( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,B_3)
=> ( ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,A_5)
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
=> ( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) ) ) ) ) ) ) ) ),
file('theBenchmark.p',fact_7__C1_C) ).
fof(fact_8__C4_C,axiom,
! [P_1,Pa,Ca,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,Ca)
=> ( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ca)
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
=> ( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Ca)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Ca)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) ) ) ) ) ) ) ),
file('theBenchmark.p',fact_8__C4_C) ).
fof(fact_9_pairwise__neutrality,axiom,
! [P_1,Pa,A_5,B_3,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( ti(arrow_490897120le_alt,A_5) != ti(arrow_490897120le_alt,B_3)
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
=> ( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) ) ) ) ) ) ),
file('theBenchmark.p',fact_9_pairwise__neutrality) ).
fof(fact_10__C3_C,axiom,
! [P_1,Pa,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
=> ( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) ) ) ) ) ),
file('theBenchmark.p',fact_10__C3_C) ).
fof(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)))
<=> ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> ( ( hAPP(arrow_660593299e_indi,nat,h,I_2) != n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) )
& ( hAPP(arrow_660593299e_indi,nat,h,I_2) = n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e))) ) ) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) ) ) ),
file('theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).
fof(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_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_3,B_2] : 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_3),B_2))) ),
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_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
file('theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
fof(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_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_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
file('theBenchmark.p',fact_19_n_I1_J) ).
fof(fact_20_injh,axiom,
hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_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_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),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_4)
=> ~ ( ti(X_a,A_2) = ti(X_a,A_6)
=> ti(X_b,B_1) != ti(X_b,B_4) ) ),
file('theBenchmark.p',fact_21_Pair__inject) ).
fof(fact_22_Pair__eq,axiom,
! [X_b,X_a,Aa,Ba,A_5,B_3] :
( 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_3)
<=> ( ti(X_b,Ba) = ti(X_b,B_3)
& 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_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,Fa))
<=> ! [X_2] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof))
=> ! [Xa] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Xa),arrow_1111136790e_Prof))
=> ! [A_3,B_2] :
( ! [I_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Xa,I_2))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2)))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,Xa))) ) ) ) ) ),
file('theBenchmark.p',fact_23_IIA__def) ).
fof(fact_24_unanimity__def,axiom,
! [Fa] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,Fa))
<=> ! [X_2] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof))
=> ! [A_3,B_2] :
( ! [I_2] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2)))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2))) ) ) ),
file('theBenchmark.p',fact_24_unanimity__def) ).
fof(fact_25_top1I,axiom,
! [X_a,X_1] : hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_1)),
file('theBenchmark.p',fact_25_top1I) ).
fof(fact_26_UNIV__I,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_26_UNIV__I) ).
fof(fact_27_iso__tuple__UNIV__I,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_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_1] : hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_1) = 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_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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__096Lab_A_058_ALin_096,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
file('theBenchmark.p',fact_34__096Lab_A_058_ALin_096) ).
fof(fact_35__096Lba_A_058_ALin_096,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
file('theBenchmark.p',fact_35__096Lba_A_058_ALin_096) ).
fof(fact_36__096a_A_126_061_Ab_096,axiom,
a != b,
file('theBenchmark.p',fact_36__096a_A_126_061_Ab_096) ).
fof(fact_37__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
file('theBenchmark.p',fact_37__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
fof(fact_38__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
file('theBenchmark.p',fact_38__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
fof(fact_39__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
file('theBenchmark.p',fact_39__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
fof(fact_40__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
file('theBenchmark.p',fact_40__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
fof(fact_41_PiProf,axiom,
! [Na] : hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),Na))),lab)),lba)),arrow_1111136790e_Prof)),
file('theBenchmark.p',fact_41_PiProf) ).
fof(fact_42__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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),Lab))
=> ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),Lab),arrow_2064824852le_Lin)) ),
file('theBenchmark.p',fact_42__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).
fof(fact_43__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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),Lba))
=> ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),Lba),arrow_2064824852le_Lin)) ),
file('theBenchmark.p',fact_43__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).
fof(fact_44__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
! [I_2] :
( ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> ( ( hAPP(arrow_660593299e_indi,nat,h,I_2) != n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) )
& ( hAPP(arrow_660593299e_indi,nat,h,I_2) = n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e))) ) ) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) ) )
<=> ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ) ) ),
file('theBenchmark.p',fact_44__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).
fof(fact_45_n_I2_J,axiom,
! [M] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),M))),lab)),lba)))) ),
file('theBenchmark.p',fact_45_n_I2_J) ).
fof(fact_46_notin__Lin__iff,axiom,
! [X_1,Y_2,L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2)
=> ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Y_2),X_1)),L_3)) ) ) ),
file('theBenchmark.p',fact_46_notin__Lin__iff) ).
fof(fact_47_Lin__irrefl,axiom,
! [Aa,Ba,L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),L_3))
=> ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),L_3)) ) ),
file('theBenchmark.p',fact_47_Lin__irrefl) ).
fof(fact_48_mktop__Lin,axiom,
! [X_1,L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_3),X_1)),arrow_2064824852le_Lin)) ),
file('theBenchmark.p',fact_48_mktop__Lin) ).
fof(fact_49_mkbot__Lin,axiom,
! [X_1,L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_3),X_1)),arrow_2064824852le_Lin)) ),
file('theBenchmark.p',fact_49_mkbot__Lin) ).
fof(fact_50_above__Lin,axiom,
! [L_3,X_1,Y_2] :
( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_3),X_1),Y_2)),arrow_2064824852le_Lin)) ) ),
file('theBenchmark.p',fact_50_above__Lin) ).
fof(fact_51_const__Lin__Prof,axiom,
! [L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),L_3)),arrow_1111136790e_Prof)) ),
file('theBenchmark.p',fact_51_const__Lin__Prof) ).
fof(fact_52_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_52_linorder__cases) ).
fof(fact_53_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_53_order__less__asym) ).
fof(fact_54_xt1_I10_J,axiom,
! [X_a] :
( order(X_a)
=> ! [Z_1,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_1),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)) ) ) ),
file('theBenchmark.p',fact_54_xt1_I10_J) ).
fof(fact_55_order__less__trans,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Z_1,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_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)) ) ) ),
file('theBenchmark.p',fact_55_order__less__trans) ).
fof(fact_56_xt1_I2_J,axiom,
! [X_a] :
( order(X_a)
=> ! [C,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)
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_2)) ) ) ),
file('theBenchmark.p',fact_56_xt1_I2_J) ).
fof(fact_57_ord__less__eq__trans,axiom,
! [X_a] :
( ord(X_a)
=> ! [C,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
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C)) ) ) ),
file('theBenchmark.p',fact_57_ord__less__eq__trans) ).
fof(fact_58_xt1_I1_J,axiom,
! [X_a] :
( order(X_a)
=> ! [C,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),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_2)) ) ) ),
file('theBenchmark.p',fact_58_xt1_I1_J) ).
fof(fact_59_ord__eq__less__trans,axiom,
! [X_a] :
( ord(X_a)
=> ! [C,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))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C)) ) ) ),
file('theBenchmark.p',fact_59_ord__eq__less__trans) ).
fof(fact_60_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_60_xt1_I9_J) ).
fof(fact_61_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_61_order__less__asym_H) ).
fof(fact_62_order__less__imp__triv,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Pa,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))
=> hBOOL(Pa) ) ) ),
file('theBenchmark.p',fact_62_order__less__imp__triv) ).
fof(fact_63_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_63_order__less__imp__not__eq2) ).
fof(fact_64_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_64_order__less__imp__not__eq) ).
fof(fact_65_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_65_order__less__imp__not__less) ).
fof(fact_66_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_66_order__less__not__sym) ).
fof(fact_67_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_67_less__imp__neq) ).
fof(fact_68_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_68_linorder__neqE) ).
fof(fact_69_linorder__antisym__conv3,axiom,
! [X_a] :
( linorder(X_a)
=> ! [Y_2,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ),
file('theBenchmark.p',fact_69_linorder__antisym__conv3) ).
fof(fact_70_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_70_linorder__less__linear) ).
fof(fact_71_not__less__iff__gr__or__eq,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X_1,Y_2] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
<=> ( ti(X_a,X_1) = ti(X_a,Y_2)
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)) ) ) ),
file('theBenchmark.p',fact_71_not__less__iff__gr__or__eq) ).
fof(fact_72_linorder__neq__iff,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X_1,Y_2] :
( ti(X_a,X_1) != ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) ) ) ),
file('theBenchmark.p',fact_72_linorder__neq__iff) ).
fof(fact_73_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_73_order__less__irrefl) ).
fof(fact_74_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_74_UNIV__def) ).
fof(fact_75_ext,axiom,
! [X_a,X_b,F,G] :
( ! [X_2] : hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)
=> 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_1,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(X_a,bool,A_1,X_1)) ),
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_in__above,axiom,
! [X_1,Y_2,L_3,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_3),Aa),Ba)))
<=> ( ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Ba)
=> ( ( ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Ba)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3)) )
& ( ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Ba)
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Aa)),L_3))
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa) ) ) ) )
& ( ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Ba)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Y_2)),L_3)) )
& ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2) ) ) ) ),
file('theBenchmark.p',fact_78_in__above) ).
fof(fact_79_pred__equals__eq2,axiom,
! [X_a,X_b,S_1,R_1] :
( ! [X_2,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_2),Xa)),R_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),Xa)),S_1)) )
<=> ti(fun(product_prod(X_a,X_b),bool),R_1) = ti(fun(product_prod(X_a,X_b),bool),S_1) ),
file('theBenchmark.p',fact_79_pred__equals__eq2) ).
fof(fact_80_n_I3_J,axiom,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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_80_n_I3_J) ).
fof(fact_81__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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
<=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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_81__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).
fof(fact_82__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
! [I_2] :
( ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> ( ( hAPP(arrow_660593299e_indi,nat,h,I_2) != n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) )
& ( hAPP(arrow_660593299e_indi,nat,h,I_2) = n
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e))) ) ) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e))) ) )
<=> ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ) ) ),
file('theBenchmark.p',fact_82__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).
fof(fact_83_inv__f__eq,axiom,
! [X_a,X_b,X_1,Y_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_a,X_b,F,X_1) = ti(X_b,Y_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),top_top(fun(X_a,bool))),F),Y_2) = ti(X_a,X_1) ) ),
file('theBenchmark.p',fact_83_inv__f__eq) ).
fof(fact_84_inv__f__f,axiom,
! [X_a,X_b,X_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_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_1)) = ti(X_a,X_1) ),
file('theBenchmark.p',fact_84_inv__f__f) ).
fof(fact_85_dictatorI,axiom,
! [I_1,Fa] :
( hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Fa),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
=> ( ! [X_2] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof))
=> ! [A_3,B_2] :
( ti(arrow_490897120le_alt,A_3) != ti(arrow_490897120le_alt,B_2)
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_1)))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2))) ) ) )
=> hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_1)) ) ),
file('theBenchmark.p',fact_85_dictatorI) ).
fof(fact_86_PiE,axiom,
! [X_a,X_b,X_1,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_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)) ) ),
file('theBenchmark.p',fact_86_PiE) ).
fof(fact_87_complete__Lin,axiom,
! [Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ? [X_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),X_2))
& hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X_2),arrow_2064824852le_Lin)) ) ),
file('theBenchmark.p',fact_87_complete__Lin) ).
fof(fact_88_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_88_Pi__UNIV) ).
fof(fact_89_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_89_inj__fun) ).
fof(fact_90_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_90_order__refl) ).
fof(fact_91__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_,axiom,
? [N] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))))),lab)),lba))))
& ! [M] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),M))),lab)),lba)))) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))) ),
file('theBenchmark.p',fact_91__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_) ).
fof(fact_92__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O,axiom,
~ ! [N] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
=> ( ! [M] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),M))),lab)),lba)))) )
=> ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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_92__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O) ).
fof(fact_93_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_93_linorder__le__cases) ).
fof(fact_94_le__funE,axiom,
! [X_a,X_b] :
( ord(X_b)
=> ! [X_1,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_1)),hAPP(X_a,X_b,G,X_1))) ) ),
file('theBenchmark.p',fact_94_le__funE) ).
fof(fact_95_xt1_I6_J,axiom,
! [X_a] :
( order(X_a)
=> ! [Z_1,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_1),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X)) ) ) ),
file('theBenchmark.p',fact_95_xt1_I6_J) ).
fof(fact_96_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_96_xt1_I5_J) ).
fof(fact_97_order__trans,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Z_1,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_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1)) ) ) ),
file('theBenchmark.p',fact_97_order__trans) ).
fof(fact_98_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_98_order__antisym) ).
fof(fact_99_xt1_I4_J,axiom,
! [X_a] :
( order(X_a)
=> ! [C,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)
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_2)) ) ) ),
file('theBenchmark.p',fact_99_xt1_I4_J) ).
fof(fact_100_ord__le__eq__trans,axiom,
! [X_a] :
( ord(X_a)
=> ! [C,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
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C)) ) ) ),
file('theBenchmark.p',fact_100_ord__le__eq__trans) ).
fof(fact_101_xt1_I3_J,axiom,
! [X_a] :
( order(X_a)
=> ! [C,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),B_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_2)) ) ) ),
file('theBenchmark.p',fact_101_xt1_I3_J) ).
fof(fact_102_ord__eq__le__trans,axiom,
! [X_a] :
( ord(X_a)
=> ! [C,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))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C)) ) ) ),
file('theBenchmark.p',fact_102_ord__eq__le__trans) ).
fof(fact_103_order__antisym__conv,axiom,
! [X_a] :
( order(X_a)
=> ! [Y_2,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ),
file('theBenchmark.p',fact_103_order__antisym__conv) ).
fof(fact_104_le__funD,axiom,
! [X_a,X_b] :
( ord(X_b)
=> ! [X_1,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_1)),hAPP(X_a,X_b,G,X_1))) ) ),
file('theBenchmark.p',fact_104_le__funD) ).
fof(fact_105_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_105_order__eq__refl) ).
fof(fact_106_order__eq__iff,axiom,
! [X_a] :
( order(X_a)
=> ! [X_1,Y_2] :
( ti(X_a,X_1) = ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2)) ) ) ),
file('theBenchmark.p',fact_106_order__eq__iff) ).
fof(fact_107_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_107_linorder__linear) ).
fof(fact_108_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_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_2)),hAPP(X_a,X_b,G,X_2))) ) ),
file('theBenchmark.p',fact_108_le__fun__def) ).
fof(fact_109_linorder__not__less,axiom,
! [X_a] :
( linorder(X_a)
=> ! [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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_1)) ) ),
file('theBenchmark.p',fact_109_linorder__not__less) ).
fof(fact_110_linorder__not__le,axiom,
! [X_a] :
( linorder(X_a)
=> ! [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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)) ) ),
file('theBenchmark.p',fact_110_linorder__not__le) ).
fof(fact_111_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_111_linorder__le__less__linear) ).
fof(fact_112_order__less__le,axiom,
! [X_a] :
( order(X_a)
=> ! [X_1,Y_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
<=> ( ti(X_a,X_1) != ti(X_a,Y_2)
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2)) ) ) ),
file('theBenchmark.p',fact_112_order__less__le) ).
fof(fact_113_less__le__not__le,axiom,
! [X_a] :
( preorder(X_a)
=> ! [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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_1))
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2)) ) ) ),
file('theBenchmark.p',fact_113_less__le__not__le) ).
fof(fact_114_order__le__less,axiom,
! [X_a] :
( order(X_a)
=> ! [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))
<=> ( ti(X_a,X_1) = ti(X_a,Y_2)
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) ) ) ),
file('theBenchmark.p',fact_114_order__le__less) ).
fof(fact_115_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_115_leI) ).
fof(fact_116_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_116_not__leE) ).
fof(fact_117_linorder__antisym__conv1,axiom,
! [X_a] :
( linorder(X_a)
=> ! [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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ),
file('theBenchmark.p',fact_117_linorder__antisym__conv1) ).
fof(fact_118_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_118_order__neq__le__trans) ).
fof(fact_119_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_119_xt1_I12_J) ).
fof(fact_120_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_120_leD) ).
fof(fact_121_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_121_order__less__imp__le) ).
fof(fact_122_linorder__antisym__conv2,axiom,
! [X_a] :
( linorder(X_a)
=> ! [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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ),
file('theBenchmark.p',fact_122_linorder__antisym__conv2) ).
fof(fact_123_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_123_order__le__imp__less__or__eq) ).
fof(fact_124_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_124_order__le__neq__trans) ).
fof(fact_125_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_125_xt1_I11_J) ).
fof(fact_126_order__less__le__trans,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Z_1,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_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)) ) ) ),
file('theBenchmark.p',fact_126_order__less__le__trans) ).
fof(fact_127_xt1_I7_J,axiom,
! [X_a] :
( order(X_a)
=> ! [Z_1,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_1),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)) ) ) ),
file('theBenchmark.p',fact_127_xt1_I7_J) ).
fof(fact_128_order__le__less__trans,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Z_1,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_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)) ) ) ),
file('theBenchmark.p',fact_128_order__le__less__trans) ).
fof(fact_129_xt1_I8_J,axiom,
! [X_a] :
( order(X_a)
=> ! [Z_1,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_1),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)) ) ) ),
file('theBenchmark.p',fact_129_xt1_I8_J) ).
fof(fact_130_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_130_top__greatest) ).
fof(fact_131_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_131_top__unique) ).
fof(fact_132_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_132_top__le) ).
fof(fact_133_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_2] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),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_2) = hAPP(X_a,X_b,F,Xa)
=> ti(X_a,X_2) = ti(X_a,Xa) ) ) ) ),
file('theBenchmark.p',fact_133_inj__on__def) ).
fof(fact_134_inj__on__contraD,axiom,
! [X_a,X_b,X_1,Y_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))
=> ( ti(X_a,X_1) != ti(X_a,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) ) ) ) ),
file('theBenchmark.p',fact_134_inj__on__contraD) ).
fof(fact_135_inj__on__iff,axiom,
! [X_a,X_b,Y_2,X_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_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) ) ) ) ),
file('theBenchmark.p',fact_135_inj__on__iff) ).
fof(fact_136_inj__onD,axiom,
! [X_a,X_b,X_1,Y_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))
=> ( 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),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))
=> ti(X_a,X_1) = ti(X_a,Y_2) ) ) ) ),
file('theBenchmark.p',fact_136_inj__onD) ).
fof(fact_137_Pi__mem,axiom,
! [X_a,X_b,X_1,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_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))) ) ),
file('theBenchmark.p',fact_137_Pi__mem) ).
fof(fact_138_Prof__def,axiom,
arrow_1111136790e_Prof = hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)),
file('theBenchmark.p',fact_138_Prof__def) ).
fof(fact_139_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_139_inj__on__id2) ).
fof(fact_140_funcset__mem,axiom,
! [X_a,X_b,X_1,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_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)) ) ),
file('theBenchmark.p',fact_140_funcset__mem) ).
fof(fact_141_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_141_funcset__id) ).
fof(fact_142_dictator__def,axiom,
! [Fa,I_1] :
( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_1))
<=> ! [X_2] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof))
=> hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_1) ) ),
file('theBenchmark.p',fact_142_dictator__def) ).
fof(fact_143_inj__eq,axiom,
! [X_a,X_b,X_1,Y_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_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2)
<=> ti(X_a,X_1) = ti(X_a,Y_2) ) ),
file('theBenchmark.p',fact_143_inj__eq) ).
fof(fact_144_injD,axiom,
! [X_a,X_b,X_1,Y_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_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2)
=> ti(X_a,X_1) = ti(X_a,Y_2) ) ),
file('theBenchmark.p',fact_144_injD) ).
fof(fact_145_inv__into__f__f,axiom,
! [X_a,X_b,X_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_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),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_1)) = ti(X_a,X_1) ) ),
file('theBenchmark.p',fact_145_inv__into__f__f) ).
fof(fact_146_inv__into__f__eq,axiom,
! [X_a,X_b,Y_2,X_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_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) = ti(X_b,Y_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_2) = ti(X_a,X_1) ) ) ),
file('theBenchmark.p',fact_146_inv__into__f__eq) ).
fof(fact_147_Pi__I,axiom,
! [X_b,X_a,F,B,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))
=> 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))) ),
file('theBenchmark.p',fact_147_Pi__I) ).
fof(fact_148_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_2] : hAPP(X_a,X_b,F,hAPP(X_b,X_a,G,X_2)) = ti(X_b,X_2)
=> 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_148_inj__imp__inv__eq) ).
fof(fact_149_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_149_less__add__one) ).
fof(fact_150_add__less__le__mono,axiom,
! [X_a] :
( ordere223160158up_add(X_a)
=> ! [C,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),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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
file('theBenchmark.p',fact_150_add__less__le__mono) ).
fof(fact_151_add__le__less__mono,axiom,
! [X_a] :
( ordere223160158up_add(X_a)
=> ! [C,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),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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
file('theBenchmark.p',fact_151_add__le__less__mono) ).
fof(fact_152_injI,axiom,
! [X_a,X_b,F] :
( ! [X_2,Y_3] :
( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_3)
=> ti(X_a,X_2) = ti(X_a,Y_3) )
=> 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_152_injI) ).
fof(fact_153_dense__le,axiom,
! [X_a] :
( dense_linorder(X_a)
=> ! [Z_1,Y] :
( ! [X_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y))
=> 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),Z_1)) ) ),
file('theBenchmark.p',fact_153_dense__le) ).
fof(fact_154_dense__le__bounded,axiom,
! [X_a] :
( dense_linorder(X_a)
=> ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ( ! [W] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1)) ) )
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) ) ) ),
file('theBenchmark.p',fact_154_dense__le__bounded) ).
fof(fact_155_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_155_less__fun__def) ).
fof(fact_156_Pi__anti__mono,axiom,
! [X_b,X_a,B,A_4,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_4),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_4),B))) ),
file('theBenchmark.p',fact_156_Pi__anti__mono) ).
fof(fact_157_pred__subset__eq2,axiom,
! [X_a,X_b,R_1,S_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))),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_1)),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_1)))
<=> 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_1),S_1)) ),
file('theBenchmark.p',fact_157_pred__subset__eq2) ).
fof(fact_158_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_158_subset__UNIV) ).
fof(fact_159_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_159_subset__inj__on) ).
fof(fact_160_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_160_linorder__neqE__linordered__idom) ).
fof(fact_161_add__right__imp__eq,axiom,
! [X_a] :
( cancel_semigroup_add(X_a)
=> ! [B_1,A_2,C] :
( 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),A_2)
=> ti(X_a,B_1) = ti(X_a,C) ) ),
file('theBenchmark.p',fact_161_add__right__imp__eq) ).
fof(fact_162_add__imp__eq,axiom,
! [X_a] :
( cancel146912293up_add(X_a)
=> ! [A_2,B_1,C] :
( 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)
=> ti(X_a,B_1) = ti(X_a,C) ) ),
file('theBenchmark.p',fact_162_add__imp__eq) ).
fof(fact_163_add__left__imp__eq,axiom,
! [X_a] :
( cancel_semigroup_add(X_a)
=> ! [A_2,B_1,C] :
( 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)
=> ti(X_a,B_1) = ti(X_a,C) ) ),
file('theBenchmark.p',fact_163_add__left__imp__eq) ).
fof(fact_164_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_164_add__right__cancel) ).
fof(fact_165_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_165_add__left__cancel) ).
fof(fact_166_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X_a] :
( ab_semigroup_add(X_a)
=> ! [A_2,B_1,C] : 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) = 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)) ),
file('theBenchmark.p',fact_166_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_167_one__reorient,axiom,
! [X_a] :
( one(X_a)
=> ! [X_1] :
( one_one(X_a) = ti(X_a,X_1)
<=> ti(X_a,X_1) = one_one(X_a) ) ),
file('theBenchmark.p',fact_167_one__reorient) ).
fof(fact_168_add__le__imp__le__left,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [C,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),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),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_168_add__le__imp__le__left) ).
fof(fact_169_add__le__imp__le__right,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [A_2,C,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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)))
=> 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_169_add__le__imp__le__right) ).
fof(fact_170_add__mono,axiom,
! [X_a] :
( ordere779506340up_add(X_a)
=> ! [C,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),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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
file('theBenchmark.p',fact_170_add__mono) ).
fof(fact_171_add__left__mono,axiom,
! [X_a] :
( ordere779506340up_add(X_a)
=> ! [C,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),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) ) ),
file('theBenchmark.p',fact_171_add__left__mono) ).
fof(fact_172_add__right__mono,axiom,
! [X_a] :
( ordere779506340up_add(X_a)
=> ! [C,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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))) ) ),
file('theBenchmark.p',fact_172_add__right__mono) ).
fof(fact_173_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_173_add__le__cancel__left) ).
fof(fact_174_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_174_add__le__cancel__right) ).
fof(fact_175_add__less__imp__less__left,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [C,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),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),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_175_add__less__imp__less__left) ).
fof(fact_176_add__less__imp__less__right,axiom,
! [X_a] :
( ordere236663937imp_le(X_a)
=> ! [A_2,C,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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) ) ),
file('theBenchmark.p',fact_176_add__less__imp__less__right) ).
fof(fact_177_add__strict__mono,axiom,
! [X_a] :
( ordere223160158up_add(X_a)
=> ! [C,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),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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
file('theBenchmark.p',fact_177_add__strict__mono) ).
fof(fact_178_add__strict__left__mono,axiom,
! [X_a] :
( ordere223160158up_add(X_a)
=> ! [C,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),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) ) ),
file('theBenchmark.p',fact_178_add__strict__left__mono) ).
fof(fact_179_add__strict__right__mono,axiom,
! [X_a] :
( ordere223160158up_add(X_a)
=> ! [C,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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))) ) ),
file('theBenchmark.p',fact_179_add__strict__right__mono) ).
fof(fact_180_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_180_add__less__cancel__left) ).
fof(fact_181_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_181_add__less__cancel__right) ).
fof(fact_182_le__funI,axiom,
! [X_a,X_b] :
( ord(X_b)
=> ! [F,G] :
( ! [X_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_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)) ) ),
file('theBenchmark.p',fact_182_le__funI) ).
fof(fact_183_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_2,Y_3] :
( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_3),X_2))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_3)),hAPP(X_b,X_a,F,X_2))) )
=> 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_183_xt6) ).
fof(fact_184_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_2,Y_3] :
( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_3),X_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_3)),hAPP(X_b,X_a,F,X_2))) )
=> 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_184_xt4) ).
fof(fact_185_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_2,Y_3] :
( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_3))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_3))) )
=> 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_185_order__le__less__subst1) ).
fof(fact_186_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_2,Y_3] :
( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_3))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_3))) )
=> 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_186_order__less__le__subst1) ).
fof(fact_187_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_2,Y_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_3))
=> 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,F,Y_3))) )
=> 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_187_order__le__less__subst2) ).
fof(fact_188_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_188_equalityI) ).
fof(fact_189_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_189_subsetD) ).
fof(fact_190_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_190_psubset__eq) ).
fof(fact_191_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_191_subset__iff__psubset__eq) ).
fof(fact_192_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_192_psubset__imp__subset) ).
fof(fact_193_psubset__subset__trans,axiom,
! [X_a,C_1,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_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),C_1)) ) ),
file('theBenchmark.p',fact_193_psubset__subset__trans) ).
fof(fact_194_subset__psubset__trans,axiom,
! [X_a,C_1,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_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),C_1)) ) ),
file('theBenchmark.p',fact_194_subset__psubset__trans) ).
fof(fact_195_rev__predicate2D,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(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_1),Y_2)) ) ),
file('theBenchmark.p',fact_195_rev__predicate2D) ).
fof(fact_196_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_196_equalityE) ).
fof(fact_197_predicate2D,axiom,
! [X_a,X_b,X_1,Y_2,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_1),Y_2))
=> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_2)) ) ),
file('theBenchmark.p',fact_197_predicate2D) ).
fof(fact_198_subset__trans,axiom,
! [X_a,C_1,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_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_1)) ) ),
file('theBenchmark.p',fact_198_subset__trans) ).
fof(fact_199_set__mp,axiom,
! [X_a,X_1,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_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)) ) ),
file('theBenchmark.p',fact_199_set__mp) ).
fof(fact_200_set__rev__mp,axiom,
! [X_a,B,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),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_1),B)) ) ),
file('theBenchmark.p',fact_200_set__rev__mp) ).
fof(fact_201_predicate1D,axiom,
! [X_a,X_1,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_1))
=> hBOOL(hAPP(X_a,bool,Q_1,X_1)) ) ),
file('theBenchmark.p',fact_201_predicate1D) ).
fof(fact_202_in__mono,axiom,
! [X_a,X_1,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_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)) ) ),
file('theBenchmark.p',fact_202_in__mono) ).
fof(fact_203_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_203_equalityD2) ).
fof(fact_204_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_204_equalityD1) ).
fof(fact_205_rev__predicate1D,axiom,
! [X_a,Q_1,Pa,X_1] :
( hBOOL(hAPP(X_a,bool,Pa,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))
=> hBOOL(hAPP(X_a,bool,Q_1,X_1)) ) ),
file('theBenchmark.p',fact_205_rev__predicate1D) ).
fof(fact_206_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_206_set__eq__subset) ).
fof(fact_207_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_207_subset__refl) ).
fof(fact_208_pred__subset__eq,axiom,
! [X_a,R_1,S_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,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_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)),S_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)),R_1),S_1)) ),
file('theBenchmark.p',fact_208_pred__subset__eq) ).
fof(fact_209_predicate2I,axiom,
! [X_b,X_a,Q_1,Pa] :
( ! [X_2,Y_3] :
( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_2),Y_3))
=> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_3)) )
=> 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_209_predicate2I) ).
fof(fact_210_Pi__mono,axiom,
! [X_b,X_a,B,C_1,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))
=> 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_2)),hAPP(X_a,fun(X_b,bool),C_1,X_2))) )
=> 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_1))) ),
file('theBenchmark.p',fact_210_Pi__mono) ).
fof(fact_211_subsetI,axiom,
! [X_a,B,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))
=> 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)) ),
file('theBenchmark.p',fact_211_subsetI) ).
fof(fact_212_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_2,Y_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_3),X_2))
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_3)),hAPP(X_a,X_b,F,X_2))) )
=> 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_212_xt5) ).
fof(fact_213_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_2,Y_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_3),X_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_3)),hAPP(X_a,X_b,F,X_2))) )
=> 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_213_xt7) ).
fof(fact_214_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_214_psubsetD) ).
fof(fact_215_psubset__trans,axiom,
! [X_a,C_1,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_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),C_1)) ) ),
file('theBenchmark.p',fact_215_psubset__trans) ).
fof(fact_216_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_2,Y_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_3))
=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_3))) )
=> 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_216_order__less__le__subst2) ).
fof(fact_217_in__below,axiom,
! [X_1,Y_2,L_3,Aa,Ba] :
( ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_3),Aa),Ba)))
<=> ( ( ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Aa)
=> ( ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Aa)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3)) )
& ( ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa)
=> ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Y_2)),L_3))
| ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Ba) ) ) ) )
& ( ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Aa)
=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Ba)),L_3)) )
& ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2) ) ) ) ),
file('theBenchmark.p',fact_217_in__below) ).
fof(fact_218_add__leE,axiom,
! [M_3,K_1,N_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),M_3),K_1)),N_1))
=> ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) ) ),
file('theBenchmark.p',fact_218_add__leE) ).
fof(fact_219_add__leD1,axiom,
! [M_3,K_1,N_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),M_3),K_1)),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
file('theBenchmark.p',fact_219_add__leD1) ).
fof(fact_220_add__leD2,axiom,
! [M_3,K_1,N_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),M_3),K_1)),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) ),
file('theBenchmark.p',fact_220_add__leD2) ).
fof(fact_221_less__not__refl,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)),
file('theBenchmark.p',fact_221_less__not__refl) ).
fof(fact_222_nat__neq__iff,axiom,
! [M_2,Na] :
( M_2 != Na
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) ),
file('theBenchmark.p',fact_222_nat__neq__iff) ).
fof(fact_223_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_223_linorder__neqE__nat) ).
fof(fact_224_less__irrefl__nat,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)),
file('theBenchmark.p',fact_224_less__irrefl__nat) ).
fof(fact_225_less__not__refl2,axiom,
! [N_1,M_3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_3))
=> M_3 != N_1 ),
file('theBenchmark.p',fact_225_less__not__refl2) ).
fof(fact_226_less__not__refl3,axiom,
! [S,T_3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))
=> S != T_3 ),
file('theBenchmark.p',fact_226_less__not__refl3) ).
fof(fact_227_nat__less__cases,axiom,
! [Pa,M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2)) )
=> ( ( M_2 = Na
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2)) )
=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2)) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2)) ) ) ),
file('theBenchmark.p',fact_227_nat__less__cases) ).
fof(fact_228_nat__add__commute,axiom,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_3),
file('theBenchmark.p',fact_228_nat__add__commute) ).
fof(fact_229_nat__add__left__commute,axiom,
! [X,Y,Z_1] : 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_1)) = 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_1)),
file('theBenchmark.p',fact_229_nat__add__left__commute) ).
fof(fact_230_nat__add__assoc,axiom,
! [M_3,N_1,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1)),K_1) = 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_1),K_1)),
file('theBenchmark.p',fact_230_nat__add__assoc) ).
fof(fact_231_nat__add__left__cancel,axiom,
! [K,M_2,Na] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)
<=> M_2 = Na ),
file('theBenchmark.p',fact_231_nat__add__left__cancel) ).
fof(fact_232_nat__add__right__cancel,axiom,
! [M_2,K,Na] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K)
<=> M_2 = Na ),
file('theBenchmark.p',fact_232_nat__add__right__cancel) ).
fof(fact_233_le__refl,axiom,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1)),
file('theBenchmark.p',fact_233_le__refl) ).
fof(fact_234_nat__le__linear,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
file('theBenchmark.p',fact_234_nat__le__linear) ).
fof(fact_235_eq__imp__le,axiom,
! [M_3,N_1] :
( M_3 = N_1
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
file('theBenchmark.p',fact_235_eq__imp__le) ).
fof(fact_236_le__trans,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K_1)) ) ),
file('theBenchmark.p',fact_236_le__trans) ).
fof(fact_237_le__antisym,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_3))
=> M_3 = N_1 ) ),
file('theBenchmark.p',fact_237_le__antisym) ).
fof(fact_238_below__Lin,axiom,
! [L_3,X_1,Y_2] :
( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_3),X_1),Y_2)),arrow_2064824852le_Lin)) ) ),
file('theBenchmark.p',fact_238_below__Lin) ).
fof(fact_239_inj__on__add__nat,axiom,
! [K,N_3] : 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_3)),
file('theBenchmark.p',fact_239_inj__on__add__nat) ).
fof(fact_240_not__add__less1,axiom,
! [I,J_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),J_2)),I)),
file('theBenchmark.p',fact_240_not__add__less1) ).
fof(fact_241_not__add__less2,axiom,
! [J_2,I] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),I)),
file('theBenchmark.p',fact_241_not__add__less2) ).
fof(fact_242_nat__add__left__cancel__less,axiom,
! [K,M_2,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_2)),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_2),Na)) ),
file('theBenchmark.p',fact_242_nat__add__left__cancel__less) ).
fof(fact_243_trans__less__add1,axiom,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M_3))) ),
file('theBenchmark.p',fact_243_trans__less__add1) ).
fof(fact_244_trans__less__add2,axiom,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),J_2))) ),
file('theBenchmark.p',fact_244_trans__less__add2) ).
fof(fact_245_add__less__mono1,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_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),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_1))) ),
file('theBenchmark.p',fact_245_add__less__mono1) ).
fof(fact_246_add__less__mono,axiom,
! [K_1,L_2,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_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),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_2))) ) ),
file('theBenchmark.p',fact_246_add__less__mono) ).
fof(fact_247_less__add__eq__less,axiom,
! [M_3,N_1,K_1,L_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_2))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),L_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ) ),
file('theBenchmark.p',fact_247_less__add__eq__less) ).
fof(fact_248_add__lessD1,axiom,
! [I,J_2,K_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),J_2)),K_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_1)) ),
file('theBenchmark.p',fact_248_add__lessD1) ).
fof(fact_249_nat__less__le,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
<=> ( M_2 != Na
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) ) ),
file('theBenchmark.p',fact_249_nat__less__le) ).
fof(fact_250_le__eq__less__or__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
<=> ( M_2 = Na
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) ),
file('theBenchmark.p',fact_250_le__eq__less__or__eq) ).
fof(fact_251_less__imp__le__nat,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
file('theBenchmark.p',fact_251_less__imp__le__nat) ).
fof(fact_252_le__neq__implies__less,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> ( M_3 != N_1
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ) ),
file('theBenchmark.p',fact_252_le__neq__implies__less) ).
fof(fact_253_less__or__eq__imp__le,axiom,
! [M_3,N_1] :
( ( M_3 = N_1
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
file('theBenchmark.p',fact_253_less__or__eq__imp__le) ).
fof(fact_254_le__add2,axiom,
! [N_1,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1))),
file('theBenchmark.p',fact_254_le__add2) ).
fof(fact_255_le__add1,axiom,
! [N_1,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_3))),
file('theBenchmark.p',fact_255_le__add1) ).
fof(fact_256_le__iff__add,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
<=> ? [K_2] : Na = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_2) ),
file('theBenchmark.p',fact_256_le__iff__add) ).
fof(fact_257_nat__add__left__cancel__le,axiom,
! [K,M_2,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_2)),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_2),Na)) ),
file('theBenchmark.p',fact_257_nat__add__left__cancel__le) ).
fof(fact_258_trans__le__add1,axiom,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M_3))) ),
file('theBenchmark.p',fact_258_trans__le__add1) ).
fof(fact_259_trans__le__add2,axiom,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),J_2))) ),
file('theBenchmark.p',fact_259_trans__le__add2) ).
fof(fact_260_add__le__mono1,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_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),I),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_1))) ),
file('theBenchmark.p',fact_260_add__le__mono1) ).
fof(fact_261_add__le__mono,axiom,
! [K_1,L_2,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),L_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),I),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_2))) ) ),
file('theBenchmark.p',fact_261_add__le__mono) ).
fof(fact_262_mono__nat__linear__lb,axiom,
! [M_2,K,F] :
( ! [M,N] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M)),hAPP(nat,nat,F,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),hAPP(nat,nat,F,M_2)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K)))) ),
file('theBenchmark.p',fact_262_mono__nat__linear__lb) ).
fof(fact_263_less__mono__imp__le__mono,axiom,
! [I_1,J_1,F] :
( ! [I_2,J] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1))) ) ),
file('theBenchmark.p',fact_263_less__mono__imp__le__mono) ).
fof(fact_264_termination__basic__simps_I3_J,axiom,
! [Z_1,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_1))) ),
file('theBenchmark.p',fact_264_termination__basic__simps_I3_J) ).
fof(fact_265_termination__basic__simps_I4_J,axiom,
! [Y,X,Z_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z_1))
=> 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_1))) ),
file('theBenchmark.p',fact_265_termination__basic__simps_I4_J) ).
fof(fact_266_termination__basic__simps_I2_J,axiom,
! [Y,X,Z_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1))
=> 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_1))) ),
file('theBenchmark.p',fact_266_termination__basic__simps_I2_J) ).
fof(fact_267_termination__basic__simps_I1_J,axiom,
! [Z_1,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_1))) ),
file('theBenchmark.p',fact_267_termination__basic__simps_I1_J) ).
fof(fact_268_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_268_termination__basic__simps_I5_J) ).
fof(fact_269_in__rel__def,axiom,
! [X_b,X_a,R_1,X_1,Y_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_1),X_1),Y_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),Y_2)),R_1)) ),
file('theBenchmark.p',fact_269_in__rel__def) ).
fof(fact_270_funcsetI,axiom,
! [X_b,X_a,F,B,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))
=> 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(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_1] : hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)),
file('theBenchmark.p',fact_271_linear__alt) ).
fof(fact_272_Pi__cong,axiom,
! [X_b,X_a,B,F,G,A_1] :
( ! [W] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W),A_1))
=> hAPP(X_a,X_b,F,W) = hAPP(X_a,X_b,G,W) )
=> ( 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_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_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))) ),
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__onI,axiom,
! [X_b,X_a,F,A_1] :
( ! [X_2,Y_3] :
( 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_3),A_1))
=> ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_3)
=> ti(X_a,X_2) = ti(X_a,Y_3) ) ) )
=> 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__onI) ).
fof(fact_276_inj__on__cong,axiom,
! [X_b,X_a,F,G,A_1] :
( ! [A_3] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1))
=> hAPP(X_a,X_b,F,A_3) = hAPP(X_a,X_b,G,A_3) )
=> ( 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_276_inj__on__cong) ).
fof(fact_277_finite__indi,axiom,
hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
file('theBenchmark.p',fact_277_finite__indi) ).
fof(fact_278_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_278_card__bij) ).
fof(fact_279_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_279_finite__Collect__subsets) ).
fof(fact_280_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_280_card__psubset) ).
fof(fact_281_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_281_psubset__card__mono) ).
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__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_283_finite__Collect__conjI) ).
fof(fact_284_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_284_finite__Collect__less__nat) ).
fof(fact_285_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_285_finite__Collect__le__nat) ).
fof(fact_286_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_286_finite) ).
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_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_288_card__UNIV__unit) ).
fof(fact_289_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_289_finite__Collect__disjI) ).
fof(fact_290_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_290_card__Collect__less__nat) ).
fof(fact_291_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_291_finite__subset) ).
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__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_293_finite__UNIV) ).
fof(fact_294_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_294_finite__Prod__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__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_296_finite__option__UNIV) ).
fof(fact_297_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_297_finite__Collect__not) ).
fof(fact_298_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_298_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_299_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_299_finite__fun__UNIVD2) ).
fof(fact_300_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_300_card__seteq) ).
fof(fact_301_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_3] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) ) ),
file('theBenchmark.p',fact_301_ex__new__if__finite) ).
fof(fact_302_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_302_card__Plus) ).
fof(fact_303_folding__image__simple__idem_Osubset__idem,axiom,
! [X_b,X_a,B,A_1,F,Z,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),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_303_folding__image__simple__idem_Osubset__idem) ).
fof(fact_304_infinite__UNIV__nat,axiom,
~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
file('theBenchmark.p',fact_304_infinite__UNIV__nat) ).
fof(fact_305_folding__image__simple__idem_Oidem,axiom,
! [X_b,X_a,X_1,F,Z,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),G),Fa))
=> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_1),X_1) = ti(X_a,X_1) ),
file('theBenchmark.p',fact_305_folding__image__simple__idem_Oidem) ).
fof(fact_306_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_306_finite__Plus__iff) ).
fof(fact_307_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_307_finite__Plus) ).
fof(fact_308_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_308_finite__PlusD_I1_J) ).
fof(fact_309_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_309_finite__PlusD_I2_J) ).
fof(fact_310_folding__image__simple__idem_Oin__idem,axiom,
! [X_b,X_a,X_1,A_1,F,Z,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),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_1),A_1))
=> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_1)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1) ) ) ),
file('theBenchmark.p',fact_310_folding__image__simple__idem_Oin__idem) ).
fof(fact_311_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_311_UNIV__Plus__UNIV) ).
fof(fact_312_finite__M__bounded__by__nat,axiom,
! [Pa,I_1] : 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_1))))),
file('theBenchmark.p',fact_312_finite__M__bounded__by__nat) ).
fof(fact_313_finite__nat__set__iff__bounded__le,axiom,
! [N_3] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))
<=> ? [M] :
! [X_2] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M)) ) ),
file('theBenchmark.p',fact_313_finite__nat__set__iff__bounded__le) ).
fof(fact_314_finite__nat__set__iff__bounded,axiom,
! [N_3] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))
<=> ? [M] :
! [X_2] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M)) ) ),
file('theBenchmark.p',fact_314_finite__nat__set__iff__bounded) ).
fof(fact_315_finite__less__ub,axiom,
! [U,F] :
( ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,F,N)))
=> 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_315_finite__less__ub) ).
fof(fact_316_bounded__nat__set__is__finite,axiom,
! [Na,N_3] :
( ! [X_2] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Na)) )
=> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) ),
file('theBenchmark.p',fact_316_bounded__nat__set__is__finite) ).
fof(fact_317_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_317_card__Plus__conv__if) ).
fof(fact_318_less__zeroE,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))),
file('theBenchmark.p',fact_318_less__zeroE) ).
fof(fact_319_le0,axiom,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1)),
file('theBenchmark.p',fact_319_le0) ).
fof(fact_320_gr0I,axiom,
! [N_1] :
( N_1 != zero_zero(nat)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) ),
file('theBenchmark.p',fact_320_gr0I) ).
fof(fact_321_gr__implies__not0,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> N_1 != zero_zero(nat) ),
file('theBenchmark.p',fact_321_gr__implies__not0) ).
fof(fact_322_less__nat__zero__code,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))),
file('theBenchmark.p',fact_322_less__nat__zero__code) ).
fof(fact_323_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_323_neq0__conv) ).
fof(fact_324_not__less0,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))),
file('theBenchmark.p',fact_324_not__less0) ).
fof(fact_325_plus__nat_Oadd__0,axiom,
! [N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_1) = N_1,
file('theBenchmark.p',fact_325_plus__nat_Oadd__0) ).
fof(fact_326_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_326_Nat_Oadd__0__right) ).
fof(fact_327_add__is__0,axiom,
! [M_2,Na] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na) = zero_zero(nat)
<=> ( Na = zero_zero(nat)
& M_2 = zero_zero(nat) ) ),
file('theBenchmark.p',fact_327_add__is__0) ).
fof(fact_328_add__eq__self__zero,axiom,
! [M_3,N_1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1) = M_3
=> N_1 = zero_zero(nat) ),
file('theBenchmark.p',fact_328_add__eq__self__zero) ).
fof(fact_329_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_329_le__0__eq) ).
fof(fact_330_less__eq__nat_Osimps_I1_J,axiom,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1)),
file('theBenchmark.p',fact_330_less__eq__nat_Osimps_I1_J) ).
fof(fact_331_zero__reorient,axiom,
! [X_a] :
( zero(X_a)
=> ! [X_1] :
( zero_zero(X_a) = ti(X_a,X_1)
<=> ti(X_a,X_1) = zero_zero(X_a) ) ),
file('theBenchmark.p',fact_331_zero__reorient) ).
fof(fact_332_zero__neq__one,axiom,
! [X_a] :
( zero_neq_one(X_a)
=> zero_zero(X_a) != one_one(X_a) ),
file('theBenchmark.p',fact_332_zero__neq__one) ).
fof(fact_333_one__neq__zero,axiom,
! [X_a] :
( zero_neq_one(X_a)
=> one_one(X_a) != zero_zero(X_a) ),
file('theBenchmark.p',fact_333_one__neq__zero) ).
fof(fact_334_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_334_add_Ocomm__neutral) ).
fof(fact_335_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_335_add__0__right) ).
fof(fact_336_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_336_double__zero__sym) ).
fof(fact_337_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_337_add__0) ).
fof(fact_338_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_338_add__0__left) ).
fof(fact_339_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_339_add__nonpos__nonpos) ).
fof(fact_340_add__increasing2,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,A_2,C] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C))
=> ( 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))) ) ) ),
file('theBenchmark.p',fact_340_add__increasing2) ).
fof(fact_341_add__increasing,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,C,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))
=> 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))) ) ) ),
file('theBenchmark.p',fact_341_add__increasing) ).
fof(fact_342_add__nonneg__eq__0__iff,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [Y_2,X_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y_2))
=> ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_2) = zero_zero(X_a)
<=> ( ti(X_a,Y_2) = zero_zero(X_a)
& ti(X_a,X_1) = zero_zero(X_a) ) ) ) ) ),
file('theBenchmark.p',fact_342_add__nonneg__eq__0__iff) ).
fof(fact_343_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_343_add__nonneg__nonneg) ).
fof(fact_344_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_344_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_345_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_345_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_346_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_346_add__neg__neg) ).
fof(fact_347_pos__add__strict,axiom,
! [X_a] :
( linordered_semidom(X_a)
=> ! [B_1,C,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))
=> 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))) ) ) ),
file('theBenchmark.p',fact_347_pos__add__strict) ).
fof(fact_348_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_348_add__pos__pos) ).
fof(fact_349_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_349_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_350_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_350_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_351_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_351_zero__le__one) ).
fof(fact_352_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_352_not__one__le__zero) ).
fof(fact_353_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_353_zero__less__one) ).
fof(fact_354_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_354_not__one__less__zero) ).
fof(fact_355_add__gr__0,axiom,
! [M_2,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_2),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_2)) ) ),
file('theBenchmark.p',fact_355_add__gr__0) ).
fof(fact_356_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_356_card__infinite) ).
fof(fact_357_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_357_add__nonpos__neg) ).
fof(fact_358_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_358_add__neg__nonpos) ).
fof(fact_359_add__strict__increasing2,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,C,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))
=> 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))) ) ) ),
file('theBenchmark.p',fact_359_add__strict__increasing2) ).
fof(fact_360_add__strict__increasing,axiom,
! [X_a] :
( ordere216010020id_add(X_a)
=> ! [B_1,C,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))
=> 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))) ) ) ),
file('theBenchmark.p',fact_360_add__strict__increasing) ).
fof(fact_361_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_361_add__nonneg__pos) ).
fof(fact_362_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_362_add__pos__nonneg) ).
fof(fact_363_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_363_zero__less__two) ).
fof(fact_364_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_364_card__ge__0__finite) ).
fof(fact_365_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_365_finite__UNIV__card__ge__0) ).
fof(fact_366_ex__least__nat__less,axiom,
! [Na,Pa] :
( ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,Pa,Na))
=> ? [K_2] :
( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),one_one(nat))))
& ! [I_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_2))
=> ~ hBOOL(hAPP(nat,bool,Pa,I_2)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),Na)) ) ) ),
file('theBenchmark.p',fact_366_ex__least__nat__less) ).
fof(fact_367_card_Oneutral,axiom,
! [X_a,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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))
=> 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_367_card_Oneutral) ).
fof(fact_368_ex__least__nat__le,axiom,
! [Na,Pa] :
( ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,Pa,Na))
=> ? [K_2] :
( hBOOL(hAPP(nat,bool,Pa,K_2))
& ! [I_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_2))
=> ~ hBOOL(hAPP(nat,bool,Pa,I_2)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na)) ) ) ),
file('theBenchmark.p',fact_368_ex__least__nat__le) ).
fof(fact_369_less__imp__add__positive,axiom,
! [I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> ? [K_2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2) = J_2
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2)) ) ),
file('theBenchmark.p',fact_369_less__imp__add__positive) ).
fof(fact_370_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_370_even__less__0__iff) ).
fof(fact_371_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_371_double__eq__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_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_373_add__0__iff) ).
fof(fact_374_lessI,axiom,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,N_1))),
file('theBenchmark.p',fact_374_lessI) ).
fof(fact_375_Suc__mono,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),hAPP(nat,nat,suc,N_1))) ),
file('theBenchmark.p',fact_375_Suc__mono) ).
fof(fact_376_zero__less__Suc,axiom,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))),
file('theBenchmark.p',fact_376_zero__less__Suc) ).
fof(fact_377_Suc__n__not__le__n,axiom,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1)),
file('theBenchmark.p',fact_377_Suc__n__not__le__n) ).
fof(fact_378_not__less__eq__eq,axiom,
! [M_2,Na] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_2)) ),
file('theBenchmark.p',fact_378_not__less__eq__eq) ).
fof(fact_379_le__Suc__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,Na)))
<=> ( M_2 = hAPP(nat,nat,suc,Na)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) ) ),
file('theBenchmark.p',fact_379_le__Suc__eq) ).
fof(fact_380_Suc__le__mono,axiom,
! [Na,M_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_2)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_2)) ),
file('theBenchmark.p',fact_380_Suc__le__mono) ).
fof(fact_381_le__SucI,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,N_1))) ),
file('theBenchmark.p',fact_381_le__SucI) ).
fof(fact_382_le__SucE,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,N_1)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> M_3 = hAPP(nat,nat,suc,N_1) ) ),
file('theBenchmark.p',fact_382_le__SucE) ).
fof(fact_383_Suc__leD,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
file('theBenchmark.p',fact_383_Suc__leD) ).
fof(fact_384_Suc__inject,axiom,
! [X,Y] :
( hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y)
=> X = Y ),
file('theBenchmark.p',fact_384_Suc__inject) ).
fof(fact_385_nat_Oinject,axiom,
! [Nat_4,Nat_3] :
( hAPP(nat,nat,suc,Nat_4) = hAPP(nat,nat,suc,Nat_3)
<=> Nat_4 = Nat_3 ),
file('theBenchmark.p',fact_385_nat_Oinject) ).
fof(fact_386_Suc__n__not__n,axiom,
! [N_1] : hAPP(nat,nat,suc,N_1) != N_1,
file('theBenchmark.p',fact_386_Suc__n__not__n) ).
fof(fact_387_n__not__Suc__n,axiom,
! [N_1] : N_1 != hAPP(nat,nat,suc,N_1),
file('theBenchmark.p',fact_387_n__not__Suc__n) ).
fof(fact_388_add__Suc__shift,axiom,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,suc,N_1)),
file('theBenchmark.p',fact_388_add__Suc__shift) ).
fof(fact_389_add__Suc,axiom,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1)),
file('theBenchmark.p',fact_389_add__Suc) ).
fof(fact_390_add__Suc__right,axiom,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1)),
file('theBenchmark.p',fact_390_add__Suc__right) ).
fof(fact_391_not__less__eq,axiom,
! [M_2,Na] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2))) ),
file('theBenchmark.p',fact_391_not__less__eq) ).
fof(fact_392_less__Suc__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na)))
<=> ( M_2 = Na
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) ),
file('theBenchmark.p',fact_392_less__Suc__eq) ).
fof(fact_393_Suc__less__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_2)),hAPP(nat,nat,suc,Na)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ),
file('theBenchmark.p',fact_393_Suc__less__eq) ).
fof(fact_394_not__less__less__Suc__eq,axiom,
! [Na,M_2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2)))
<=> Na = M_2 ) ),
file('theBenchmark.p',fact_394_not__less__less__Suc__eq) ).
fof(fact_395_less__antisym,axiom,
! [N_1,M_3] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_3))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_3)))
=> M_3 = N_1 ) ),
file('theBenchmark.p',fact_395_less__antisym) ).
fof(fact_396_less__SucI,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N_1))) ),
file('theBenchmark.p',fact_396_less__SucI) ).
fof(fact_397_Suc__lessI,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> ( hAPP(nat,nat,suc,M_3) != N_1
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),N_1)) ) ),
file('theBenchmark.p',fact_397_Suc__lessI) ).
fof(fact_398_less__trans__Suc,axiom,
! [K_1,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K_1)) ) ),
file('theBenchmark.p',fact_398_less__trans__Suc) ).
fof(fact_399_less__SucE,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N_1)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> M_3 = N_1 ) ),
file('theBenchmark.p',fact_399_less__SucE) ).
fof(fact_400_Suc__lessD,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ),
file('theBenchmark.p',fact_400_Suc__lessD) ).
fof(fact_401_Suc__less__SucD,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),hAPP(nat,nat,suc,N_1)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ),
file('theBenchmark.p',fact_401_Suc__less__SucD) ).
fof(fact_402_One__nat__def,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('theBenchmark.p',fact_402_One__nat__def) ).
fof(fact_403_Suc__le__lessD,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ),
file('theBenchmark.p',fact_403_Suc__le__lessD) ).
fof(fact_404_le__less__Suc__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2)))
<=> Na = M_2 ) ),
file('theBenchmark.p',fact_404_le__less__Suc__eq) ).
fof(fact_405_Suc__leI,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N_1)) ),
file('theBenchmark.p',fact_405_Suc__leI) ).
fof(fact_406_le__imp__less__Suc,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N_1))) ),
file('theBenchmark.p',fact_406_le__imp__less__Suc) ).
fof(fact_407_Suc__le__eq,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),Na))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ),
file('theBenchmark.p',fact_407_Suc__le__eq) ).
fof(fact_408_less__Suc__eq__le,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) ),
file('theBenchmark.p',fact_408_less__Suc__eq__le) ).
fof(fact_409_less__eq__Suc__le,axiom,
! [Na,M_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_2)) ),
file('theBenchmark.p',fact_409_less__eq__Suc__le) ).
fof(fact_410_less__iff__Suc__add,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
<=> ? [K_2] : Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_2)) ),
file('theBenchmark.p',fact_410_less__iff__Suc__add) ).
fof(fact_411_less__add__Suc2,axiom,
! [I,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),I)))),
file('theBenchmark.p',fact_411_less__add__Suc2) ).
fof(fact_412_less__add__Suc1,axiom,
! [I,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M_3)))),
file('theBenchmark.p',fact_412_less__add__Suc1) ).
fof(fact_413_one__is__add,axiom,
! [M_2,Na] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na)
<=> ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
& M_2 = zero_zero(nat) )
| ( Na = zero_zero(nat)
& M_2 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
file('theBenchmark.p',fact_413_one__is__add) ).
fof(fact_414_add__is__1,axiom,
! [M_2,Na] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
& M_2 = zero_zero(nat) )
| ( Na = zero_zero(nat)
& M_2 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
file('theBenchmark.p',fact_414_add__is__1) ).
fof(fact_415_gr0__conv__Suc,axiom,
! [Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
<=> ? [M] : Na = hAPP(nat,nat,suc,M) ),
file('theBenchmark.p',fact_415_gr0__conv__Suc) ).
fof(fact_416_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_416_less__Suc0) ).
fof(fact_417_less__Suc__eq__0__disj,axiom,
! [M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na)))
<=> ( ? [J] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),Na))
& M_2 = hAPP(nat,nat,suc,J) )
| M_2 = zero_zero(nat) ) ),
file('theBenchmark.p',fact_417_less__Suc__eq__0__disj) ).
fof(fact_418_inj__Suc,axiom,
! [N_3] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),N_3)),
file('theBenchmark.p',fact_418_inj__Suc) ).
fof(fact_419_Suc__neq__Zero,axiom,
! [M_3] : hAPP(nat,nat,suc,M_3) != zero_zero(nat),
file('theBenchmark.p',fact_419_Suc__neq__Zero) ).
fof(fact_420_Zero__neq__Suc,axiom,
! [M_3] : zero_zero(nat) != hAPP(nat,nat,suc,M_3),
file('theBenchmark.p',fact_420_Zero__neq__Suc) ).
fof(fact_421_nat_Osimps_I3_J,axiom,
! [Nat_2] : hAPP(nat,nat,suc,Nat_2) != zero_zero(nat),
file('theBenchmark.p',fact_421_nat_Osimps_I3_J) ).
fof(fact_422_Suc__not__Zero,axiom,
! [M_3] : hAPP(nat,nat,suc,M_3) != zero_zero(nat),
file('theBenchmark.p',fact_422_Suc__not__Zero) ).
fof(fact_423_nat_Osimps_I2_J,axiom,
! [Nat_1] : zero_zero(nat) != hAPP(nat,nat,suc,Nat_1),
file('theBenchmark.p',fact_423_nat_Osimps_I2_J) ).
fof(fact_424_Zero__not__Suc,axiom,
! [M_3] : zero_zero(nat) != hAPP(nat,nat,suc,M_3),
file('theBenchmark.p',fact_424_Zero__not__Suc) ).
fof(fact_425_less__eq__Suc__le__raw,axiom,
! [X_2] : hAPP(nat,fun(nat,bool),ord_less(nat),X_2) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2)),
file('theBenchmark.p',fact_425_less__eq__Suc__le__raw) ).
fof(fact_426_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_426_card__Collect__le__nat) ).
fof(fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_2) ),
file('theBenchmark.p',fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,C,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),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),D)) ),
file('theBenchmark.p',fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,C,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),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)),D) ),
file('theBenchmark.p',fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,B_1,C] : 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) = 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)) ),
file('theBenchmark.p',fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,B_1,C] : 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) = 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)),B_1) ),
file('theBenchmark.p',fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X_a] :
( comm_semiring_1(X_a)
=> ! [A_2,B_1,C,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),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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)) ),
file('theBenchmark.p',fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_433_card__less__Suc,axiom,
! [I_1,M_4] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_4))
=> 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_4))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))) = 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_4))),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_1))))) ),
file('theBenchmark.p',fact_433_card__less__Suc) ).
fof(fact_434_card__less,axiom,
! [I_1,M_4] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_4))
=> 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_4))),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_1))))) != zero_zero(nat) ),
file('theBenchmark.p',fact_434_card__less) ).
fof(fact_435_card__less__Suc2,axiom,
! [I_1,M_4] :
( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_4))
=> 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_4))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))) = 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_4))),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_1))))) ),
file('theBenchmark.p',fact_435_card__less__Suc2) ).
fof(fact_436_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_436_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_437_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_437_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_438_inc__induct,axiom,
! [Pa,I_1,J_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1))
=> ( hBOOL(hAPP(nat,bool,Pa,J_1))
=> ( ! [I_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))
=> ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I_2)))
=> hBOOL(hAPP(nat,bool,Pa,I_2)) ) )
=> hBOOL(hAPP(nat,bool,Pa,I_1)) ) ) ),
file('theBenchmark.p',fact_438_inc__induct) ).
fof(fact_439_less__imp__Suc__add,axiom,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
=> ? [K_2] : N_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_2)) ),
file('theBenchmark.p',fact_439_less__imp__Suc__add) ).
fof(fact_440_gr0__implies__Suc,axiom,
! [N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))
=> ? [M] : N_1 = hAPP(nat,nat,suc,M) ),
file('theBenchmark.p',fact_440_gr0__implies__Suc) ).
fof(fact_441_lift__Suc__mono__le,axiom,
! [X_a] :
( order(X_a)
=> ! [Na,N_2,F] :
( ! [N] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_2))
=> 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_2))) ) ) ),
file('theBenchmark.p',fact_441_lift__Suc__mono__le) ).
fof(fact_442_lift__Suc__mono__less,axiom,
! [X_a] :
( order(X_a)
=> ! [Na,N_2,F] :
( ! [N] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),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,N_2))) ) ) ),
file('theBenchmark.p',fact_442_lift__Suc__mono__less) ).
fof(fact_443_lift__Suc__mono__less__iff,axiom,
! [X_a] :
( order(X_a)
=> ! [Na,M_2,F] :
( ! [N] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N))))
=> ( 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_2)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2)) ) ) ),
file('theBenchmark.p',fact_443_lift__Suc__mono__less__iff) ).
fof(fact_444_Suc__eq__plus1__left,axiom,
! [N_1] : hAPP(nat,nat,suc,N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1),
file('theBenchmark.p',fact_444_Suc__eq__plus1__left) ).
fof(fact_445_Suc__eq__plus1,axiom,
! [N_1] : hAPP(nat,nat,suc,N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)),
file('theBenchmark.p',fact_445_Suc__eq__plus1) ).
fof(fact_446_Suc__le__D,axiom,
! [N_1,M_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_1))
=> ? [M] : M_1 = hAPP(nat,nat,suc,M) ),
file('theBenchmark.p',fact_446_Suc__le__D) ).
fof(fact_447_lessE,axiom,
! [I,K_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_1))
=> ( K_1 != hAPP(nat,nat,suc,I)
=> ~ ! [J] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))
=> K_1 != hAPP(nat,nat,suc,J) ) ) ),
file('theBenchmark.p',fact_447_lessE) ).
fof(fact_448_Suc__lessE,axiom,
! [I,K_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K_1))
=> ~ ! [J] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))
=> K_1 != hAPP(nat,nat,suc,J) ) ),
file('theBenchmark.p',fact_448_Suc__lessE) ).
fof(fact_449_not0__implies__Suc,axiom,
! [N_1] :
( N_1 != zero_zero(nat)
=> ? [M] : N_1 = hAPP(nat,nat,suc,M) ),
file('theBenchmark.p',fact_449_not0__implies__Suc) ).
fof(fact_450_nat_Oexhaust,axiom,
! [Y] :
( Y != zero_zero(nat)
=> ~ ! [Nat] : Y != hAPP(nat,nat,suc,Nat) ),
file('theBenchmark.p',fact_450_nat_Oexhaust) ).
fof(fact_451_zero__induct,axiom,
! [Pa,K] :
( hBOOL(hAPP(nat,bool,Pa,K))
=> ( ! [N] :
( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N)))
=> hBOOL(hAPP(nat,bool,Pa,N)) )
=> hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ) ),
file('theBenchmark.p',fact_451_zero__induct) ).
fof(fact_452_nat__induct,axiom,
! [Na,Pa] :
( hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
=> ( ! [N] :
( hBOOL(hAPP(nat,bool,Pa,N))
=> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N))) )
=> hBOOL(hAPP(nat,bool,Pa,Na)) ) ),
file('theBenchmark.p',fact_452_nat__induct) ).
fof(fact_453_field__le__epsilon,axiom,
! [X_a] :
( linordered_field(X_a)
=> ! [X,Y] :
( ! [E] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E))
=> 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))) )
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
file('theBenchmark.p',fact_453_field__le__epsilon) ).
fof(fact_454_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_454_card_Oeq__fold__g) ).
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_surjh,axiom,
hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
file('theBenchmark.p',fact_456_surjh) ).
fof(fact_457_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_457_Ints__odd__less__0) ).
fof(fact_458_image__eqI,axiom,
! [X_a,X_b,A_1,Ba,F,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))
=> 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_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),H),top_top(fun(arrow_660593299e_indi,bool))))
=> hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),H),top_top(fun(arrow_660593299e_indi,bool))) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_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_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_462_atLeastLessThan__subset__iff) ).
fof(fact_463_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_463_funcset__image) ).
fof(fact_464_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_464_finite__surj__inj) ).
fof(fact_465_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_465_endo__inj__surj) ).
fof(fact_466_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_466_finite__UNIV__inj__surj) ).
fof(fact_467_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_467_finite__UNIV__surj__inj) ).
fof(fact_468_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_468_inj__image__subset__iff) ).
fof(fact_469_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_469_card__image__le) ).
fof(fact_470_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_470_eq__card__imp__inj__on) ).
fof(fact_471_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_471_inj__on__iff__eq__card) ).
fof(fact_472_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_472_pigeonhole) ).
fof(fact_473_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_473_Ints__double__eq__0__iff) ).
fof(fact_474_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_474_Ints__0) ).
fof(fact_475_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_475_Ints__1) ).
fof(fact_476_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_476_Ints__add) ).
fof(fact_477_inv__into__injective,axiom,
! [X_b,X_a,A_1,F,X_1,Y_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),X_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_2)
=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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),A_1)))
=> ( 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),A_1)))
=> ti(X_b,X_1) = ti(X_b,Y_2) ) ) ),
file('theBenchmark.p',fact_477_inv__into__injective) ).
fof(fact_478_inv__into__into,axiom,
! [X_a,X_b,X_1,F,A_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_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_1)),A_1)) ),
file('theBenchmark.p',fact_478_inv__into__into) ).
fof(fact_479_f__inv__into__f,axiom,
! [X_a,X_b,Y_2,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_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)))
=> 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_2)) = ti(X_a,Y_2) ),
file('theBenchmark.p',fact_479_f__inv__into__f) ).
fof(fact_480_rev__image__eqI,axiom,
! [X_b,X_a,Ba,F,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),A_1))
=> ( 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),A_1))) ) ),
file('theBenchmark.p',fact_480_rev__image__eqI) ).
fof(fact_481_imageI,axiom,
! [X_b,X_a,F,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),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(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_481_imageI) ).
fof(fact_482_image__iff,axiom,
! [X_a,X_b,Z,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),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_2] :
( ti(X_a,Z) = 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)) ) ),
file('theBenchmark.p',fact_482_image__iff) ).
fof(fact_483_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_483_image__image) ).
fof(fact_484_image__ident,axiom,
! [X_a,Y_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),combi(X_a)),Y_1) = ti(fun(X_a,bool),Y_1),
file('theBenchmark.p',fact_484_image__ident) ).
fof(fact_485_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_485_subset__image__iff) ).
fof(fact_486_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_486_image__mono) ).
fof(fact_487_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_487_atLeastLessThan__eq__iff) ).
fof(fact_488_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_488_atLeastLessThan__inj_I1_J) ).
fof(fact_489_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_489_atLeastLessThan__inj_I2_J) ).
fof(fact_490_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_490_range__composition) ).
fof(fact_491_range__eqI,axiom,
! [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))))) ),
file('theBenchmark.p',fact_491_range__eqI) ).
fof(fact_492_rangeI,axiom,
! [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),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))))),
file('theBenchmark.p',fact_492_rangeI) ).
fof(fact_493_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_493_finite__range__imageI) ).
fof(fact_494_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_494_subset__card__intvl__is__intvl) ).
fof(fact_495_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_495_inj__on__strict__subset) ).
fof(fact_496_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_496_image__surj__f__inv__f) ).
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___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___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___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__semidom,axiom,
linordered_semidom(nat),
file('theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
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___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_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__add,axiom,
monoid_add(nat),
file('theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
fof(arity_Nat_Onat___Orderings_Oorder,axiom,
order(nat),
file('theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
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___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___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_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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
file('theBenchmark.p',conj_0) ).
fof(f_1_1,plain,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OIIA_res]) ).
cnf(f_1_2,plain,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
inference(clausify,[status(thm)],[f_1_1]) ).
fof(f_2_1,plain,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OLin_res]) ).
cnf(f_2_2,plain,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OProf_res]) ).
cnf(f_3_2,plain,
ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Oabove_res]) ).
cnf(f_4_2,plain,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Obelow_res]) ).
cnf(f_5_2,plain,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Odictator_res]) ).
cnf(f_6_2,plain,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omkbot_res]) ).
cnf(f_7_2,plain,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omktop_res]) ).
cnf(f_8_2,plain,
ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Ounanimity_res]) ).
cnf(f_9_2,plain,
ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_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_10_2,plain,
! [U_2,U_1,U_0] : ti(fun(fun(U_2,U_1),fun(fun(U_0,U_2),fun(U_0,U_1))),combb(U_2,U_1,U_0)) = combb(U_2,U_1,U_0),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
ti(fun(fun(U_2,U_1),fun(fun(U_0,U_2),fun(U_0,U_1))),combb(U_2,U_1,U_0)) = combb(U_2,U_1,U_0),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_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_11_2,plain,
! [U_5,U_4,U_3] : ti(fun(fun(U_5,fun(U_4,U_3)),fun(U_4,fun(U_5,U_3))),combc(U_5,U_4,U_3)) = combc(U_5,U_4,U_3),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
ti(fun(fun(U_5,fun(U_4,U_3)),fun(U_4,fun(U_5,U_3))),combc(U_5,U_4,U_3)) = combc(U_5,U_4,U_3),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_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_12_2,plain,
! [U_6] : ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_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_13_2,plain,
! [U_8,U_7] : ti(fun(U_8,fun(U_7,U_8)),combk(U_8,U_7)) = combk(U_8,U_7),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
ti(fun(U_8,fun(U_7,U_8)),combk(U_8,U_7)) = combk(U_8,U_7),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_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_14_2,plain,
! [U_11,U_10,U_9] : ti(fun(fun(U_11,fun(U_10,U_9)),fun(fun(U_11,U_10),fun(U_11,U_9))),combs(U_11,U_10,U_9)) = combs(U_11,U_10,U_9),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
ti(fun(fun(U_11,fun(U_10,U_9)),fun(fun(U_11,U_10),fun(U_11,U_9))),combs(U_11,U_10,U_9)) = combs(U_11,U_10,U_9),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_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_15_2,plain,
! [U_12] : ti(fun(fun(U_12,bool),nat),finite_card(U_12)) = finite_card(U_12),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
ti(fun(fun(U_12,bool),nat),finite_card(U_12)) = finite_card(U_12),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_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_16_2,plain,
! [U_13] : ti(fun(fun(U_13,bool),bool),finite_finite_1(U_13)) = finite_finite_1(U_13),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
ti(fun(fun(U_13,bool),bool),finite_finite_1(U_13)) = finite_finite_1(U_13),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [X_a] : ti(fun(fun(nat,fun(nat,nat)),fun(fun(X_a,nat),fun(nat,fun(fun(X_a,bool),nat)))),finite_fold_image(nat,X_a)) = finite_fold_image(nat,X_a),
inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofold__image_res]) ).
fof(f_17_2,plain,
! [U_14] : ti(fun(fun(nat,fun(nat,nat)),fun(fun(U_14,nat),fun(nat,fun(fun(U_14,bool),nat)))),finite_fold_image(nat,U_14)) = finite_fold_image(nat,U_14),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
ti(fun(fun(nat,fun(nat,nat)),fun(fun(U_14,nat),fun(nat,fun(fun(U_14,bool),nat)))),finite_fold_image(nat,U_14)) = finite_fold_image(nat,U_14),
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(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_18_2,plain,
! [U_16,U_15] : ti(fun(fun(U_16,fun(U_16,U_16)),fun(U_16,fun(fun(U_15,U_16),fun(fun(fun(U_15,bool),U_16),bool)))),finite908156982e_idem(U_16,U_15)) = finite908156982e_idem(U_16,U_15),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
ti(fun(fun(U_16,fun(U_16,U_16)),fun(U_16,fun(fun(U_15,U_16),fun(fun(fun(U_15,bool),U_16),bool)))),finite908156982e_idem(U_16,U_15)) = finite908156982e_idem(U_16,U_15),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_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_19_2,plain,
! [U_18,U_17] : ti(fun(fun(product_prod(U_18,U_17),bool),fun(U_18,fun(U_17,bool))),in_rel(U_18,U_17)) = in_rel(U_18,U_17),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
ti(fun(fun(product_prod(U_18,U_17),bool),fun(U_18,fun(U_17,bool))),in_rel(U_18,U_17)) = in_rel(U_18,U_17),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_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_20_2,plain,
! [U_20,U_19] : ti(fun(fun(U_20,U_19),fun(fun(U_20,bool),bool)),inj_on(U_20,U_19)) = inj_on(U_20,U_19),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
ti(fun(fun(U_20,U_19),fun(fun(U_20,bool),bool)),inj_on(U_20,U_19)) = inj_on(U_20,U_19),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_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_21_2,plain,
! [U_22,U_21] : ti(fun(fun(U_22,bool),fun(fun(U_22,fun(U_21,bool)),fun(fun(U_22,U_21),bool))),pi(U_22,U_21)) = pi(U_22,U_21),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
ti(fun(fun(U_22,bool),fun(fun(U_22,fun(U_21,bool)),fun(fun(U_22,U_21),bool))),pi(U_22,U_21)) = pi(U_22,U_21),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_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_22_2,plain,
! [U_23] :
( ti(U_23,one_one(U_23)) = one_one(U_23)
| ~ one(U_23) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( ti(U_23,one_one(U_23)) = one_one(U_23)
| ~ one(U_23) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_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_23_2,plain,
! [U_24] :
( ti(fun(U_24,fun(U_24,U_24)),plus_plus(U_24)) = plus_plus(U_24)
| ~ monoid_add(U_24) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( ti(fun(U_24,fun(U_24,U_24)),plus_plus(U_24)) = plus_plus(U_24)
| ~ monoid_add(U_24) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_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_24_2,plain,
! [U_25] :
( ti(fun(U_25,fun(U_25,U_25)),plus_plus(U_25)) = plus_plus(U_25)
| ~ ab_semigroup_add(U_25) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( ti(fun(U_25,fun(U_25,U_25)),plus_plus(U_25)) = plus_plus(U_25)
| ~ ab_semigroup_add(U_25) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_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_25_2,plain,
! [U_26] :
( ti(fun(U_26,fun(U_26,U_26)),plus_plus(U_26)) = plus_plus(U_26)
| ~ cancel_semigroup_add(U_26) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( ti(fun(U_26,fun(U_26,U_26)),plus_plus(U_26)) = plus_plus(U_26)
| ~ cancel_semigroup_add(U_26) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_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_26_2,plain,
! [U_27] :
( ti(U_27,zero_zero(U_27)) = zero_zero(U_27)
| ~ zero(U_27) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( ti(U_27,zero_zero(U_27)) = zero_zero(U_27)
| ~ zero(U_27) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_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_27_2,plain,
! [U_28] : ti(U_28,undefined(U_28)) = undefined(U_28),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
ti(U_28,undefined(U_28)) = undefined(U_28),
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),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_28_2,plain,
! [U_30,U_29] : ti(fun(fun(U_30,bool),fun(fun(U_30,U_29),fun(U_29,U_30))),hilbert_inv_into(U_30,U_29)) = hilbert_inv_into(U_30,U_29),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
ti(fun(fun(U_30,bool),fun(fun(U_30,U_29),fun(U_29,U_30))),hilbert_inv_into(U_30,U_29)) = hilbert_inv_into(U_30,U_29),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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_29_2,plain,
! [U_31] : ti(fun(bool,fun(U_31,fun(U_31,U_31))),if(U_31)) = if(U_31),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
ti(fun(bool,fun(U_31,fun(U_31,U_31))),if(U_31)) = if(U_31),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_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_30_2,plain,
! [U_32] :
( ti(fun(U_32,bool),ring_1_Ints(U_32)) = ring_1_Ints(U_32)
| ~ ring_1(U_32) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( ti(fun(U_32,bool),ring_1_Ints(U_32)) = ring_1_Ints(U_32)
| ~ ring_1(U_32) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
ti(fun(nat,nat),suc) = suc,
inference(fof_nnf,[status(thm)],[tsy_c_Nat_OSuc_res]) ).
cnf(f_31_2,plain,
ti(fun(nat,nat),suc) = suc,
inference(clausify,[status(thm)],[f_31_1]) ).
fof(f_32_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_32_2,plain,
! [U_33] :
( ti(fun(U_33,fun(U_33,bool)),ord_less(U_33)) = ord_less(U_33)
| ~ ord(U_33) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( ti(fun(U_33,fun(U_33,bool)),ord_less(U_33)) = ord_less(U_33)
| ~ ord(U_33) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_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_33_2,plain,
! [U_34] :
( ti(fun(U_34,fun(U_34,bool)),ord_less_eq(U_34)) = ord_less_eq(U_34)
| ~ ord(U_34) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( ti(fun(U_34,fun(U_34,bool)),ord_less_eq(U_34)) = ord_less_eq(U_34)
| ~ ord(U_34) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_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_34_2,plain,
! [U_35] :
( ti(U_35,top_top(U_35)) = top_top(U_35)
| ~ top(U_35) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( ti(U_35,top_top(U_35)) = top_top(U_35)
| ~ top(U_35) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_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_35_2,plain,
! [U_37,U_36] : ti(fun(U_37,fun(U_36,product_prod(U_37,U_36))),product_Pair(U_37,U_36)) = product_Pair(U_37,U_36),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
ti(fun(U_37,fun(U_36,product_prod(U_37,U_36))),product_Pair(U_37,U_36)) = product_Pair(U_37,U_36),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_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_36_2,plain,
! [U_40,U_39,U_38] : ti(fun(fun(U_40,fun(U_39,U_38)),fun(product_prod(U_40,U_39),U_38)),product_prod_rec(U_40,U_39,U_38)) = product_prod_rec(U_40,U_39,U_38),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
ti(fun(fun(U_40,fun(U_39,U_38)),fun(product_prod(U_40,U_39),U_38)),product_prod_rec(U_40,U_39,U_38)) = product_prod_rec(U_40,U_39,U_38),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_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_37_2,plain,
! [U_41] :
( ti(fun(U_41,fun(U_41,fun(U_41,bool))),ord_atLeastLessThan(U_41)) = ord_atLeastLessThan(U_41)
| ~ linorder(U_41) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( ti(fun(U_41,fun(U_41,fun(U_41,bool))),ord_atLeastLessThan(U_41)) = ord_atLeastLessThan(U_41)
| ~ linorder(U_41) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_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_38_2,plain,
! [U_42] : ti(fun(fun(U_42,bool),fun(U_42,bool)),collect(U_42)) = collect(U_42),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
ti(fun(fun(U_42,bool),fun(U_42,bool)),collect(U_42)) = collect(U_42),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_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_39_2,plain,
! [U_44,U_43] : ti(fun(fun(U_44,U_43),fun(fun(U_44,bool),fun(U_43,bool))),image(U_44,U_43)) = image(U_44,U_43),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
ti(fun(fun(U_44,U_43),fun(fun(U_44,bool),fun(U_43,bool))),image(U_44,U_43)) = image(U_44,U_43),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_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_40_2,plain,
! [U_46,U_45] : ti(fun(fun(U_46,bool),fun(fun(U_45,bool),fun(sum_sum(U_46,U_45),bool))),sum_Plus(U_46,U_45)) = sum_Plus(U_46,U_45),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
ti(fun(fun(U_46,bool),fun(fun(U_45,bool),fun(sum_sum(U_46,U_45),bool))),sum_Plus(U_46,U_45)) = sum_Plus(U_46,U_45),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
ti(bool,fFalse) = fFalse,
inference(fof_nnf,[status(thm)],[tsy_c_fFalse_res]) ).
cnf(f_41_2,plain,
ti(bool,fFalse) = fFalse,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,plain,
ti(fun(bool,bool),fNot) = fNot,
inference(fof_nnf,[status(thm)],[tsy_c_fNot_res]) ).
cnf(f_42_2,plain,
ti(fun(bool,bool),fNot) = fNot,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,plain,
ti(bool,fTrue) = fTrue,
inference(fof_nnf,[status(thm)],[tsy_c_fTrue_res]) ).
cnf(f_43_2,plain,
ti(bool,fTrue) = fTrue,
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_44_1,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(fof_nnf,[status(thm)],[tsy_c_fconj_res]) ).
cnf(f_44_2,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(clausify,[status(thm)],[f_44_1]) ).
fof(f_45_1,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(fof_nnf,[status(thm)],[tsy_c_fdisj_res]) ).
cnf(f_45_2,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(clausify,[status(thm)],[f_45_1]) ).
fof(f_46_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_46_2,plain,
! [U_47] : ti(fun(U_47,fun(U_47,bool)),fequal(U_47)) = fequal(U_47),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
ti(fun(U_47,fun(U_47,bool)),fequal(U_47)) = fequal(U_47),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_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_47_2,plain,
! [U_51,U_50,U_49,U_48] : hAPP(U_51,U_50,ti(fun(U_51,U_50),U_49),U_48) = hAPP(U_51,U_50,U_49,U_48),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
hAPP(U_51,U_50,ti(fun(U_51,U_50),U_49),U_48) = hAPP(U_51,U_50,U_49,U_48),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_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_48_2,plain,
! [U_55,U_54,U_53,U_52] : hAPP(U_55,U_54,U_53,ti(U_55,U_52)) = hAPP(U_55,U_54,U_53,U_52),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
hAPP(U_55,U_54,U_53,ti(U_55,U_52)) = hAPP(U_55,U_54,U_53,U_52),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_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_49_2,plain,
! [U_59,U_58,U_57,U_56] : ti(U_59,hAPP(U_58,U_59,U_57,U_56)) = hAPP(U_58,U_59,U_57,U_56),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
ti(U_59,hAPP(U_58,U_59,U_57,U_56)) = hAPP(U_58,U_59,U_57,U_56),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_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_50_2,plain,
! [U_60] :
( ( hBOOL(ti(bool,U_60))
| ~ hBOOL(U_60) )
& ( hBOOL(U_60)
| ~ hBOOL(ti(bool,U_60)) ) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
( ! [U_62] :
( hBOOL(ti(bool,U_62))
| ~ hBOOL(U_62) )
& ! [U_61] :
( hBOOL(U_61)
| ~ hBOOL(ti(bool,U_61)) ) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
( hBOOL(U_61)
| ~ hBOOL(ti(bool,U_61)) ),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_5,plain,
( hBOOL(ti(bool,U_62))
| ~ hBOOL(U_62) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_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_51_2,plain,
! [U_63] : ti(fun(U_63,fun(fun(U_63,bool),bool)),member(U_63)) = member(U_63),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
ti(fun(U_63,fun(fun(U_63,bool),bool)),member(U_63)) = member(U_63),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f,
inference(fof_nnf,[status(thm)],[tsy_v_F_res]) ).
cnf(f_52_2,plain,
ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f,
inference(clausify,[status(thm)],[f_52_1]) ).
fof(f_53_1,plain,
ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
inference(fof_nnf,[status(thm)],[tsy_v_Lab_____res]) ).
cnf(f_53_2,plain,
ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
inference(clausify,[status(thm)],[f_53_1]) ).
fof(f_54_1,plain,
ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
inference(fof_nnf,[status(thm)],[tsy_v_Lba_____res]) ).
cnf(f_54_2,plain,
ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
inference(clausify,[status(thm)],[f_54_1]) ).
fof(f_55_1,plain,
ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p,
inference(fof_nnf,[status(thm)],[tsy_v_P_____res]) ).
cnf(f_55_2,plain,
ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p,
inference(clausify,[status(thm)],[f_55_1]) ).
fof(f_56_1,plain,
ti(arrow_490897120le_alt,a) = a,
inference(fof_nnf,[status(thm)],[tsy_v_a_____res]) ).
cnf(f_56_2,plain,
ti(arrow_490897120le_alt,a) = a,
inference(clausify,[status(thm)],[f_56_1]) ).
fof(f_57_1,plain,
ti(arrow_490897120le_alt,b) = b,
inference(fof_nnf,[status(thm)],[tsy_v_b_____res]) ).
cnf(f_57_2,plain,
ti(arrow_490897120le_alt,b) = b,
inference(clausify,[status(thm)],[f_57_1]) ).
fof(f_58_1,plain,
ti(arrow_490897120le_alt,c) = c,
inference(fof_nnf,[status(thm)],[tsy_v_c_____res]) ).
cnf(f_58_2,plain,
ti(arrow_490897120le_alt,c) = c,
inference(clausify,[status(thm)],[f_58_1]) ).
fof(f_59_1,plain,
ti(arrow_490897120le_alt,d) = d,
inference(fof_nnf,[status(thm)],[tsy_v_d_____res]) ).
cnf(f_59_2,plain,
ti(arrow_490897120le_alt,d) = d,
inference(clausify,[status(thm)],[f_59_1]) ).
fof(f_60_1,plain,
ti(arrow_490897120le_alt,e) = e,
inference(fof_nnf,[status(thm)],[tsy_v_e_____res]) ).
cnf(f_60_2,plain,
ti(arrow_490897120le_alt,e) = e,
inference(clausify,[status(thm)],[f_60_1]) ).
fof(f_61_1,plain,
ti(fun(arrow_660593299e_indi,nat),h) = h,
inference(fof_nnf,[status(thm)],[tsy_v_h_____res]) ).
cnf(f_61_2,plain,
ti(fun(arrow_660593299e_indi,nat),h) = h,
inference(clausify,[status(thm)],[f_61_1]) ).
fof(f_62_1,plain,
ti(nat,n) = n,
inference(fof_nnf,[status(thm)],[tsy_v_n_____res]) ).
cnf(f_62_2,plain,
ti(nat,n) = n,
inference(clausify,[status(thm)],[f_62_1]) ).
fof(f_63_1,plain,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
inference(fof_nnf,[status(thm)],[fact_0_assms_I3_J]) ).
cnf(f_63_2,plain,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
inference(clausify,[status(thm)],[f_63_1]) ).
fof(f_64_1,plain,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)),
inference(fof_nnf,[status(thm)],[fact_1_u]) ).
cnf(f_64_2,plain,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)),
inference(clausify,[status(thm)],[f_64_1]) ).
fof(f_65_1,plain,
c != d,
inference(fof_nnf,[status(thm)],[fact_2__096c_A_126_061_Ad_096]) ).
cnf(f_65_2,plain,
c != d,
inference(clausify,[status(thm)],[f_65_1]) ).
fof(f_66_1,plain,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
inference(fof_nnf,[status(thm)],[fact_3__096P_A_058_AProf_096]) ).
cnf(f_66_2,plain,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
inference(clausify,[status(thm)],[f_66_1]) ).
fof(f_67_1,plain,
! [X_1,Y_2,L_3,Z] :
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_3),Z)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
& ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Z) )
| ( ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Y_2)
& ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Z) )
| ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Z) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Z) )
& ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2)
| ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Z) )
& ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Z) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_3),Z))) ) ),
inference(fof_nnf,[status(thm)],[fact_4_in__mkbot]) ).
fof(f_67_2,plain,
! [U_67,U_66,U_65,U_64] :
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_67),U_66)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_65),U_64)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_67),U_66)),U_65))
& ti(arrow_490897120le_alt,U_67) != ti(arrow_490897120le_alt,U_64) )
| ( ti(arrow_490897120le_alt,U_67) = ti(arrow_490897120le_alt,U_66)
& ti(arrow_490897120le_alt,U_67) = ti(arrow_490897120le_alt,U_64) )
| ti(arrow_490897120le_alt,U_66) = ti(arrow_490897120le_alt,U_64) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_67),U_66)),U_65))
| ti(arrow_490897120le_alt,U_67) = ti(arrow_490897120le_alt,U_64) )
& ( ti(arrow_490897120le_alt,U_67) != ti(arrow_490897120le_alt,U_66)
| ti(arrow_490897120le_alt,U_67) != ti(arrow_490897120le_alt,U_64) )
& ti(arrow_490897120le_alt,U_66) != ti(arrow_490897120le_alt,U_64) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_67),U_66)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_65),U_64))) ) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ! [U_75,U_73,U_71,U_69] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_75),U_73)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_71),U_69)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_75),U_73)),U_71))
& ti(arrow_490897120le_alt,U_75) != ti(arrow_490897120le_alt,U_69) )
| ( ti(arrow_490897120le_alt,U_75) = ti(arrow_490897120le_alt,U_73)
& ti(arrow_490897120le_alt,U_75) = ti(arrow_490897120le_alt,U_69) )
| ti(arrow_490897120le_alt,U_73) = ti(arrow_490897120le_alt,U_69) )
& ! [U_74,U_72,U_70,U_68] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_74),U_72)),U_70))
| ti(arrow_490897120le_alt,U_74) = ti(arrow_490897120le_alt,U_68) )
& ( ti(arrow_490897120le_alt,U_74) != ti(arrow_490897120le_alt,U_72)
| ti(arrow_490897120le_alt,U_74) != ti(arrow_490897120le_alt,U_68) )
& ti(arrow_490897120le_alt,U_72) != ti(arrow_490897120le_alt,U_68) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_74),U_72)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_70),U_68))) ) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
cnf(f_67_4,plain,
( ti(arrow_490897120le_alt,U_72) != ti(arrow_490897120le_alt,U_68)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_74),U_72)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_70),U_68))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_5,plain,
( ti(arrow_490897120le_alt,U_74) != ti(arrow_490897120le_alt,U_72)
| ti(arrow_490897120le_alt,U_74) != ti(arrow_490897120le_alt,U_68)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_74),U_72)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_70),U_68))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_74),U_72)),U_70))
| ti(arrow_490897120le_alt,U_74) = ti(arrow_490897120le_alt,U_68)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_74),U_72)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_70),U_68))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_7,plain,
( ti(arrow_490897120le_alt,U_75) != ti(arrow_490897120le_alt,U_69)
| ti(arrow_490897120le_alt,U_75) = ti(arrow_490897120le_alt,U_69)
| ti(arrow_490897120le_alt,U_73) = ti(arrow_490897120le_alt,U_69)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_75),U_73)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_71),U_69))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_8,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_75),U_73)),U_71))
| ti(arrow_490897120le_alt,U_75) = ti(arrow_490897120le_alt,U_69)
| ti(arrow_490897120le_alt,U_73) = ti(arrow_490897120le_alt,U_69)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_75),U_73)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_71),U_69))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_9,plain,
( ti(arrow_490897120le_alt,U_75) != ti(arrow_490897120le_alt,U_69)
| ti(arrow_490897120le_alt,U_75) = ti(arrow_490897120le_alt,U_73)
| ti(arrow_490897120le_alt,U_73) = ti(arrow_490897120le_alt,U_69)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_75),U_73)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_71),U_69))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_10,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_75),U_73)),U_71))
| ti(arrow_490897120le_alt,U_75) = ti(arrow_490897120le_alt,U_73)
| ti(arrow_490897120le_alt,U_73) = ti(arrow_490897120le_alt,U_69)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_75),U_73)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_71),U_69))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [X_1,Y_2,L_3,Z] :
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_3),Z)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
& ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Z) )
| ( ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Y_2)
& ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Z) )
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Z) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
| ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Z) )
& ( ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2)
| ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Z) )
& ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Z) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_3),Z))) ) ),
inference(fof_nnf,[status(thm)],[fact_5_in__mktop]) ).
fof(f_68_2,plain,
! [U_79,U_78,U_77,U_76] :
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_79),U_78)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_77),U_76)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_79),U_78)),U_77))
& ti(arrow_490897120le_alt,U_78) != ti(arrow_490897120le_alt,U_76) )
| ( ti(arrow_490897120le_alt,U_79) = ti(arrow_490897120le_alt,U_78)
& ti(arrow_490897120le_alt,U_78) = ti(arrow_490897120le_alt,U_76) )
| ti(arrow_490897120le_alt,U_79) = ti(arrow_490897120le_alt,U_76) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_79),U_78)),U_77))
| ti(arrow_490897120le_alt,U_78) = ti(arrow_490897120le_alt,U_76) )
& ( ti(arrow_490897120le_alt,U_79) != ti(arrow_490897120le_alt,U_78)
| ti(arrow_490897120le_alt,U_78) != ti(arrow_490897120le_alt,U_76) )
& ti(arrow_490897120le_alt,U_79) != ti(arrow_490897120le_alt,U_76) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_79),U_78)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_77),U_76))) ) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
( ! [U_87,U_85,U_83,U_81] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_87),U_85)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_83),U_81)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_87),U_85)),U_83))
& ti(arrow_490897120le_alt,U_85) != ti(arrow_490897120le_alt,U_81) )
| ( ti(arrow_490897120le_alt,U_87) = ti(arrow_490897120le_alt,U_85)
& ti(arrow_490897120le_alt,U_85) = ti(arrow_490897120le_alt,U_81) )
| ti(arrow_490897120le_alt,U_87) = ti(arrow_490897120le_alt,U_81) )
& ! [U_86,U_84,U_82,U_80] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_86),U_84)),U_82))
| ti(arrow_490897120le_alt,U_84) = ti(arrow_490897120le_alt,U_80) )
& ( ti(arrow_490897120le_alt,U_86) != ti(arrow_490897120le_alt,U_84)
| ti(arrow_490897120le_alt,U_84) != ti(arrow_490897120le_alt,U_80) )
& ti(arrow_490897120le_alt,U_86) != ti(arrow_490897120le_alt,U_80) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_86),U_84)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_82),U_80))) ) ),
inference(miniscope,[status(thm)],[f_68_2]) ).
cnf(f_68_4,plain,
( ti(arrow_490897120le_alt,U_86) != ti(arrow_490897120le_alt,U_80)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_86),U_84)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_82),U_80))) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_5,plain,
( ti(arrow_490897120le_alt,U_86) != ti(arrow_490897120le_alt,U_84)
| ti(arrow_490897120le_alt,U_84) != ti(arrow_490897120le_alt,U_80)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_86),U_84)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_82),U_80))) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_86),U_84)),U_82))
| ti(arrow_490897120le_alt,U_84) = ti(arrow_490897120le_alt,U_80)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_86),U_84)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_82),U_80))) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_7,plain,
( ti(arrow_490897120le_alt,U_85) != ti(arrow_490897120le_alt,U_81)
| ti(arrow_490897120le_alt,U_85) = ti(arrow_490897120le_alt,U_81)
| ti(arrow_490897120le_alt,U_87) = ti(arrow_490897120le_alt,U_81)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_87),U_85)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_83),U_81))) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_8,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_87),U_85)),U_83))
| ti(arrow_490897120le_alt,U_85) = ti(arrow_490897120le_alt,U_81)
| ti(arrow_490897120le_alt,U_87) = ti(arrow_490897120le_alt,U_81)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_87),U_85)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_83),U_81))) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_9,plain,
( ti(arrow_490897120le_alt,U_85) != ti(arrow_490897120le_alt,U_81)
| ti(arrow_490897120le_alt,U_87) = ti(arrow_490897120le_alt,U_85)
| ti(arrow_490897120le_alt,U_87) = ti(arrow_490897120le_alt,U_81)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_87),U_85)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_83),U_81))) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_10,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_87),U_85)),U_83))
| ti(arrow_490897120le_alt,U_87) = ti(arrow_490897120le_alt,U_85)
| ti(arrow_490897120le_alt,U_87) = ti(arrow_490897120le_alt,U_81)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_87),U_85)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_83),U_81))) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
! [P_1,Pa,A_5,B_3,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa))) ) )
| ? [I_2] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,Ba) = ti(arrow_490897120le_alt,A_5)
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,B_3)
| ti(arrow_490897120le_alt,A_5) = ti(arrow_490897120le_alt,B_3)
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_6__C2_C]) ).
fof(f_69_2,plain,
! [U_94,U_93,U_92,U_91,U_90,U_89] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93))) ) )
| ? [U_88] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,U_88)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,U_88))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,U_88)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,U_88))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_94,U_93,U_92,U_91,U_90,U_89] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93))) ) )
| ? [U_96] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,U_96)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,U_96))) )
| ? [U_95] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,U_95)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,U_95))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
fof(f_69_4,plain,
! [U_94,U_93,U_92,U_91,U_90,U_89] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93))) ) )
| ? [U_96] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,U_96)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,U_96))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK1(U_94,U_93,U_92,U_91,U_90,U_89))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK1(U_94,U_93,U_92,U_91,U_90,U_89)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_95,sK1(U_94,U_93,U_92,U_91,U_90,U_89))],[f_69_3]) ).
fof(f_69_5,plain,
! [U_94,U_93,U_92,U_91,U_90,U_89] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK2(U_94,U_93,U_92,U_91,U_90,U_89))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK2(U_94,U_93,U_92,U_91,U_90,U_89)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK1(U_94,U_93,U_92,U_91,U_90,U_89))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK1(U_94,U_93,U_92,U_91,U_90,U_89)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_96,sK2(U_94,U_93,U_92,U_91,U_90,U_89))],[f_69_4]) ).
cnf(f_69_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK2(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK1(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK2(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK1(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK2(U_94,U_93,U_92,U_91,U_90,U_89))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK1(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK2(U_94,U_93,U_92,U_91,U_90,U_89))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK1(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK2(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK1(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK2(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK1(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_12,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK2(U_94,U_93,U_92,U_91,U_90,U_89))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK1(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_93,sK2(U_94,U_93,U_92,U_91,U_90,U_89))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_94,sK1(U_94,U_93,U_92,U_91,U_90,U_89))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_90),U_89)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_93)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_92),U_91)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_94)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_94),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_93),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_89) = ti(arrow_490897120le_alt,U_92)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_92) = ti(arrow_490897120le_alt,U_91)
| ti(arrow_490897120le_alt,U_90) = ti(arrow_490897120le_alt,U_89) ),
inference(clausify,[status(thm)],[f_69_5]) ).
fof(f_70_1,plain,
! [P_1,Pa,A_5,B_3,Aa,Ba] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
| ? [I_2] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,Ba) = ti(arrow_490897120le_alt,A_5)
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,B_3)
| ti(arrow_490897120le_alt,A_5) = ti(arrow_490897120le_alt,B_3)
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_7__C1_C]) ).
fof(f_70_2,plain,
! [U_103,U_102,U_101,U_100,U_99,U_98] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_103)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_102)))
| ? [U_97] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,U_97)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,U_97))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,U_97)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,U_97))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_103),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_102),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_98) = ti(arrow_490897120le_alt,U_101)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_101) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_98) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_103,U_102,U_101,U_100,U_99,U_98] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_103)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_102)))
| ? [U_105] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,U_105)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,U_105))) )
| ? [U_104] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,U_104)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,U_104))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_103),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_102),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_98) = ti(arrow_490897120le_alt,U_101)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_101) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_98) ),
inference(miniscope,[status(thm)],[f_70_2]) ).
fof(f_70_4,plain,
! [U_103,U_102,U_101,U_100,U_99,U_98] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_103)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_102)))
| ? [U_105] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,U_105)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,U_105))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,sK3(U_103,U_102,U_101,U_100,U_99,U_98))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,sK3(U_103,U_102,U_101,U_100,U_99,U_98)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_103),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_102),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_98) = ti(arrow_490897120le_alt,U_101)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_101) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_98) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_104,sK3(U_103,U_102,U_101,U_100,U_99,U_98))],[f_70_3]) ).
fof(f_70_5,plain,
! [U_103,U_102,U_101,U_100,U_99,U_98] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_103)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_102)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,sK4(U_103,U_102,U_101,U_100,U_99,U_98))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,sK4(U_103,U_102,U_101,U_100,U_99,U_98)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,sK3(U_103,U_102,U_101,U_100,U_99,U_98))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,sK3(U_103,U_102,U_101,U_100,U_99,U_98)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_103),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_102),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_98) = ti(arrow_490897120le_alt,U_101)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_101) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_98) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_105,sK4(U_103,U_102,U_101,U_100,U_99,U_98))],[f_70_4]) ).
cnf(f_70_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,sK4(U_103,U_102,U_101,U_100,U_99,U_98))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,sK3(U_103,U_102,U_101,U_100,U_99,U_98))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_103)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_102)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_103),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_102),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_98) = ti(arrow_490897120le_alt,U_101)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_101) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_98) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,sK4(U_103,U_102,U_101,U_100,U_99,U_98))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,sK3(U_103,U_102,U_101,U_100,U_99,U_98))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_103)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_102)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_103),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_102),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_98) = ti(arrow_490897120le_alt,U_101)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_101) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_98) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,sK4(U_103,U_102,U_101,U_100,U_99,U_98))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,sK3(U_103,U_102,U_101,U_100,U_99,U_98))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_103)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_102)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_103),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_102),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_98) = ti(arrow_490897120le_alt,U_101)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_101) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_98) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_102,sK4(U_103,U_102,U_101,U_100,U_99,U_98))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_103,sK3(U_103,U_102,U_101,U_100,U_99,U_98))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_101),U_100)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_103)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_99),U_98)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_102)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_103),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_102),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_98) = ti(arrow_490897120le_alt,U_101)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_101) = ti(arrow_490897120le_alt,U_100)
| ti(arrow_490897120le_alt,U_99) = ti(arrow_490897120le_alt,U_98) ),
inference(clausify,[status(thm)],[f_70_5]) ).
fof(f_71_1,plain,
! [P_1,Pa,Ca,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Ca)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Ca)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa))) ) )
| ? [I_2] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Ca)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Ca)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,Ca)
| ti(arrow_490897120le_alt,Ba) = ti(arrow_490897120le_alt,Ca)
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_8__C4_C]) ).
fof(f_71_2,plain,
! [U_111,U_110,U_109,U_108,U_107] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110))) ) )
| ? [U_106] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,U_106)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,U_106))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,U_106)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,U_106))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_111,U_110,U_109,U_108,U_107] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110))) ) )
| ? [U_113] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,U_113)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,U_113))) )
| ? [U_112] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,U_112)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,U_112))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(miniscope,[status(thm)],[f_71_2]) ).
fof(f_71_4,plain,
! [U_111,U_110,U_109,U_108,U_107] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110))) ) )
| ? [U_113] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,U_113)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,U_113))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK5(U_111,U_110,U_109,U_108,U_107))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK5(U_111,U_110,U_109,U_108,U_107)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_112,sK5(U_111,U_110,U_109,U_108,U_107))],[f_71_3]) ).
fof(f_71_5,plain,
! [U_111,U_110,U_109,U_108,U_107] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK6(U_111,U_110,U_109,U_108,U_107))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK6(U_111,U_110,U_109,U_108,U_107)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK5(U_111,U_110,U_109,U_108,U_107))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK5(U_111,U_110,U_109,U_108,U_107)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_113,sK6(U_111,U_110,U_109,U_108,U_107))],[f_71_4]) ).
cnf(f_71_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK6(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK5(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK6(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK5(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK6(U_111,U_110,U_109,U_108,U_107))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK5(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK6(U_111,U_110,U_109,U_108,U_107))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK5(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK6(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK5(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK6(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK5(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_12,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK6(U_111,U_110,U_109,U_108,U_107))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK5(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_110,sK6(U_111,U_110,U_109,U_108,U_107))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_111,sK5(U_111,U_110,U_109,U_108,U_107))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_108),U_107)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_110)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_107),U_109)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_111)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_111),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_110),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_107) = ti(arrow_490897120le_alt,U_109)
| ti(arrow_490897120le_alt,U_108) = ti(arrow_490897120le_alt,U_107) ),
inference(clausify,[status(thm)],[f_71_5]) ).
fof(f_72_1,plain,
! [P_1,Pa,A_5,B_3,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa))) ) )
| ? [I_2] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,A_5) = ti(arrow_490897120le_alt,B_3)
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_9_pairwise__neutrality]) ).
fof(f_72_2,plain,
! [U_120,U_119,U_118,U_117,U_116,U_115] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119))) ) )
| ? [U_114] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,U_114)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,U_114))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,U_114)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,U_114))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_120,U_119,U_118,U_117,U_116,U_115] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119))) ) )
| ? [U_122] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,U_122)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,U_122))) )
| ? [U_121] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,U_121)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,U_121))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(miniscope,[status(thm)],[f_72_2]) ).
fof(f_72_4,plain,
! [U_120,U_119,U_118,U_117,U_116,U_115] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119))) ) )
| ? [U_122] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,U_122)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,U_122))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK7(U_120,U_119,U_118,U_117,U_116,U_115))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK7(U_120,U_119,U_118,U_117,U_116,U_115)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_121,sK7(U_120,U_119,U_118,U_117,U_116,U_115))],[f_72_3]) ).
fof(f_72_5,plain,
! [U_120,U_119,U_118,U_117,U_116,U_115] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK8(U_120,U_119,U_118,U_117,U_116,U_115))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK8(U_120,U_119,U_118,U_117,U_116,U_115)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK7(U_120,U_119,U_118,U_117,U_116,U_115))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK7(U_120,U_119,U_118,U_117,U_116,U_115)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_122,sK8(U_120,U_119,U_118,U_117,U_116,U_115))],[f_72_4]) ).
cnf(f_72_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK8(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK7(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK8(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK7(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK8(U_120,U_119,U_118,U_117,U_116,U_115))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK7(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK8(U_120,U_119,U_118,U_117,U_116,U_115))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK7(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK8(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK7(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK8(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK7(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_12,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK8(U_120,U_119,U_118,U_117,U_116,U_115))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK7(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_119,sK8(U_120,U_119,U_118,U_117,U_116,U_115))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_120,sK7(U_120,U_119,U_118,U_117,U_116,U_115))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_116),U_115)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_119)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_118),U_117)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_120)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_120),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_119),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_118) = ti(arrow_490897120le_alt,U_117)
| ti(arrow_490897120le_alt,U_116) = ti(arrow_490897120le_alt,U_115) ),
inference(clausify,[status(thm)],[f_72_5]) ).
fof(f_73_1,plain,
! [P_1,Pa,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa))) ) )
| ? [I_2] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_1,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I_2))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_1),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_10__C3_C]) ).
fof(f_73_2,plain,
! [U_127,U_126,U_125,U_124] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126))) ) )
| ? [U_123] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,U_123)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,U_123))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,U_123)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,U_123))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_127,U_126,U_125,U_124] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126))) ) )
| ? [U_129] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,U_129)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,U_129))) )
| ? [U_128] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,U_128)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,U_128))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
fof(f_73_4,plain,
! [U_127,U_126,U_125,U_124] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126))) ) )
| ? [U_129] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,U_129)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,U_129))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK9(U_127,U_126,U_125,U_124))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK9(U_127,U_126,U_125,U_124)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_128,sK9(U_127,U_126,U_125,U_124))],[f_73_3]) ).
fof(f_73_5,plain,
! [U_127,U_126,U_125,U_124] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK10(U_127,U_126,U_125,U_124))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK10(U_127,U_126,U_125,U_124)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK9(U_127,U_126,U_125,U_124))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK9(U_127,U_126,U_125,U_124)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_129,sK10(U_127,U_126,U_125,U_124))],[f_73_4]) ).
cnf(f_73_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK10(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK9(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(clausify,[status(thm)],[f_73_5]) ).
cnf(f_73_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK10(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK9(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(clausify,[status(thm)],[f_73_5]) ).
cnf(f_73_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK10(U_127,U_126,U_125,U_124))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK9(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(clausify,[status(thm)],[f_73_5]) ).
cnf(f_73_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK10(U_127,U_126,U_125,U_124))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK9(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(clausify,[status(thm)],[f_73_5]) ).
cnf(f_73_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK10(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK9(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(clausify,[status(thm)],[f_73_5]) ).
cnf(f_73_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK10(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK9(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(clausify,[status(thm)],[f_73_5]) ).
cnf(f_73_12,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK10(U_127,U_126,U_125,U_124))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK9(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(clausify,[status(thm)],[f_73_5]) ).
cnf(f_73_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_126,sK10(U_127,U_126,U_125,U_124))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_127,sK9(U_127,U_126,U_125,U_124))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_125),U_124)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_126)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_124),U_125)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,U_127)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_127),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_126),arrow_1111136790e_Prof))
| ti(arrow_490897120le_alt,U_125) = ti(arrow_490897120le_alt,U_124) ),
inference(clausify,[status(thm)],[f_73_5]) ).
fof(f_74_1,plain,
! [I_2] :
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
& hAPP(arrow_660593299e_indi,nat,h,I_2) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e)))
& hAPP(arrow_660593299e_indi,nat,h,I_2) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) ) )
& ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
| hAPP(arrow_660593299e_indi,nat,h,I_2) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,I_2) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) ) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J]) ).
fof(f_74_2,plain,
! [U_130] :
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_130)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_130)),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_130) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_130)),c),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_130) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_130)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_130)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_130)),n)) ) )
& ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_130)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_130) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_130)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_130) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_130)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_130)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_130)),n)) ) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_130))) ) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
( ! [U_132] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_132) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),c),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_132) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_132)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_132)),n)) ) )
& ! [U_131] :
( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_131)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_131) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_131)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_131) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_131)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_131)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_131)),n)) ) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_131))) ) ),
inference(miniscope,[status(thm)],[f_74_2]) ).
cnf(f_74_4,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_131)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_131)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_131))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_5,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_131)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_131) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_131)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_131))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_131)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_131) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_131)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_131))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_7,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_132)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_132)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_8,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_132) != n
| hAPP(arrow_660593299e_indi,nat,h,U_132) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_132)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_132) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_132)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_10,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_132) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_132)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_132)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_12,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_132)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_13,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_132) != n
| hAPP(arrow_660593299e_indi,nat,h,U_132) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_14,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_132) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_15,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_132) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_16,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_132))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_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_75_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_indi,bool))),h),n)))),
inference(clausify,[status(thm)],[f_75_1]) ).
fof(f_76_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_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_76_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
inference(clausify,[status(thm)],[f_76_1]) ).
fof(f_77_1,plain,
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ) ),
inference(fof_nnf,[status(thm)],[fact_14_PW]) ).
cnf(f_77_2,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ),
inference(clausify,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
inference(clausify,[status(thm)],[f_77_1]) ).
fof(f_78_1,plain,
! [X_a,X_b,Pa] :
( ( ! [X1] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))
| ? [A_3,B_2] : ~ 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_3),B_2))) )
& ( ! [A_3,B_2] : 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_3),B_2)))
| ? [X1] : ~ hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1)) ) ),
inference(fof_nnf,[status(thm)],[fact_15_split__paired__All]) ).
fof(f_78_2,plain,
! [U_141,U_140,U_139] :
( ( ! [U_138] : hBOOL(hAPP(product_prod(U_141,U_140),bool,U_139,U_138))
| ? [U_137,U_136] : ~ hBOOL(hAPP(product_prod(U_141,U_140),bool,U_139,hAPP(U_140,product_prod(U_141,U_140),hAPP(U_141,fun(U_140,product_prod(U_141,U_140)),product_Pair(U_141,U_140),U_137),U_136))) )
& ( ! [U_135,U_134] : hBOOL(hAPP(product_prod(U_141,U_140),bool,U_139,hAPP(U_140,product_prod(U_141,U_140),hAPP(U_141,fun(U_140,product_prod(U_141,U_140)),product_Pair(U_141,U_140),U_135),U_134)))
| ? [U_133] : ~ hBOOL(hAPP(product_prod(U_141,U_140),bool,U_139,U_133)) ) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
( ! [U_147,U_145,U_143] :
( ! [U_138] : hBOOL(hAPP(product_prod(U_147,U_145),bool,U_143,U_138))
| ? [U_137,U_136] : ~ hBOOL(hAPP(product_prod(U_147,U_145),bool,U_143,hAPP(U_145,product_prod(U_147,U_145),hAPP(U_147,fun(U_145,product_prod(U_147,U_145)),product_Pair(U_147,U_145),U_137),U_136))) )
& ! [U_146,U_144,U_142] :
( ! [U_135,U_134] : hBOOL(hAPP(product_prod(U_146,U_144),bool,U_142,hAPP(U_144,product_prod(U_146,U_144),hAPP(U_146,fun(U_144,product_prod(U_146,U_144)),product_Pair(U_146,U_144),U_135),U_134)))
| ? [U_133] : ~ hBOOL(hAPP(product_prod(U_146,U_144),bool,U_142,U_133)) ) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
fof(f_78_4,plain,
( ! [U_147,U_145,U_143] :
( ! [U_138] : hBOOL(hAPP(product_prod(U_147,U_145),bool,U_143,U_138))
| ? [U_137,U_136] : ~ hBOOL(hAPP(product_prod(U_147,U_145),bool,U_143,hAPP(U_145,product_prod(U_147,U_145),hAPP(U_147,fun(U_145,product_prod(U_147,U_145)),product_Pair(U_147,U_145),U_137),U_136))) )
& ! [U_146,U_144,U_142] :
( ! [U_135,U_134] : hBOOL(hAPP(product_prod(U_146,U_144),bool,U_142,hAPP(U_144,product_prod(U_146,U_144),hAPP(U_146,fun(U_144,product_prod(U_146,U_144)),product_Pair(U_146,U_144),U_135),U_134)))
| ~ hBOOL(hAPP(product_prod(U_146,U_144),bool,U_142,sK11(U_146,U_144,U_142))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_133,sK11(U_146,U_144,U_142))],[f_78_3]) ).
fof(f_78_5,plain,
( ! [U_147,U_145,U_143] :
( ! [U_138] : hBOOL(hAPP(product_prod(U_147,U_145),bool,U_143,U_138))
| ? [U_136] : ~ hBOOL(hAPP(product_prod(U_147,U_145),bool,U_143,hAPP(U_145,product_prod(U_147,U_145),hAPP(U_147,fun(U_145,product_prod(U_147,U_145)),product_Pair(U_147,U_145),sK12(U_147,U_145,U_143)),U_136))) )
& ! [U_146,U_144,U_142] :
( ! [U_135,U_134] : hBOOL(hAPP(product_prod(U_146,U_144),bool,U_142,hAPP(U_144,product_prod(U_146,U_144),hAPP(U_146,fun(U_144,product_prod(U_146,U_144)),product_Pair(U_146,U_144),U_135),U_134)))
| ~ hBOOL(hAPP(product_prod(U_146,U_144),bool,U_142,sK11(U_146,U_144,U_142))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_137,sK12(U_147,U_145,U_143))],[f_78_4]) ).
fof(f_78_6,plain,
( ! [U_147,U_145,U_143] :
( ! [U_138] : hBOOL(hAPP(product_prod(U_147,U_145),bool,U_143,U_138))
| ~ hBOOL(hAPP(product_prod(U_147,U_145),bool,U_143,hAPP(U_145,product_prod(U_147,U_145),hAPP(U_147,fun(U_145,product_prod(U_147,U_145)),product_Pair(U_147,U_145),sK12(U_147,U_145,U_143)),sK13(U_147,U_145,U_143)))) )
& ! [U_146,U_144,U_142] :
( ! [U_135,U_134] : hBOOL(hAPP(product_prod(U_146,U_144),bool,U_142,hAPP(U_144,product_prod(U_146,U_144),hAPP(U_146,fun(U_144,product_prod(U_146,U_144)),product_Pair(U_146,U_144),U_135),U_134)))
| ~ hBOOL(hAPP(product_prod(U_146,U_144),bool,U_142,sK11(U_146,U_144,U_142))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_136,sK13(U_147,U_145,U_143))],[f_78_5]) ).
cnf(f_78_7,plain,
( hBOOL(hAPP(product_prod(U_146,U_144),bool,U_142,hAPP(U_144,product_prod(U_146,U_144),hAPP(U_146,fun(U_144,product_prod(U_146,U_144)),product_Pair(U_146,U_144),U_135),U_134)))
| ~ hBOOL(hAPP(product_prod(U_146,U_144),bool,U_142,sK11(U_146,U_144,U_142))) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_8,plain,
( hBOOL(hAPP(product_prod(U_147,U_145),bool,U_143,U_138))
| ~ hBOOL(hAPP(product_prod(U_147,U_145),bool,U_143,hAPP(U_145,product_prod(U_147,U_145),hAPP(U_147,fun(U_145,product_prod(U_147,U_145)),product_Pair(U_147,U_145),sK12(U_147,U_145,U_143)),sK13(U_147,U_145,U_143)))) ),
inference(clausify,[status(thm)],[f_78_6]) ).
fof(f_79_1,plain,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_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_79_2,plain,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_Prof)),
inference(clausify,[status(thm)],[f_79_1]) ).
fof(f_80_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_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_80_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
inference(clausify,[status(thm)],[f_80_1]) ).
fof(f_81_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_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_81_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
inference(clausify,[status(thm)],[f_81_1]) ).
fof(f_82_1,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
inference(fof_nnf,[status(thm)],[fact_19_n_I1_J]) ).
cnf(f_82_2,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
inference(clausify,[status(thm)],[f_82_1]) ).
fof(f_83_1,plain,
hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))),
inference(fof_nnf,[status(thm)],[fact_20_injh]) ).
cnf(f_83_2,plain,
hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))),
inference(clausify,[status(thm)],[f_83_1]) ).
fof(f_84_1,plain,
! [X_b,X_a,A_2,B_1,A_6,B_4] :
( ( ti(X_b,B_1) = ti(X_b,B_4)
& 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_4) ),
inference(fof_nnf,[status(thm)],[fact_21_Pair__inject]) ).
fof(f_84_2,plain,
! [U_153,U_152,U_151,U_150,U_149,U_148] :
( ( ti(U_153,U_150) = ti(U_153,U_148)
& ti(U_152,U_151) = ti(U_152,U_149) )
| hAPP(U_153,product_prod(U_152,U_153),hAPP(U_152,fun(U_153,product_prod(U_152,U_153)),product_Pair(U_152,U_153),U_151),U_150) != hAPP(U_153,product_prod(U_152,U_153),hAPP(U_152,fun(U_153,product_prod(U_152,U_153)),product_Pair(U_152,U_153),U_149),U_148) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( ti(U_152,U_151) = ti(U_152,U_149)
| hAPP(U_153,product_prod(U_152,U_153),hAPP(U_152,fun(U_153,product_prod(U_152,U_153)),product_Pair(U_152,U_153),U_151),U_150) != hAPP(U_153,product_prod(U_152,U_153),hAPP(U_152,fun(U_153,product_prod(U_152,U_153)),product_Pair(U_152,U_153),U_149),U_148) ),
inference(clausify,[status(thm)],[f_84_2]) ).
cnf(f_84_4,plain,
( ti(U_153,U_150) = ti(U_153,U_148)
| hAPP(U_153,product_prod(U_152,U_153),hAPP(U_152,fun(U_153,product_prod(U_152,U_153)),product_Pair(U_152,U_153),U_151),U_150) != hAPP(U_153,product_prod(U_152,U_153),hAPP(U_152,fun(U_153,product_prod(U_152,U_153)),product_Pair(U_152,U_153),U_149),U_148) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [X_b,X_a,Aa,Ba,A_5,B_3] :
( ( 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_3)
| ti(X_b,Ba) != ti(X_b,B_3)
| ti(X_a,Aa) != ti(X_a,A_5) )
& ( ( ti(X_b,Ba) = ti(X_b,B_3)
& 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_3) ) ),
inference(fof_nnf,[status(thm)],[fact_22_Pair__eq]) ).
fof(f_85_2,plain,
! [U_159,U_158,U_157,U_156,U_155,U_154] :
( ( hAPP(U_159,product_prod(U_158,U_159),hAPP(U_158,fun(U_159,product_prod(U_158,U_159)),product_Pair(U_158,U_159),U_157),U_156) = hAPP(U_159,product_prod(U_158,U_159),hAPP(U_158,fun(U_159,product_prod(U_158,U_159)),product_Pair(U_158,U_159),U_155),U_154)
| ti(U_159,U_156) != ti(U_159,U_154)
| ti(U_158,U_157) != ti(U_158,U_155) )
& ( ( ti(U_159,U_156) = ti(U_159,U_154)
& ti(U_158,U_157) = ti(U_158,U_155) )
| hAPP(U_159,product_prod(U_158,U_159),hAPP(U_158,fun(U_159,product_prod(U_158,U_159)),product_Pair(U_158,U_159),U_157),U_156) != hAPP(U_159,product_prod(U_158,U_159),hAPP(U_158,fun(U_159,product_prod(U_158,U_159)),product_Pair(U_158,U_159),U_155),U_154) ) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
( ! [U_171,U_169,U_167,U_165,U_163,U_161] :
( hAPP(U_171,product_prod(U_169,U_171),hAPP(U_169,fun(U_171,product_prod(U_169,U_171)),product_Pair(U_169,U_171),U_167),U_165) = hAPP(U_171,product_prod(U_169,U_171),hAPP(U_169,fun(U_171,product_prod(U_169,U_171)),product_Pair(U_169,U_171),U_163),U_161)
| ti(U_171,U_165) != ti(U_171,U_161)
| ti(U_169,U_167) != ti(U_169,U_163) )
& ! [U_170,U_168,U_166,U_164,U_162,U_160] :
( ( ti(U_170,U_164) = ti(U_170,U_160)
& ti(U_168,U_166) = ti(U_168,U_162) )
| hAPP(U_170,product_prod(U_168,U_170),hAPP(U_168,fun(U_170,product_prod(U_168,U_170)),product_Pair(U_168,U_170),U_166),U_164) != hAPP(U_170,product_prod(U_168,U_170),hAPP(U_168,fun(U_170,product_prod(U_168,U_170)),product_Pair(U_168,U_170),U_162),U_160) ) ),
inference(miniscope,[status(thm)],[f_85_2]) ).
cnf(f_85_4,plain,
( ti(U_168,U_166) = ti(U_168,U_162)
| hAPP(U_170,product_prod(U_168,U_170),hAPP(U_168,fun(U_170,product_prod(U_168,U_170)),product_Pair(U_168,U_170),U_166),U_164) != hAPP(U_170,product_prod(U_168,U_170),hAPP(U_168,fun(U_170,product_prod(U_168,U_170)),product_Pair(U_168,U_170),U_162),U_160) ),
inference(clausify,[status(thm)],[f_85_3]) ).
cnf(f_85_5,plain,
( ti(U_170,U_164) = ti(U_170,U_160)
| hAPP(U_170,product_prod(U_168,U_170),hAPP(U_168,fun(U_170,product_prod(U_168,U_170)),product_Pair(U_168,U_170),U_166),U_164) != hAPP(U_170,product_prod(U_168,U_170),hAPP(U_168,fun(U_170,product_prod(U_168,U_170)),product_Pair(U_168,U_170),U_162),U_160) ),
inference(clausify,[status(thm)],[f_85_3]) ).
cnf(f_85_6,plain,
( hAPP(U_171,product_prod(U_169,U_171),hAPP(U_169,fun(U_171,product_prod(U_169,U_171)),product_Pair(U_169,U_171),U_167),U_165) = hAPP(U_171,product_prod(U_169,U_171),hAPP(U_169,fun(U_171,product_prod(U_169,U_171)),product_Pair(U_169,U_171),U_163),U_161)
| ti(U_171,U_165) != ti(U_171,U_161)
| ti(U_169,U_167) != ti(U_169,U_163) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [Fa] :
( ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,Fa))
| ? [X_2] :
( ? [Xa] :
( ? [A_3,B_2] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,Xa))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,Xa)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2))) ) )
& ! [I_2] :
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Xa,I_2))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Xa,I_2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2))) ) ) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Xa),arrow_1111136790e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) ) )
& ( ! [X_2] :
( ! [Xa] :
( ! [A_3,B_2] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,Xa))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,Xa)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2))) ) )
| ? [I_2] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Xa,I_2))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Xa,I_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2))) ) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Xa),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,Fa)) ) ),
inference(fof_nnf,[status(thm)],[fact_23_IIA__def]) ).
fof(f_86_2,plain,
! [U_182] :
( ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_182))
| ? [U_181] :
( ? [U_180] :
( ? [U_179,U_178] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_182,U_181)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_182,U_180))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_182,U_180)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_182,U_181))) ) )
& ! [U_177] :
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_181,U_177)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_180,U_177))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_180,U_177)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_181,U_177))) ) ) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_180),arrow_1111136790e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_181),arrow_1111136790e_Prof)) ) )
& ( ! [U_176] :
( ! [U_175] :
( ! [U_174,U_173] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_182,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_182,U_175))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_182,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_182,U_176))) ) )
| ? [U_172] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,U_172)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,U_172))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,U_172)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,U_172))) ) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_182)) ) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
( ! [U_188] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188))
| ? [U_181] :
( ? [U_180] :
( ? [U_179,U_178] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_181)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_180))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_180)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_181))) ) )
& ! [U_186] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_181,U_186)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_180,U_186))) )
& ! [U_185] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_180,U_185)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_181,U_185))) ) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_180),arrow_1111136790e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_181),arrow_1111136790e_Prof)) ) )
& ! [U_187] :
( ! [U_176] :
( ! [U_175] :
( ! [U_174,U_173] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176))) ) )
| ? [U_184] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,U_184)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,U_184))) )
| ? [U_183] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,U_183)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,U_183))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ) ),
inference(miniscope,[status(thm)],[f_86_2]) ).
fof(f_86_4,plain,
( ! [U_188] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188))
| ? [U_181] :
( ? [U_180] :
( ? [U_179,U_178] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_181)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_180))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_180)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_181))) ) )
& ! [U_186] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_181,U_186)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_180,U_186))) )
& ! [U_185] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_180,U_185)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_181,U_185))) ) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_180),arrow_1111136790e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_181),arrow_1111136790e_Prof)) ) )
& ! [U_187] :
( ! [U_176] :
( ! [U_175] :
( ! [U_174,U_173] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176))) ) )
| ? [U_184] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,U_184)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,U_184))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK14(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK14(U_187,U_176,U_175,U_174,U_173)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_183,sK14(U_187,U_176,U_175,U_174,U_173))],[f_86_3]) ).
fof(f_86_5,plain,
( ! [U_188] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188))
| ? [U_181] :
( ? [U_180] :
( ? [U_179,U_178] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_181)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_180))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_180)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_181))) ) )
& ! [U_186] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_181,U_186)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_180,U_186))) )
& ! [U_185] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_180,U_185)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_181,U_185))) ) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_180),arrow_1111136790e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_181),arrow_1111136790e_Prof)) ) )
& ! [U_187] :
( ! [U_176] :
( ! [U_175] :
( ! [U_174,U_173] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK15(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK15(U_187,U_176,U_175,U_174,U_173)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK14(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK14(U_187,U_176,U_175,U_174,U_173)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_184,sK15(U_187,U_176,U_175,U_174,U_173))],[f_86_4]) ).
fof(f_86_6,plain,
( ! [U_188] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188))
| ( ? [U_180] :
( ? [U_179,U_178] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_180))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,U_180)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188)))) ) )
& ! [U_186] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK16(U_188),U_186)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_180,U_186))) )
& ! [U_185] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_180,U_185)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK16(U_188),U_185))) ) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_180),arrow_1111136790e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK16(U_188)),arrow_1111136790e_Prof)) ) )
& ! [U_187] :
( ! [U_176] :
( ! [U_175] :
( ! [U_174,U_173] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK15(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK15(U_187,U_176,U_175,U_174,U_173)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK14(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK14(U_187,U_176,U_175,U_174,U_173)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_181,sK16(U_188))],[f_86_5]) ).
fof(f_86_7,plain,
( ! [U_188] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188))
| ( ? [U_179,U_178] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK17(U_188)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK17(U_188))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188)))) ) )
& ! [U_186] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK16(U_188),U_186)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK17(U_188),U_186))) )
& ! [U_185] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK17(U_188),U_185)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_179),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK16(U_188),U_185))) ) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK17(U_188)),arrow_1111136790e_Prof))
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK16(U_188)),arrow_1111136790e_Prof)) ) )
& ! [U_187] :
( ! [U_176] :
( ! [U_175] :
( ! [U_174,U_173] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK15(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK15(U_187,U_176,U_175,U_174,U_173)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK14(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK14(U_187,U_176,U_175,U_174,U_173)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_180,sK17(U_188))],[f_86_6]) ).
fof(f_86_8,plain,
( ! [U_188] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188))
| ( ? [U_178] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK17(U_188)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK17(U_188))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),U_178)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188)))) ) )
& ! [U_186] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK16(U_188),U_186)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK17(U_188),U_186))) )
& ! [U_185] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK17(U_188),U_185)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),U_178)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK16(U_188),U_185))) ) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK17(U_188)),arrow_1111136790e_Prof))
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK16(U_188)),arrow_1111136790e_Prof)) ) )
& ! [U_187] :
( ! [U_176] :
( ! [U_175] :
( ! [U_174,U_173] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK15(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK15(U_187,U_176,U_175,U_174,U_173)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK14(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK14(U_187,U_176,U_175,U_174,U_173)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_179,sK18(U_188))],[f_86_7]) ).
fof(f_86_9,plain,
( ! [U_188] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK17(U_188)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK17(U_188))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188)))) ) )
& ! [U_186] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK16(U_188),U_186)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK17(U_188),U_186))) )
& ! [U_185] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK17(U_188),U_185)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK16(U_188),U_185))) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK17(U_188)),arrow_1111136790e_Prof))
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK16(U_188)),arrow_1111136790e_Prof)) ) )
& ! [U_187] :
( ! [U_176] :
( ! [U_175] :
( ! [U_174,U_173] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK15(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK15(U_187,U_176,U_175,U_174,U_173)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK14(U_187,U_176,U_175,U_174,U_173))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK14(U_187,U_176,U_175,U_174,U_173)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_178,sK19(U_188))],[f_86_8]) ).
cnf(f_86_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK15(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK14(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK15(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK14(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_12,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK15(U_187,U_176,U_175,U_174,U_173))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK14(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK15(U_187,U_176,U_175,U_174,U_173))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK14(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_14,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK15(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK14(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_15,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK15(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK14(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_16,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK15(U_187,U_176,U_175,U_174,U_173))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK14(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_17,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_176,sK15(U_187,U_176,U_175,U_174,U_173))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_175,sK14(U_187,U_176,U_175,U_174,U_173))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_176)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_174),U_173)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_187,U_175)))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_175),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_176),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_187)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_18,plain,
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK16(U_188)),arrow_1111136790e_Prof))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_19,plain,
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK17(U_188)),arrow_1111136790e_Prof))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_20,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK17(U_188),U_185)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK16(U_188),U_185)))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_21,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK16(U_188),U_186)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK17(U_188),U_186)))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_22,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK17(U_188))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188))))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_23,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188))))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_24,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK17(U_188))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK17(U_188))))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
cnf(f_86_25,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK16(U_188))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK18(U_188)),sK19(U_188))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_188,sK17(U_188))))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,U_188)) ),
inference(clausify,[status(thm)],[f_86_9]) ).
fof(f_87_1,plain,
! [Fa] :
( ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,Fa))
| ? [X_2] :
( ? [A_3,B_2] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2)))
& ! [I_2] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2))) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) ) )
& ( ! [X_2] :
( ! [A_3,B_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2)))
| ? [I_2] : ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,Fa)) ) ),
inference(fof_nnf,[status(thm)],[fact_24_unanimity__def]) ).
fof(f_87_2,plain,
! [U_197] :
( ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_197))
| ? [U_196] :
( ? [U_195,U_194] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_195),U_194)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_197,U_196)))
& ! [U_193] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_195),U_194)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_196,U_193))) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_196),arrow_1111136790e_Prof)) ) )
& ( ! [U_192] :
( ! [U_191,U_190] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_197,U_192)))
| ? [U_189] : ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_192,U_189))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_192),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_197)) ) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
( ! [U_199] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_199))
| ? [U_196] :
( ? [U_195,U_194] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_195),U_194)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_199,U_196)))
& ! [U_193] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_195),U_194)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_196,U_193))) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_196),arrow_1111136790e_Prof)) ) )
& ! [U_198] :
( ! [U_192] :
( ! [U_191,U_190] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_198,U_192)))
| ? [U_189] : ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_192,U_189))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_192),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_198)) ) ),
inference(miniscope,[status(thm)],[f_87_2]) ).
fof(f_87_4,plain,
( ! [U_199] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_199))
| ? [U_196] :
( ? [U_195,U_194] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_195),U_194)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_199,U_196)))
& ! [U_193] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_195),U_194)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_196,U_193))) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_196),arrow_1111136790e_Prof)) ) )
& ! [U_198] :
( ! [U_192] :
( ! [U_191,U_190] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_198,U_192)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_192,sK20(U_198,U_192,U_191,U_190)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_192),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_198)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_189,sK20(U_198,U_192,U_191,U_190))],[f_87_3]) ).
fof(f_87_5,plain,
( ! [U_199] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_199))
| ( ? [U_195,U_194] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_195),U_194)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_199,sK21(U_199))))
& ! [U_193] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_195),U_194)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK21(U_199),U_193))) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK21(U_199)),arrow_1111136790e_Prof)) ) )
& ! [U_198] :
( ! [U_192] :
( ! [U_191,U_190] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_198,U_192)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_192,sK20(U_198,U_192,U_191,U_190)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_192),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_198)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_196,sK21(U_199))],[f_87_4]) ).
fof(f_87_6,plain,
( ! [U_199] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_199))
| ( ? [U_194] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK22(U_199)),U_194)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_199,sK21(U_199))))
& ! [U_193] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK22(U_199)),U_194)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK21(U_199),U_193))) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK21(U_199)),arrow_1111136790e_Prof)) ) )
& ! [U_198] :
( ! [U_192] :
( ! [U_191,U_190] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_198,U_192)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_192,sK20(U_198,U_192,U_191,U_190)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_192),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_198)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_195,sK22(U_199))],[f_87_5]) ).
fof(f_87_7,plain,
( ! [U_199] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_199))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK22(U_199)),sK23(U_199))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_199,sK21(U_199))))
& ! [U_193] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK22(U_199)),sK23(U_199))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK21(U_199),U_193)))
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK21(U_199)),arrow_1111136790e_Prof)) ) )
& ! [U_198] :
( ! [U_192] :
( ! [U_191,U_190] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_198,U_192)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_192,sK20(U_198,U_192,U_191,U_190)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_192),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_198)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_194,sK23(U_199))],[f_87_6]) ).
cnf(f_87_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_198,U_192)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_191),U_190)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_192,sK20(U_198,U_192,U_191,U_190))))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_192),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_198)) ),
inference(clausify,[status(thm)],[f_87_7]) ).
cnf(f_87_9,plain,
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK21(U_199)),arrow_1111136790e_Prof))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_199)) ),
inference(clausify,[status(thm)],[f_87_7]) ).
cnf(f_87_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK22(U_199)),sK23(U_199))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK21(U_199),U_193)))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_199)) ),
inference(clausify,[status(thm)],[f_87_7]) ).
cnf(f_87_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK22(U_199)),sK23(U_199))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_199,sK21(U_199))))
| hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,U_199)) ),
inference(clausify,[status(thm)],[f_87_7]) ).
fof(f_88_1,plain,
! [X_a,X_1] : hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_1)),
inference(fof_nnf,[status(thm)],[fact_25_top1I]) ).
fof(f_88_2,plain,
! [U_201,U_200] : hBOOL(hAPP(U_201,bool,top_top(fun(U_201,bool)),U_200)),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
hBOOL(hAPP(U_201,bool,top_top(fun(U_201,bool)),U_200)),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_26_UNIV__I]) ).
fof(f_89_2,plain,
! [U_203,U_202] : hBOOL(hAPP(fun(U_203,bool),bool,hAPP(U_203,fun(fun(U_203,bool),bool),member(U_203),U_202),top_top(fun(U_203,bool)))),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
hBOOL(hAPP(fun(U_203,bool),bool,hAPP(U_203,fun(fun(U_203,bool),bool),member(U_203),U_202),top_top(fun(U_203,bool)))),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_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_27_iso__tuple__UNIV__I]) ).
fof(f_90_2,plain,
! [U_205,U_204] : hBOOL(hAPP(fun(U_205,bool),bool,hAPP(U_205,fun(fun(U_205,bool),bool),member(U_205),U_204),top_top(fun(U_205,bool)))),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
hBOOL(hAPP(fun(U_205,bool),bool,hAPP(U_205,fun(fun(U_205,bool),bool),member(U_205),U_204),top_top(fun(U_205,bool)))),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_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_91_2,plain,
! [U_211,U_210,U_209,U_208,U_207,U_206] : hAPP(product_prod(U_211,U_210),U_209,hAPP(fun(U_211,fun(U_210,U_209)),fun(product_prod(U_211,U_210),U_209),product_prod_rec(U_211,U_210,U_209),U_208),hAPP(U_210,product_prod(U_211,U_210),hAPP(U_211,fun(U_210,product_prod(U_211,U_210)),product_Pair(U_211,U_210),U_207),U_206)) = hAPP(U_210,U_209,hAPP(U_211,fun(U_210,U_209),U_208,U_207),U_206),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
hAPP(product_prod(U_211,U_210),U_209,hAPP(fun(U_211,fun(U_210,U_209)),fun(product_prod(U_211,U_210),U_209),product_prod_rec(U_211,U_210,U_209),U_208),hAPP(U_210,product_prod(U_211,U_210),hAPP(U_211,fun(U_210,product_prod(U_211,U_210)),product_Pair(U_211,U_210),U_207),U_206)) = hAPP(U_210,U_209,hAPP(U_211,fun(U_210,U_209),U_208,U_207),U_206),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [X_b,X_a] :
( ! [X_1] : hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_1) = top_top(X_a)
| ~ top(X_a) ),
inference(fof_nnf,[status(thm)],[fact_29_top__apply]) ).
fof(f_92_2,plain,
! [U_214,U_213] :
( ! [U_212] : hAPP(U_214,U_213,top_top(fun(U_214,U_213)),U_212) = top_top(U_213)
| ~ top(U_213) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( hAPP(U_214,U_213,top_top(fun(U_214,U_213)),U_212) = top_top(U_213)
| ~ top(U_213) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_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_93_2,plain,
! [U_216] :
( ! [U_215] : ~ hBOOL(hAPP(U_216,bool,hAPP(U_216,fun(U_216,bool),ord_less(U_216),top_top(U_216)),U_215))
| ~ top(U_216) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( ~ hBOOL(hAPP(U_216,bool,hAPP(U_216,fun(U_216,bool),ord_less(U_216),top_top(U_216)),U_215))
| ~ top(U_216) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_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_94_2,plain,
! [U_218] :
( ! [U_217] :
( ( ti(U_218,U_217) != top_top(U_218)
| ~ hBOOL(hAPP(U_218,bool,hAPP(U_218,fun(U_218,bool),ord_less(U_218),U_217),top_top(U_218))) )
& ( hBOOL(hAPP(U_218,bool,hAPP(U_218,fun(U_218,bool),ord_less(U_218),U_217),top_top(U_218)))
| ti(U_218,U_217) = top_top(U_218) ) )
| ~ top(U_218) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_218] :
( ( ! [U_220] :
( ti(U_218,U_220) != top_top(U_218)
| ~ hBOOL(hAPP(U_218,bool,hAPP(U_218,fun(U_218,bool),ord_less(U_218),U_220),top_top(U_218))) )
& ! [U_219] :
( hBOOL(hAPP(U_218,bool,hAPP(U_218,fun(U_218,bool),ord_less(U_218),U_219),top_top(U_218)))
| ti(U_218,U_219) = top_top(U_218) ) )
| ~ top(U_218) ),
inference(miniscope,[status(thm)],[f_94_2]) ).
cnf(f_94_4,plain,
( hBOOL(hAPP(U_218,bool,hAPP(U_218,fun(U_218,bool),ord_less(U_218),U_219),top_top(U_218)))
| ti(U_218,U_219) = top_top(U_218)
| ~ top(U_218) ),
inference(clausify,[status(thm)],[f_94_3]) ).
cnf(f_94_5,plain,
( ti(U_218,U_220) != top_top(U_218)
| ~ hBOOL(hAPP(U_218,bool,hAPP(U_218,fun(U_218,bool),ord_less(U_218),U_220),top_top(U_218)))
| ~ top(U_218) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))),
inference(fof_nnf,[status(thm)],[fact_32_assms_I1_J]) ).
cnf(f_95_2,plain,
hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))),
inference(clausify,[status(thm)],[f_95_1]) ).
fof(f_96_1,plain,
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_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_96_2,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
inference(clausify,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
inference(clausify,[status(thm)],[f_96_1]) ).
fof(f_97_1,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
inference(fof_nnf,[status(thm)],[fact_34__096Lab_A_058_ALin_096]) ).
cnf(f_97_2,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
inference(clausify,[status(thm)],[f_97_1]) ).
fof(f_98_1,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
inference(fof_nnf,[status(thm)],[fact_35__096Lba_A_058_ALin_096]) ).
cnf(f_98_2,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
inference(clausify,[status(thm)],[f_98_1]) ).
fof(f_99_1,plain,
a != b,
inference(fof_nnf,[status(thm)],[fact_36__096a_A_126_061_Ab_096]) ).
cnf(f_99_2,plain,
a != b,
inference(clausify,[status(thm)],[f_99_1]) ).
fof(f_100_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
inference(fof_nnf,[status(thm)],[fact_37__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096]) ).
cnf(f_100_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
inference(clausify,[status(thm)],[f_100_1]) ).
fof(f_101_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
inference(fof_nnf,[status(thm)],[fact_38__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096]) ).
cnf(f_101_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
inference(clausify,[status(thm)],[f_101_1]) ).
fof(f_102_1,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
inference(fof_nnf,[status(thm)],[fact_39__096_Ia_M_Ab_J_A_126_058_ALba_096]) ).
cnf(f_102_2,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
inference(clausify,[status(thm)],[f_102_1]) ).
fof(f_103_1,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
inference(fof_nnf,[status(thm)],[fact_40__096_Ib_M_Aa_J_A_126_058_ALab_096]) ).
cnf(f_103_2,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
inference(clausify,[status(thm)],[f_103_1]) ).
fof(f_104_1,plain,
! [Na] : hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),Na))),lab)),lba)),arrow_1111136790e_Prof)),
inference(fof_nnf,[status(thm)],[fact_41_PiProf]) ).
fof(f_104_2,plain,
! [U_221] : hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),U_221))),lab)),lba)),arrow_1111136790e_Prof)),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),U_221))),lab)),lba)),arrow_1111136790e_Prof)),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
? [Lab] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),Lab),arrow_2064824852le_Lin))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),Lab)) ),
inference(fof_nnf,[status(thm)],[fact_42__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_]) ).
fof(f_105_2,plain,
? [U_222] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_222),arrow_2064824852le_Lin))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),U_222)) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sK24),arrow_2064824852le_Lin))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),sK24)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_222,sK24)],[f_105_2]) ).
cnf(f_105_4,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),sK24)),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_5,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sK24),arrow_2064824852le_Lin)),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
? [Lba] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),Lba),arrow_2064824852le_Lin))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),Lba)) ),
inference(fof_nnf,[status(thm)],[fact_43__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_]) ).
fof(f_106_2,plain,
? [U_223] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_223),arrow_2064824852le_Lin))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),U_223)) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sK25),arrow_2064824852le_Lin))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),sK25)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_223,sK25)],[f_106_2]) ).
cnf(f_106_4,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),sK25)),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_5,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sK25),arrow_2064824852le_Lin)),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [I_2] :
( ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
| hAPP(arrow_660593299e_indi,nat,h,I_2) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,I_2) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) ) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) ) )
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
& hAPP(arrow_660593299e_indi,nat,h,I_2) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e)))
& hAPP(arrow_660593299e_indi,nat,h,I_2) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_44__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).
fof(f_107_2,plain,
! [U_224] :
( ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_224)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_224) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_224)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_224) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_224)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_224)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_224)),n)) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_224)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_224)),n)) ) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_224)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_224)),n)) ) )
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_224)),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_224) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_224)),c),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_224) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_224)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_224)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_224)),n)) ) ) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
( ! [U_226] :
( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ) )
& ! [U_225] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ) )
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_225) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_225) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ) ) ),
inference(miniscope,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_5,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_225) != n
| hAPP(arrow_660593299e_indi,nat,h,U_225) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_6,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_225) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_7,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_225) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_8,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_9,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_10,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_225) != n
| hAPP(arrow_660593299e_indi,nat,h,U_225) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_225) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_12,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_225) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_14,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_15,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_225) != n
| hAPP(arrow_660593299e_indi,nat,h,U_225) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_16,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_225) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_17,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_225) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_18,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_19,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_20,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_225) != n
| hAPP(arrow_660593299e_indi,nat,h,U_225) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_21,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_225) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_22,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_225) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_23,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_24,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_25,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_26,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_27,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_28,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_29,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_30,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_31,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_32,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_33,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_34,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_35,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [M] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),M))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),n)) ),
inference(fof_nnf,[status(thm)],[fact_45_n_I2_J]) ).
fof(f_108_2,plain,
! [U_227] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),U_227))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_227),n)) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),U_227))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_227),n)) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [X_1,Y_2,L_3] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Y_2),X_1)),L_3)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Y_2),X_1)),L_3))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3)) ) )
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Y_2)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin)) ),
inference(fof_nnf,[status(thm)],[fact_46_notin__Lin__iff]) ).
fof(f_109_2,plain,
! [U_230,U_229,U_228] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_230),U_229)),U_228))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_229),U_230)),U_228)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_229),U_230)),U_228))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_230),U_229)),U_228)) ) )
| ti(arrow_490897120le_alt,U_230) = ti(arrow_490897120le_alt,U_229)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_228),arrow_2064824852le_Lin)) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_229),U_230)),U_228))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_230),U_229)),U_228))
| ti(arrow_490897120le_alt,U_230) = ti(arrow_490897120le_alt,U_229)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_228),arrow_2064824852le_Lin)) ),
inference(clausify,[status(thm)],[f_109_2]) ).
cnf(f_109_4,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_230),U_229)),U_228))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_229),U_230)),U_228))
| ti(arrow_490897120le_alt,U_230) = ti(arrow_490897120le_alt,U_229)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_228),arrow_2064824852le_Lin)) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_1,plain,
! [Aa,Ba,L_3] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),L_3))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),L_3))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin)) ),
inference(fof_nnf,[status(thm)],[fact_47_Lin__irrefl]) ).
fof(f_110_2,plain,
! [U_233,U_232,U_231] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_232),U_233)),U_231))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_233),U_232)),U_231))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_231),arrow_2064824852le_Lin)) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_232),U_233)),U_231))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_233),U_232)),U_231))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_231),arrow_2064824852le_Lin)) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_1,plain,
! [X_1,L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_3),X_1)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin)) ),
inference(fof_nnf,[status(thm)],[fact_48_mktop__Lin]) ).
fof(f_111_2,plain,
! [U_235,U_234] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_234),U_235)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_234),arrow_2064824852le_Lin)) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,U_234),U_235)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_234),arrow_2064824852le_Lin)) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [X_1,L_3] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_3),X_1)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin)) ),
inference(fof_nnf,[status(thm)],[fact_49_mkbot__Lin]) ).
fof(f_112_2,plain,
! [U_237,U_236] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_236),U_237)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_236),arrow_2064824852le_Lin)) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,U_236),U_237)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_236),arrow_2064824852le_Lin)) ),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_1,plain,
! [L_3,X_1,Y_2] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_3),X_1),Y_2)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Y_2) ),
inference(fof_nnf,[status(thm)],[fact_50_above__Lin]) ).
fof(f_113_2,plain,
! [U_240,U_239,U_238] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_240),U_239),U_238)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_240),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_239) = ti(arrow_490897120le_alt,U_238) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_240),U_239),U_238)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_240),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_239) = ti(arrow_490897120le_alt,U_238) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_1,plain,
! [L_3] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),L_3)),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin)) ),
inference(fof_nnf,[status(thm)],[fact_51_const__Lin__Prof]) ).
fof(f_114_2,plain,
! [U_241] :
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),U_241)),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_241),arrow_2064824852le_Lin)) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),U_241)),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_241),arrow_2064824852le_Lin)) ),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_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_52_linorder__cases]) ).
fof(f_115_2,plain,
! [U_244] :
( ! [U_243,U_242] :
( hBOOL(hAPP(U_244,bool,hAPP(U_244,fun(U_244,bool),ord_less(U_244),U_242),U_243))
| ti(U_244,U_243) = ti(U_244,U_242)
| hBOOL(hAPP(U_244,bool,hAPP(U_244,fun(U_244,bool),ord_less(U_244),U_243),U_242)) )
| ~ linorder(U_244) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( hBOOL(hAPP(U_244,bool,hAPP(U_244,fun(U_244,bool),ord_less(U_244),U_242),U_243))
| ti(U_244,U_243) = ti(U_244,U_242)
| hBOOL(hAPP(U_244,bool,hAPP(U_244,fun(U_244,bool),ord_less(U_244),U_243),U_242))
| ~ linorder(U_244) ),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_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_53_order__less__asym]) ).
fof(f_116_2,plain,
! [U_247] :
( ! [U_246,U_245] :
( ~ hBOOL(hAPP(U_247,bool,hAPP(U_247,fun(U_247,bool),ord_less(U_247),U_245),U_246))
| ~ hBOOL(hAPP(U_247,bool,hAPP(U_247,fun(U_247,bool),ord_less(U_247),U_246),U_245)) )
| ~ preorder(U_247) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( ~ hBOOL(hAPP(U_247,bool,hAPP(U_247,fun(U_247,bool),ord_less(U_247),U_245),U_246))
| ~ hBOOL(hAPP(U_247,bool,hAPP(U_247,fun(U_247,bool),ord_less(U_247),U_246),U_245))
| ~ preorder(U_247) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_1,plain,
! [X_a] :
( ! [Z_1,Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),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_54_xt1_I10_J]) ).
fof(f_117_2,plain,
! [U_251] :
( ! [U_250,U_249,U_248] :
( hBOOL(hAPP(U_251,bool,hAPP(U_251,fun(U_251,bool),ord_less(U_251),U_250),U_248))
| ~ hBOOL(hAPP(U_251,bool,hAPP(U_251,fun(U_251,bool),ord_less(U_251),U_250),U_249))
| ~ hBOOL(hAPP(U_251,bool,hAPP(U_251,fun(U_251,bool),ord_less(U_251),U_249),U_248)) )
| ~ order(U_251) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
( hBOOL(hAPP(U_251,bool,hAPP(U_251,fun(U_251,bool),ord_less(U_251),U_250),U_248))
| ~ hBOOL(hAPP(U_251,bool,hAPP(U_251,fun(U_251,bool),ord_less(U_251),U_250),U_249))
| ~ hBOOL(hAPP(U_251,bool,hAPP(U_251,fun(U_251,bool),ord_less(U_251),U_249),U_248))
| ~ order(U_251) ),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_1,plain,
! [X_a] :
( ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1))
| ~ 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_55_order__less__trans]) ).
fof(f_118_2,plain,
! [U_255] :
( ! [U_254,U_253,U_252] :
( hBOOL(hAPP(U_255,bool,hAPP(U_255,fun(U_255,bool),ord_less(U_255),U_253),U_254))
| ~ hBOOL(hAPP(U_255,bool,hAPP(U_255,fun(U_255,bool),ord_less(U_255),U_252),U_254))
| ~ hBOOL(hAPP(U_255,bool,hAPP(U_255,fun(U_255,bool),ord_less(U_255),U_253),U_252)) )
| ~ preorder(U_255) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( hBOOL(hAPP(U_255,bool,hAPP(U_255,fun(U_255,bool),ord_less(U_255),U_253),U_254))
| ~ hBOOL(hAPP(U_255,bool,hAPP(U_255,fun(U_255,bool),ord_less(U_255),U_252),U_254))
| ~ hBOOL(hAPP(U_255,bool,hAPP(U_255,fun(U_255,bool),ord_less(U_255),U_253),U_252))
| ~ preorder(U_255) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [X_a] :
( ! [C,B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_2))
| ti(X_a,B_1) != ti(X_a,C)
| ~ 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_56_xt1_I2_J]) ).
fof(f_119_2,plain,
! [U_259] :
( ! [U_258,U_257,U_256] :
( hBOOL(hAPP(U_259,bool,hAPP(U_259,fun(U_259,bool),ord_less(U_259),U_258),U_256))
| ti(U_259,U_257) != ti(U_259,U_258)
| ~ hBOOL(hAPP(U_259,bool,hAPP(U_259,fun(U_259,bool),ord_less(U_259),U_257),U_256)) )
| ~ order(U_259) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( hBOOL(hAPP(U_259,bool,hAPP(U_259,fun(U_259,bool),ord_less(U_259),U_258),U_256))
| ti(U_259,U_257) != ti(U_259,U_258)
| ~ hBOOL(hAPP(U_259,bool,hAPP(U_259,fun(U_259,bool),ord_less(U_259),U_257),U_256))
| ~ order(U_259) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,plain,
! [X_a] :
( ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C))
| B_1 != C
| ~ 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_57_ord__less__eq__trans]) ).
fof(f_120_2,plain,
! [U_263] :
( ! [U_262,U_261,U_260] :
( hBOOL(hAPP(U_263,bool,hAPP(U_263,fun(U_263,bool),ord_less(U_263),U_261),U_262))
| U_260 != U_262
| ~ hBOOL(hAPP(U_263,bool,hAPP(U_263,fun(U_263,bool),ord_less(U_263),U_261),U_260)) )
| ~ ord(U_263) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
( hBOOL(hAPP(U_263,bool,hAPP(U_263,fun(U_263,bool),ord_less(U_263),U_261),U_262))
| U_260 != U_262
| ~ hBOOL(hAPP(U_263,bool,hAPP(U_263,fun(U_263,bool),ord_less(U_263),U_261),U_260))
| ~ ord(U_263) ),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_1,plain,
! [X_a] :
( ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_2))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B_1))
| ti(X_a,A_2) != ti(X_a,B_1) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_58_xt1_I1_J]) ).
fof(f_121_2,plain,
! [U_267] :
( ! [U_266,U_265,U_264] :
( hBOOL(hAPP(U_267,bool,hAPP(U_267,fun(U_267,bool),ord_less(U_267),U_266),U_265))
| ~ hBOOL(hAPP(U_267,bool,hAPP(U_267,fun(U_267,bool),ord_less(U_267),U_266),U_264))
| ti(U_267,U_265) != ti(U_267,U_264) )
| ~ order(U_267) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( hBOOL(hAPP(U_267,bool,hAPP(U_267,fun(U_267,bool),ord_less(U_267),U_266),U_265))
| ~ hBOOL(hAPP(U_267,bool,hAPP(U_267,fun(U_267,bool),ord_less(U_267),U_266),U_264))
| ti(U_267,U_265) != ti(U_267,U_264)
| ~ order(U_267) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [X_a] :
( ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C))
| A_2 != B_1 )
| ~ ord(X_a) ),
inference(fof_nnf,[status(thm)],[fact_59_ord__eq__less__trans]) ).
fof(f_122_2,plain,
! [U_271] :
( ! [U_270,U_269,U_268] :
( hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_269),U_270))
| ~ hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_268),U_270))
| U_269 != U_268 )
| ~ ord(U_271) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_269),U_270))
| ~ hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_268),U_270))
| U_269 != U_268
| ~ ord(U_271) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_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_60_xt1_I9_J]) ).
fof(f_123_2,plain,
! [U_274] :
( ! [U_273,U_272] :
( ~ hBOOL(hAPP(U_274,bool,hAPP(U_274,fun(U_274,bool),ord_less(U_274),U_272),U_273))
| ~ hBOOL(hAPP(U_274,bool,hAPP(U_274,fun(U_274,bool),ord_less(U_274),U_273),U_272)) )
| ~ order(U_274) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
( ~ hBOOL(hAPP(U_274,bool,hAPP(U_274,fun(U_274,bool),ord_less(U_274),U_272),U_273))
| ~ hBOOL(hAPP(U_274,bool,hAPP(U_274,fun(U_274,bool),ord_less(U_274),U_273),U_272))
| ~ order(U_274) ),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_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_61_order__less__asym_H]) ).
fof(f_124_2,plain,
! [U_277] :
( ! [U_276,U_275] :
( ~ hBOOL(hAPP(U_277,bool,hAPP(U_277,fun(U_277,bool),ord_less(U_277),U_275),U_276))
| ~ hBOOL(hAPP(U_277,bool,hAPP(U_277,fun(U_277,bool),ord_less(U_277),U_276),U_275)) )
| ~ preorder(U_277) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
( ~ hBOOL(hAPP(U_277,bool,hAPP(U_277,fun(U_277,bool),ord_less(U_277),U_275),U_276))
| ~ hBOOL(hAPP(U_277,bool,hAPP(U_277,fun(U_277,bool),ord_less(U_277),U_276),U_275))
| ~ preorder(U_277) ),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
! [X_a] :
( ! [Pa,X_1,Y_2] :
( hBOOL(Pa)
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) )
| ~ preorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_62_order__less__imp__triv]) ).
fof(f_125_2,plain,
! [U_281] :
( ! [U_280,U_279,U_278] :
( hBOOL(U_280)
| ~ hBOOL(hAPP(U_281,bool,hAPP(U_281,fun(U_281,bool),ord_less(U_281),U_278),U_279))
| ~ hBOOL(hAPP(U_281,bool,hAPP(U_281,fun(U_281,bool),ord_less(U_281),U_279),U_278)) )
| ~ preorder(U_281) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( hBOOL(U_280)
| ~ hBOOL(hAPP(U_281,bool,hAPP(U_281,fun(U_281,bool),ord_less(U_281),U_278),U_279))
| ~ hBOOL(hAPP(U_281,bool,hAPP(U_281,fun(U_281,bool),ord_less(U_281),U_279),U_278))
| ~ preorder(U_281) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_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_63_order__less__imp__not__eq2]) ).
fof(f_126_2,plain,
! [U_284] :
( ! [U_283,U_282] :
( ti(U_284,U_282) != ti(U_284,U_283)
| ~ hBOOL(hAPP(U_284,bool,hAPP(U_284,fun(U_284,bool),ord_less(U_284),U_283),U_282)) )
| ~ order(U_284) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( ti(U_284,U_282) != ti(U_284,U_283)
| ~ hBOOL(hAPP(U_284,bool,hAPP(U_284,fun(U_284,bool),ord_less(U_284),U_283),U_282))
| ~ order(U_284) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_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_64_order__less__imp__not__eq]) ).
fof(f_127_2,plain,
! [U_287] :
( ! [U_286,U_285] :
( 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)) )
| ~ order(U_287) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( 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))
| ~ order(U_287) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_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_65_order__less__imp__not__less]) ).
fof(f_128_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_128_1]) ).
cnf(f_128_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_128_2]) ).
fof(f_129_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__not__sym]) ).
fof(f_129_2,plain,
! [U_293] :
( ! [U_292,U_291] :
( ~ hBOOL(hAPP(U_293,bool,hAPP(U_293,fun(U_293,bool),ord_less(U_293),U_291),U_292))
| ~ hBOOL(hAPP(U_293,bool,hAPP(U_293,fun(U_293,bool),ord_less(U_293),U_292),U_291)) )
| ~ preorder(U_293) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( ~ hBOOL(hAPP(U_293,bool,hAPP(U_293,fun(U_293,bool),ord_less(U_293),U_291),U_292))
| ~ hBOOL(hAPP(U_293,bool,hAPP(U_293,fun(U_293,bool),ord_less(U_293),U_292),U_291))
| ~ preorder(U_293) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_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_67_less__imp__neq]) ).
fof(f_130_2,plain,
! [U_296] :
( ! [U_295,U_294] :
( ti(U_296,U_295) != ti(U_296,U_294)
| ~ hBOOL(hAPP(U_296,bool,hAPP(U_296,fun(U_296,bool),ord_less(U_296),U_295),U_294)) )
| ~ order(U_296) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( ti(U_296,U_295) != ti(U_296,U_294)
| ~ hBOOL(hAPP(U_296,bool,hAPP(U_296,fun(U_296,bool),ord_less(U_296),U_295),U_294))
| ~ order(U_296) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_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_68_linorder__neqE]) ).
fof(f_131_2,plain,
! [U_299] :
( ! [U_298,U_297] :
( hBOOL(hAPP(U_299,bool,hAPP(U_299,fun(U_299,bool),ord_less(U_299),U_297),U_298))
| hBOOL(hAPP(U_299,bool,hAPP(U_299,fun(U_299,bool),ord_less(U_299),U_298),U_297))
| ti(U_299,U_298) = ti(U_299,U_297) )
| ~ linorder(U_299) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( hBOOL(hAPP(U_299,bool,hAPP(U_299,fun(U_299,bool),ord_less(U_299),U_297),U_298))
| hBOOL(hAPP(U_299,bool,hAPP(U_299,fun(U_299,bool),ord_less(U_299),U_298),U_297))
| ti(U_299,U_298) = ti(U_299,U_297)
| ~ linorder(U_299) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_1,plain,
! [X_a] :
( ! [Y_2,X_1] :
( ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
| ti(X_a,X_1) != ti(X_a,Y_2) )
& ( ti(X_a,X_1) = ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)) )
| ~ linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_69_linorder__antisym__conv3]) ).
fof(f_132_2,plain,
! [U_302] :
( ! [U_301,U_300] :
( ( ( ~ hBOOL(hAPP(U_302,bool,hAPP(U_302,fun(U_302,bool),ord_less(U_302),U_300),U_301))
| ti(U_302,U_300) != ti(U_302,U_301) )
& ( 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_301)) ) )
| hBOOL(hAPP(U_302,bool,hAPP(U_302,fun(U_302,bool),ord_less(U_302),U_301),U_300)) )
| ~ linorder(U_302) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( 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_301))
| hBOOL(hAPP(U_302,bool,hAPP(U_302,fun(U_302,bool),ord_less(U_302),U_301),U_300))
| ~ linorder(U_302) ),
inference(clausify,[status(thm)],[f_132_2]) ).
cnf(f_132_4,plain,
( ~ hBOOL(hAPP(U_302,bool,hAPP(U_302,fun(U_302,bool),ord_less(U_302),U_300),U_301))
| 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_301),U_300))
| ~ linorder(U_302) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_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_70_linorder__less__linear]) ).
fof(f_133_2,plain,
! [U_305] :
( ! [U_304,U_303] :
( hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less(U_305),U_303),U_304))
| ti(U_305,U_304) = ti(U_305,U_303)
| hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less(U_305),U_304),U_303)) )
| ~ linorder(U_305) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less(U_305),U_303),U_304))
| ti(U_305,U_304) = ti(U_305,U_303)
| hBOOL(hAPP(U_305,bool,hAPP(U_305,fun(U_305,bool),ord_less(U_305),U_304),U_303))
| ~ linorder(U_305) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_1,plain,
! [X_a] :
( ! [X_1,Y_2] :
( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
| ( ti(X_a,X_1) != ti(X_a,Y_2)
& ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)) ) )
& ( ti(X_a,X_1) = ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) ) )
| ~ linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_71_not__less__iff__gr__or__eq]) ).
fof(f_134_2,plain,
! [U_308] :
( ! [U_307,U_306] :
( ( ~ hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_307),U_306))
| ( ti(U_308,U_307) != ti(U_308,U_306)
& ~ hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_306),U_307)) ) )
& ( ti(U_308,U_307) = ti(U_308,U_306)
| hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_306),U_307))
| hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_307),U_306)) ) )
| ~ linorder(U_308) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_308] :
( ( ! [U_312,U_310] :
( ~ hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_312),U_310))
| ( ti(U_308,U_312) != ti(U_308,U_310)
& ~ hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_310),U_312)) ) )
& ! [U_311,U_309] :
( ti(U_308,U_311) = ti(U_308,U_309)
| hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_309),U_311))
| hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_311),U_309)) ) )
| ~ linorder(U_308) ),
inference(miniscope,[status(thm)],[f_134_2]) ).
cnf(f_134_4,plain,
( ti(U_308,U_311) = ti(U_308,U_309)
| hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_309),U_311))
| hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_311),U_309))
| ~ linorder(U_308) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_5,plain,
( ~ hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_310),U_312))
| ~ hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_312),U_310))
| ~ linorder(U_308) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_6,plain,
( ti(U_308,U_312) != ti(U_308,U_310)
| ~ hBOOL(hAPP(U_308,bool,hAPP(U_308,fun(U_308,bool),ord_less(U_308),U_312),U_310))
| ~ linorder(U_308) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_1,plain,
! [X_a] :
( ! [X_1,Y_2] :
( ( ti(X_a,X_1) != ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
| ti(X_a,X_1) = ti(X_a,Y_2) ) )
| ~ linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_72_linorder__neq__iff]) ).
fof(f_135_2,plain,
! [U_315] :
( ! [U_314,U_313] :
( ( ti(U_315,U_314) != ti(U_315,U_313)
| ( ~ hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_313),U_314))
& ~ hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_314),U_313)) ) )
& ( hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_313),U_314))
| hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_314),U_313))
| ti(U_315,U_314) = ti(U_315,U_313) ) )
| ~ linorder(U_315) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_315] :
( ( ! [U_319,U_317] :
( ti(U_315,U_319) != ti(U_315,U_317)
| ( ~ hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_317),U_319))
& ~ hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_319),U_317)) ) )
& ! [U_318,U_316] :
( hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_316),U_318))
| hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_318),U_316))
| ti(U_315,U_318) = ti(U_315,U_316) ) )
| ~ linorder(U_315) ),
inference(miniscope,[status(thm)],[f_135_2]) ).
cnf(f_135_4,plain,
( hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_316),U_318))
| hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_318),U_316))
| ti(U_315,U_318) = ti(U_315,U_316)
| ~ linorder(U_315) ),
inference(clausify,[status(thm)],[f_135_3]) ).
cnf(f_135_5,plain,
( ~ hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_319),U_317))
| ti(U_315,U_319) != ti(U_315,U_317)
| ~ linorder(U_315) ),
inference(clausify,[status(thm)],[f_135_3]) ).
cnf(f_135_6,plain,
( ~ hBOOL(hAPP(U_315,bool,hAPP(U_315,fun(U_315,bool),ord_less(U_315),U_317),U_319))
| ti(U_315,U_319) != ti(U_315,U_317)
| ~ linorder(U_315) ),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_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_73_order__less__irrefl]) ).
fof(f_136_2,plain,
! [U_321] :
( ! [U_320] : ~ hBOOL(hAPP(U_321,bool,hAPP(U_321,fun(U_321,bool),ord_less(U_321),U_320),U_320))
| ~ preorder(U_321) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( ~ hBOOL(hAPP(U_321,bool,hAPP(U_321,fun(U_321,bool),ord_less(U_321),U_320),U_320))
| ~ preorder(U_321) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_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_74_UNIV__def]) ).
fof(f_137_2,plain,
! [U_322] : top_top(fun(U_322,bool)) = hAPP(fun(U_322,bool),fun(U_322,bool),collect(U_322),hAPP(bool,fun(U_322,bool),combk(bool,U_322),fTrue)),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
top_top(fun(U_322,bool)) = hAPP(fun(U_322,bool),fun(U_322,bool),collect(U_322),hAPP(bool,fun(U_322,bool),combk(bool,U_322),fTrue)),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_1,plain,
! [X_a,X_b,F,G] :
( ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G)
| ? [X_2] : hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,G,X_2) ),
inference(fof_nnf,[status(thm)],[fact_75_ext]) ).
fof(f_138_2,plain,
! [U_327,U_326,U_325,U_324] :
( ti(fun(U_327,U_326),U_325) = ti(fun(U_327,U_326),U_324)
| ? [U_323] : hAPP(U_327,U_326,U_325,U_323) != hAPP(U_327,U_326,U_324,U_323) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_327,U_326,U_325,U_324] :
( ti(fun(U_327,U_326),U_325) = ti(fun(U_327,U_326),U_324)
| hAPP(U_327,U_326,U_325,sK26(U_327,U_326,U_325,U_324)) != hAPP(U_327,U_326,U_324,sK26(U_327,U_326,U_325,U_324)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_323,sK26(U_327,U_326,U_325,U_324))],[f_138_2]) ).
cnf(f_138_4,plain,
( ti(fun(U_327,U_326),U_325) = ti(fun(U_327,U_326),U_324)
| hAPP(U_327,U_326,U_325,sK26(U_327,U_326,U_325,U_324)) != hAPP(U_327,U_326,U_324,sK26(U_327,U_326,U_325,U_324)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
! [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),A_1))
| ~ hBOOL(hAPP(X_a,bool,A_1,X_1)) )
& ( hBOOL(hAPP(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_76_mem__def]) ).
fof(f_139_2,plain,
! [U_330,U_329,U_328] :
( ( hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),U_329),U_328))
| ~ hBOOL(hAPP(U_330,bool,U_328,U_329)) )
& ( hBOOL(hAPP(U_330,bool,U_328,U_329))
| ~ hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),U_329),U_328)) ) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
( ! [U_336,U_334,U_332] :
( hBOOL(hAPP(fun(U_336,bool),bool,hAPP(U_336,fun(fun(U_336,bool),bool),member(U_336),U_334),U_332))
| ~ hBOOL(hAPP(U_336,bool,U_332,U_334)) )
& ! [U_335,U_333,U_331] :
( hBOOL(hAPP(U_335,bool,U_331,U_333))
| ~ hBOOL(hAPP(fun(U_335,bool),bool,hAPP(U_335,fun(fun(U_335,bool),bool),member(U_335),U_333),U_331)) ) ),
inference(miniscope,[status(thm)],[f_139_2]) ).
cnf(f_139_4,plain,
( hBOOL(hAPP(U_335,bool,U_331,U_333))
| ~ hBOOL(hAPP(fun(U_335,bool),bool,hAPP(U_335,fun(fun(U_335,bool),bool),member(U_335),U_333),U_331)) ),
inference(clausify,[status(thm)],[f_139_3]) ).
cnf(f_139_5,plain,
( hBOOL(hAPP(fun(U_336,bool),bool,hAPP(U_336,fun(fun(U_336,bool),bool),member(U_336),U_334),U_332))
| ~ hBOOL(hAPP(U_336,bool,U_332,U_334)) ),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_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_140_2,plain,
! [U_338,U_337] : hAPP(fun(U_338,bool),fun(U_338,bool),collect(U_338),U_337) = ti(fun(U_338,bool),U_337),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
hAPP(fun(U_338,bool),fun(U_338,bool),collect(U_338),U_337) = ti(fun(U_338,bool),U_337),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_1,plain,
! [X_1,Y_2,L_3,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_3),Aa),Ba)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
& ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Ba) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Aa)),L_3))
& ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Aa)
& ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Ba) ) )
& ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Ba) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Y_2)),L_3))
& ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Ba) )
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Y_2) )
& ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
| ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Ba) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Aa)),L_3))
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa)
| ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Ba) ) )
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Ba) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Y_2)),L_3))
| ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Ba) )
& ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_3),Aa),Ba))) ) )
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_78_in__above]) ).
fof(f_141_2,plain,
! [U_343,U_342,U_341,U_340,U_339] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),U_341))
& ti(arrow_490897120le_alt,U_342) != ti(arrow_490897120le_alt,U_339) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_340)),U_341))
& ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_340)
& ti(arrow_490897120le_alt,U_342) = ti(arrow_490897120le_alt,U_339) ) )
& ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_339) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_340),U_342)),U_341))
& ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339) )
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342) )
& ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),U_341))
| ti(arrow_490897120le_alt,U_342) = ti(arrow_490897120le_alt,U_339) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_340)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_340)
| ti(arrow_490897120le_alt,U_342) != ti(arrow_490897120le_alt,U_339) ) )
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_340),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_339) )
& ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_342) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339))) ) )
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_342)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_4,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_340),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_339)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_5,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_340)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_340)
| ti(arrow_490897120le_alt,U_342) != ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),U_341))
| ti(arrow_490897120le_alt,U_342) = ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_7,plain,
( ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_8,plain,
( ti(arrow_490897120le_alt,U_342) != ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_342) = ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),U_341))
| ti(arrow_490897120le_alt,U_342) = ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_10,plain,
( ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_340)
| ti(arrow_490897120le_alt,U_342) != ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_340)),U_341))
| ti(arrow_490897120le_alt,U_342) != ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_12,plain,
( ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_340)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_340)),U_341))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_14,plain,
( ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_339)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_340),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_15,plain,
( ti(arrow_490897120le_alt,U_342) != ti(arrow_490897120le_alt,U_339)
| ti(arrow_490897120le_alt,U_342) = ti(arrow_490897120le_alt,U_339)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_340),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_16,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),U_341))
| ti(arrow_490897120le_alt,U_342) = ti(arrow_490897120le_alt,U_339)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_340),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_17,plain,
( ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_340)
| ti(arrow_490897120le_alt,U_342) != ti(arrow_490897120le_alt,U_339)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_340),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_18,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_340)),U_341))
| ti(arrow_490897120le_alt,U_342) != ti(arrow_490897120le_alt,U_339)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_340),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_19,plain,
( ti(arrow_490897120le_alt,U_343) != ti(arrow_490897120le_alt,U_340)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),U_341))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_340),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_20,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_340)),U_341))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),U_341))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_340),U_342)),U_341))
| ti(arrow_490897120le_alt,U_343) = ti(arrow_490897120le_alt,U_342)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_343),U_342)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,U_341),U_340),U_339)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_341),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_340) = ti(arrow_490897120le_alt,U_339) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_1,plain,
! [X_a,X_b,S_1,R_1] :
( ( ! [X_2,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_2),Xa)),R_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),Xa)),S_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),Xa)),S_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),Xa)),R_1)) ) )
| ti(fun(product_prod(X_a,X_b),bool),R_1) != ti(fun(product_prod(X_a,X_b),bool),S_1) )
& ( ti(fun(product_prod(X_a,X_b),bool),R_1) = ti(fun(product_prod(X_a,X_b),bool),S_1)
| ? [X_2,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_2),Xa)),R_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),Xa)),S_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),Xa)),S_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),Xa)),R_1)) ) ) ) ),
inference(fof_nnf,[status(thm)],[fact_79_pred__equals__eq2]) ).
fof(f_142_2,plain,
! [U_351,U_350,U_349,U_348] :
( ( ! [U_347,U_346] :
( ( hBOOL(hAPP(fun(product_prod(U_351,U_350),bool),bool,hAPP(product_prod(U_351,U_350),fun(fun(product_prod(U_351,U_350),bool),bool),member(product_prod(U_351,U_350)),hAPP(U_350,product_prod(U_351,U_350),hAPP(U_351,fun(U_350,product_prod(U_351,U_350)),product_Pair(U_351,U_350),U_347),U_346)),U_348))
| ~ hBOOL(hAPP(fun(product_prod(U_351,U_350),bool),bool,hAPP(product_prod(U_351,U_350),fun(fun(product_prod(U_351,U_350),bool),bool),member(product_prod(U_351,U_350)),hAPP(U_350,product_prod(U_351,U_350),hAPP(U_351,fun(U_350,product_prod(U_351,U_350)),product_Pair(U_351,U_350),U_347),U_346)),U_349)) )
& ( hBOOL(hAPP(fun(product_prod(U_351,U_350),bool),bool,hAPP(product_prod(U_351,U_350),fun(fun(product_prod(U_351,U_350),bool),bool),member(product_prod(U_351,U_350)),hAPP(U_350,product_prod(U_351,U_350),hAPP(U_351,fun(U_350,product_prod(U_351,U_350)),product_Pair(U_351,U_350),U_347),U_346)),U_349))
| ~ hBOOL(hAPP(fun(product_prod(U_351,U_350),bool),bool,hAPP(product_prod(U_351,U_350),fun(fun(product_prod(U_351,U_350),bool),bool),member(product_prod(U_351,U_350)),hAPP(U_350,product_prod(U_351,U_350),hAPP(U_351,fun(U_350,product_prod(U_351,U_350)),product_Pair(U_351,U_350),U_347),U_346)),U_348)) ) )
| ti(fun(product_prod(U_351,U_350),bool),U_348) != ti(fun(product_prod(U_351,U_350),bool),U_349) )
& ( ti(fun(product_prod(U_351,U_350),bool),U_348) = ti(fun(product_prod(U_351,U_350),bool),U_349)
| ? [U_345,U_344] :
( ( ~ hBOOL(hAPP(fun(product_prod(U_351,U_350),bool),bool,hAPP(product_prod(U_351,U_350),fun(fun(product_prod(U_351,U_350),bool),bool),member(product_prod(U_351,U_350)),hAPP(U_350,product_prod(U_351,U_350),hAPP(U_351,fun(U_350,product_prod(U_351,U_350)),product_Pair(U_351,U_350),U_345),U_344)),U_348))
& hBOOL(hAPP(fun(product_prod(U_351,U_350),bool),bool,hAPP(product_prod(U_351,U_350),fun(fun(product_prod(U_351,U_350),bool),bool),member(product_prod(U_351,U_350)),hAPP(U_350,product_prod(U_351,U_350),hAPP(U_351,fun(U_350,product_prod(U_351,U_350)),product_Pair(U_351,U_350),U_345),U_344)),U_349)) )
| ( ~ hBOOL(hAPP(fun(product_prod(U_351,U_350),bool),bool,hAPP(product_prod(U_351,U_350),fun(fun(product_prod(U_351,U_350),bool),bool),member(product_prod(U_351,U_350)),hAPP(U_350,product_prod(U_351,U_350),hAPP(U_351,fun(U_350,product_prod(U_351,U_350)),product_Pair(U_351,U_350),U_345),U_344)),U_349))
& hBOOL(hAPP(fun(product_prod(U_351,U_350),bool),bool,hAPP(product_prod(U_351,U_350),fun(fun(product_prod(U_351,U_350),bool),bool),member(product_prod(U_351,U_350)),hAPP(U_350,product_prod(U_351,U_350),hAPP(U_351,fun(U_350,product_prod(U_351,U_350)),product_Pair(U_351,U_350),U_345),U_344)),U_348)) ) ) ) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
( ! [U_367,U_365,U_363,U_361] :
( ( ! [U_359,U_357] :
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_361))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_363)) )
& ! [U_358,U_356] :
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_363))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_361)) ) )
| ti(fun(product_prod(U_367,U_365),bool),U_361) != ti(fun(product_prod(U_367,U_365),bool),U_363) )
& ! [U_366,U_364,U_362,U_360] :
( ti(fun(product_prod(U_366,U_364),bool),U_360) = ti(fun(product_prod(U_366,U_364),bool),U_362)
| ? [U_355,U_353] :
( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),U_355),U_353)),U_360))
& hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),U_355),U_353)),U_362)) )
| ? [U_354,U_352] :
( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),U_354),U_352)),U_362))
& hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),U_354),U_352)),U_360)) ) ) ),
inference(miniscope,[status(thm)],[f_142_2]) ).
fof(f_142_4,plain,
( ! [U_367,U_365,U_363,U_361] :
( ( ! [U_359,U_357] :
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_361))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_363)) )
& ! [U_358,U_356] :
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_363))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_361)) ) )
| ti(fun(product_prod(U_367,U_365),bool),U_361) != ti(fun(product_prod(U_367,U_365),bool),U_363) )
& ! [U_366,U_364,U_362,U_360] :
( ti(fun(product_prod(U_366,U_364),bool),U_360) = ti(fun(product_prod(U_366,U_364),bool),U_362)
| ? [U_355,U_353] :
( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),U_355),U_353)),U_360))
& hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),U_355),U_353)),U_362)) )
| ? [U_352] :
( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),U_352)),U_362))
& hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),U_352)),U_360)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_354,sK27(U_366,U_364,U_362,U_360))],[f_142_3]) ).
fof(f_142_5,plain,
( ! [U_367,U_365,U_363,U_361] :
( ( ! [U_359,U_357] :
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_361))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_363)) )
& ! [U_358,U_356] :
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_363))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_361)) ) )
| ti(fun(product_prod(U_367,U_365),bool),U_361) != ti(fun(product_prod(U_367,U_365),bool),U_363) )
& ! [U_366,U_364,U_362,U_360] :
( ti(fun(product_prod(U_366,U_364),bool),U_360) = ti(fun(product_prod(U_366,U_364),bool),U_362)
| ? [U_355,U_353] :
( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),U_355),U_353)),U_360))
& hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),U_355),U_353)),U_362)) )
| ( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),sK28(U_366,U_364,U_362,U_360))),U_362))
& hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),sK28(U_366,U_364,U_362,U_360))),U_360)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_352,sK28(U_366,U_364,U_362,U_360))],[f_142_4]) ).
fof(f_142_6,plain,
( ! [U_367,U_365,U_363,U_361] :
( ( ! [U_359,U_357] :
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_361))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_363)) )
& ! [U_358,U_356] :
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_363))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_361)) ) )
| ti(fun(product_prod(U_367,U_365),bool),U_361) != ti(fun(product_prod(U_367,U_365),bool),U_363) )
& ! [U_366,U_364,U_362,U_360] :
( ti(fun(product_prod(U_366,U_364),bool),U_360) = ti(fun(product_prod(U_366,U_364),bool),U_362)
| ? [U_353] :
( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK29(U_366,U_364,U_362,U_360)),U_353)),U_360))
& hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK29(U_366,U_364,U_362,U_360)),U_353)),U_362)) )
| ( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),sK28(U_366,U_364,U_362,U_360))),U_362))
& hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),sK28(U_366,U_364,U_362,U_360))),U_360)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_355,sK29(U_366,U_364,U_362,U_360))],[f_142_5]) ).
fof(f_142_7,plain,
( ! [U_367,U_365,U_363,U_361] :
( ( ! [U_359,U_357] :
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_361))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_363)) )
& ! [U_358,U_356] :
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_363))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_361)) ) )
| ti(fun(product_prod(U_367,U_365),bool),U_361) != ti(fun(product_prod(U_367,U_365),bool),U_363) )
& ! [U_366,U_364,U_362,U_360] :
( ti(fun(product_prod(U_366,U_364),bool),U_360) = ti(fun(product_prod(U_366,U_364),bool),U_362)
| ( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK29(U_366,U_364,U_362,U_360)),sK30(U_366,U_364,U_362,U_360))),U_360))
& hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK29(U_366,U_364,U_362,U_360)),sK30(U_366,U_364,U_362,U_360))),U_362)) )
| ( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),sK28(U_366,U_364,U_362,U_360))),U_362))
& hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),sK28(U_366,U_364,U_362,U_360))),U_360)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_353,sK30(U_366,U_364,U_362,U_360))],[f_142_6]) ).
cnf(f_142_8,plain,
( hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK29(U_366,U_364,U_362,U_360)),sK30(U_366,U_364,U_362,U_360))),U_362))
| hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),sK28(U_366,U_364,U_362,U_360))),U_360))
| ti(fun(product_prod(U_366,U_364),bool),U_360) = ti(fun(product_prod(U_366,U_364),bool),U_362) ),
inference(clausify,[status(thm)],[f_142_7]) ).
cnf(f_142_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK29(U_366,U_364,U_362,U_360)),sK30(U_366,U_364,U_362,U_360))),U_360))
| hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),sK28(U_366,U_364,U_362,U_360))),U_360))
| ti(fun(product_prod(U_366,U_364),bool),U_360) = ti(fun(product_prod(U_366,U_364),bool),U_362) ),
inference(clausify,[status(thm)],[f_142_7]) ).
cnf(f_142_10,plain,
( hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK29(U_366,U_364,U_362,U_360)),sK30(U_366,U_364,U_362,U_360))),U_362))
| ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),sK28(U_366,U_364,U_362,U_360))),U_362))
| ti(fun(product_prod(U_366,U_364),bool),U_360) = ti(fun(product_prod(U_366,U_364),bool),U_362) ),
inference(clausify,[status(thm)],[f_142_7]) ).
cnf(f_142_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK29(U_366,U_364,U_362,U_360)),sK30(U_366,U_364,U_362,U_360))),U_360))
| ~ hBOOL(hAPP(fun(product_prod(U_366,U_364),bool),bool,hAPP(product_prod(U_366,U_364),fun(fun(product_prod(U_366,U_364),bool),bool),member(product_prod(U_366,U_364)),hAPP(U_364,product_prod(U_366,U_364),hAPP(U_366,fun(U_364,product_prod(U_366,U_364)),product_Pair(U_366,U_364),sK27(U_366,U_364,U_362,U_360)),sK28(U_366,U_364,U_362,U_360))),U_362))
| ti(fun(product_prod(U_366,U_364),bool),U_360) = ti(fun(product_prod(U_366,U_364),bool),U_362) ),
inference(clausify,[status(thm)],[f_142_7]) ).
cnf(f_142_12,plain,
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_363))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_358),U_356)),U_361))
| ti(fun(product_prod(U_367,U_365),bool),U_361) != ti(fun(product_prod(U_367,U_365),bool),U_363) ),
inference(clausify,[status(thm)],[f_142_7]) ).
cnf(f_142_13,plain,
( hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_361))
| ~ hBOOL(hAPP(fun(product_prod(U_367,U_365),bool),bool,hAPP(product_prod(U_367,U_365),fun(fun(product_prod(U_367,U_365),bool),bool),member(product_prod(U_367,U_365)),hAPP(U_365,product_prod(U_367,U_365),hAPP(U_367,fun(U_365,product_prod(U_367,U_365)),product_Pair(U_367,U_365),U_359),U_357)),U_363))
| ti(fun(product_prod(U_367,U_365),bool),U_361) != ti(fun(product_prod(U_367,U_365),bool),U_363) ),
inference(clausify,[status(thm)],[f_142_7]) ).
fof(f_143_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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_80_n_I3_J]) ).
cnf(f_143_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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_143_1]) ).
fof(f_144_1,plain,
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ) ),
inference(fof_nnf,[status(thm)],[fact_81__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk]) ).
cnf(f_144_2,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
inference(clausify,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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_144_1]) ).
fof(f_145_1,plain,
! [I_2] :
( ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
| hAPP(arrow_660593299e_indi,nat,h,I_2) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,I_2) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
& hAPP(arrow_660593299e_indi,nat,h,I_2) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),c),e)))
& hAPP(arrow_660593299e_indi,nat,h,I_2) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I_2)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,I_2)),n)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_82__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).
fof(f_145_2,plain,
! [U_368] :
( ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_368)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_368) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_368)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_368) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_368)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_368)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_368)),n)) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_368)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_368)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_368)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_368)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_368)),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_368) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_368)),c),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_368) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_368)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_368)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_368)),n)) ) ) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
( ! [U_370] :
( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_370) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_370) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
& ! [U_369] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ) )
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_369) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),c),e)))
& hAPP(arrow_660593299e_indi,nat,h,U_369) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n)) ) ) ),
inference(miniscope,[status(thm)],[f_145_2]) ).
cnf(f_145_4,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_5,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_369) != n
| hAPP(arrow_660593299e_indi,nat,h,U_369) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_6,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_369) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_7,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_369) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_8,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_9,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_10,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_369) != n
| hAPP(arrow_660593299e_indi,nat,h,U_369) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_369) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_12,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_369) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_14,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_15,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_369) != n
| hAPP(arrow_660593299e_indi,nat,h,U_369) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_16,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_369) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_17,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_369) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_18,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_19,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_20,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_369) != n
| hAPP(arrow_660593299e_indi,nat,h,U_369) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_21,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_369) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_22,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_369) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_23,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_369)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_369)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_24,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),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_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_25,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_26,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_27,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_28,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),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_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_370) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_29,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_370) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_30,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),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_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_370) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_31,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_370) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_32,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_370) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_33,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_370) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_34,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_370) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_35,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_370)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_370) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_370)),n)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [X_a,X_b,X_1,Y_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),Y_2) = ti(X_a,X_1)
| hAPP(X_a,X_b,F,X_1) != ti(X_b,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)))) ),
inference(fof_nnf,[status(thm)],[fact_83_inv__f__eq]) ).
fof(f_146_2,plain,
! [U_375,U_374,U_373,U_372,U_371] :
( hAPP(U_374,U_375,hAPP(fun(U_375,U_374),fun(U_374,U_375),hAPP(fun(U_375,bool),fun(fun(U_375,U_374),fun(U_374,U_375)),hilbert_inv_into(U_375,U_374),top_top(fun(U_375,bool))),U_371),U_372) = ti(U_375,U_373)
| hAPP(U_375,U_374,U_371,U_373) != ti(U_374,U_372)
| ~ hBOOL(hAPP(fun(U_375,bool),bool,hAPP(fun(U_375,U_374),fun(fun(U_375,bool),bool),inj_on(U_375,U_374),U_371),top_top(fun(U_375,bool)))) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( hAPP(U_374,U_375,hAPP(fun(U_375,U_374),fun(U_374,U_375),hAPP(fun(U_375,bool),fun(fun(U_375,U_374),fun(U_374,U_375)),hilbert_inv_into(U_375,U_374),top_top(fun(U_375,bool))),U_371),U_372) = ti(U_375,U_373)
| hAPP(U_375,U_374,U_371,U_373) != ti(U_374,U_372)
| ~ hBOOL(hAPP(fun(U_375,bool),bool,hAPP(fun(U_375,U_374),fun(fun(U_375,bool),bool),inj_on(U_375,U_374),U_371),top_top(fun(U_375,bool)))) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
! [X_a,X_b,X_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),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),top_top(fun(X_a,bool)))) ),
inference(fof_nnf,[status(thm)],[fact_84_inv__f__f]) ).
fof(f_147_2,plain,
! [U_379,U_378,U_377,U_376] :
( hAPP(U_378,U_379,hAPP(fun(U_379,U_378),fun(U_378,U_379),hAPP(fun(U_379,bool),fun(fun(U_379,U_378),fun(U_378,U_379)),hilbert_inv_into(U_379,U_378),top_top(fun(U_379,bool))),U_376),hAPP(U_379,U_378,U_376,U_377)) = ti(U_379,U_377)
| ~ hBOOL(hAPP(fun(U_379,bool),bool,hAPP(fun(U_379,U_378),fun(fun(U_379,bool),bool),inj_on(U_379,U_378),U_376),top_top(fun(U_379,bool)))) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( hAPP(U_378,U_379,hAPP(fun(U_379,U_378),fun(U_378,U_379),hAPP(fun(U_379,bool),fun(fun(U_379,U_378),fun(U_378,U_379)),hilbert_inv_into(U_379,U_378),top_top(fun(U_379,bool))),U_376),hAPP(U_379,U_378,U_376,U_377)) = ti(U_379,U_377)
| ~ hBOOL(hAPP(fun(U_379,bool),bool,hAPP(fun(U_379,U_378),fun(fun(U_379,bool),bool),inj_on(U_379,U_378),U_376),top_top(fun(U_379,bool)))) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_1,plain,
! [I_1,Fa] :
( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_1))
| ? [X_2] :
( ? [A_3,B_2] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_3),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_1)))
& ti(arrow_490897120le_alt,A_3) != ti(arrow_490897120le_alt,B_2) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Fa),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
inference(fof_nnf,[status(thm)],[fact_85_dictatorI]) ).
fof(f_148_2,plain,
! [U_384,U_383] :
( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_383),U_384))
| ? [U_382] :
( ? [U_381,U_380] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_381),U_380)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_383,U_382)))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_381),U_380)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_382,U_384)))
& ti(arrow_490897120le_alt,U_381) != ti(arrow_490897120le_alt,U_380) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_382),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_383),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_384,U_383] :
( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_383),U_384))
| ( ? [U_381,U_380] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_381),U_380)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_383,sK31(U_384,U_383))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_381),U_380)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK31(U_384,U_383),U_384)))
& ti(arrow_490897120le_alt,U_381) != ti(arrow_490897120le_alt,U_380) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK31(U_384,U_383)),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_383),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_382,sK31(U_384,U_383))],[f_148_2]) ).
fof(f_148_4,plain,
! [U_384,U_383] :
( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_383),U_384))
| ( ? [U_380] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK32(U_384,U_383)),U_380)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_383,sK31(U_384,U_383))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK32(U_384,U_383)),U_380)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK31(U_384,U_383),U_384)))
& ti(arrow_490897120le_alt,sK32(U_384,U_383)) != ti(arrow_490897120le_alt,U_380) )
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK31(U_384,U_383)),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_383),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_381,sK32(U_384,U_383))],[f_148_3]) ).
fof(f_148_5,plain,
! [U_384,U_383] :
( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_383),U_384))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK32(U_384,U_383)),sK33(U_384,U_383))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_383,sK31(U_384,U_383))))
& hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK32(U_384,U_383)),sK33(U_384,U_383))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK31(U_384,U_383),U_384)))
& ti(arrow_490897120le_alt,sK32(U_384,U_383)) != ti(arrow_490897120le_alt,sK33(U_384,U_383))
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK31(U_384,U_383)),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_383),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_380,sK33(U_384,U_383))],[f_148_4]) ).
cnf(f_148_6,plain,
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK31(U_384,U_383)),arrow_1111136790e_Prof))
| hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_383),U_384))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_383),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
inference(clausify,[status(thm)],[f_148_5]) ).
cnf(f_148_7,plain,
( ti(arrow_490897120le_alt,sK32(U_384,U_383)) != ti(arrow_490897120le_alt,sK33(U_384,U_383))
| hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_383),U_384))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_383),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
inference(clausify,[status(thm)],[f_148_5]) ).
cnf(f_148_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK32(U_384,U_383)),sK33(U_384,U_383))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK31(U_384,U_383),U_384)))
| hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_383),U_384))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_383),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
inference(clausify,[status(thm)],[f_148_5]) ).
cnf(f_148_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sK32(U_384,U_383)),sK33(U_384,U_383))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_383,sK31(U_384,U_383))))
| hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_383),U_384))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_383),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
inference(clausify,[status(thm)],[f_148_5]) ).
fof(f_149_1,plain,
! [X_a,X_b,X_1,F,A_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))
| 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))) ),
inference(fof_nnf,[status(thm)],[fact_86_PiE]) ).
fof(f_149_2,plain,
! [U_390,U_389,U_388,U_387,U_386,U_385] :
( ~ hBOOL(hAPP(fun(U_390,bool),bool,hAPP(U_390,fun(fun(U_390,bool),bool),member(U_390),U_388),U_386))
| hBOOL(hAPP(fun(U_389,bool),bool,hAPP(U_389,fun(fun(U_389,bool),bool),member(U_389),hAPP(U_390,U_389,U_387,U_388)),hAPP(U_390,fun(U_389,bool),U_385,U_388)))
| ~ hBOOL(hAPP(fun(fun(U_390,U_389),bool),bool,hAPP(fun(U_390,U_389),fun(fun(fun(U_390,U_389),bool),bool),member(fun(U_390,U_389)),U_387),hAPP(fun(U_390,fun(U_389,bool)),fun(fun(U_390,U_389),bool),hAPP(fun(U_390,bool),fun(fun(U_390,fun(U_389,bool)),fun(fun(U_390,U_389),bool)),pi(U_390,U_389),U_386),U_385))) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
( ~ hBOOL(hAPP(fun(U_390,bool),bool,hAPP(U_390,fun(fun(U_390,bool),bool),member(U_390),U_388),U_386))
| hBOOL(hAPP(fun(U_389,bool),bool,hAPP(U_389,fun(fun(U_389,bool),bool),member(U_389),hAPP(U_390,U_389,U_387,U_388)),hAPP(U_390,fun(U_389,bool),U_385,U_388)))
| ~ hBOOL(hAPP(fun(fun(U_390,U_389),bool),bool,hAPP(fun(U_390,U_389),fun(fun(fun(U_390,U_389),bool),bool),member(fun(U_390,U_389)),U_387),hAPP(fun(U_390,fun(U_389,bool)),fun(fun(U_390,U_389),bool),hAPP(fun(U_390,bool),fun(fun(U_390,fun(U_389,bool)),fun(fun(U_390,U_389),bool)),pi(U_390,U_389),U_386),U_385))) ),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_1,plain,
! [Aa,Ba] :
( ? [X_2] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),X_2))
& hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X_2),arrow_2064824852le_Lin)) )
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_87_complete__Lin]) ).
fof(f_150_2,plain,
! [U_393,U_392] :
( ? [U_391] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_393),U_392)),U_391))
& hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_391),arrow_2064824852le_Lin)) )
| ti(arrow_490897120le_alt,U_393) = ti(arrow_490897120le_alt,U_392) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_393,U_392] :
( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_393),U_392)),sK34(U_393,U_392)))
& hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sK34(U_393,U_392)),arrow_2064824852le_Lin)) )
| ti(arrow_490897120le_alt,U_393) = ti(arrow_490897120le_alt,U_392) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_391,sK34(U_393,U_392))],[f_150_2]) ).
cnf(f_150_4,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sK34(U_393,U_392)),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_393) = ti(arrow_490897120le_alt,U_392) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_5,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_393),U_392)),sK34(U_393,U_392)))
| ti(arrow_490897120le_alt,U_393) = ti(arrow_490897120le_alt,U_392) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_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_88_Pi__UNIV]) ).
fof(f_151_2,plain,
! [U_396,U_395,U_394] : hAPP(fun(U_396,fun(U_395,bool)),fun(fun(U_396,U_395),bool),hAPP(fun(U_396,bool),fun(fun(U_396,fun(U_395,bool)),fun(fun(U_396,U_395),bool)),pi(U_396,U_395),U_394),hAPP(fun(U_395,bool),fun(U_396,fun(U_395,bool)),combk(fun(U_395,bool),U_396),top_top(fun(U_395,bool)))) = top_top(fun(fun(U_396,U_395),bool)),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
hAPP(fun(U_396,fun(U_395,bool)),fun(fun(U_396,U_395),bool),hAPP(fun(U_396,bool),fun(fun(U_396,fun(U_395,bool)),fun(fun(U_396,U_395),bool)),pi(U_396,U_395),U_394),hAPP(fun(U_395,bool),fun(U_396,fun(U_395,bool)),combk(fun(U_395,bool),U_396),top_top(fun(U_395,bool)))) = top_top(fun(fun(U_396,U_395),bool)),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_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_89_inj__fun]) ).
fof(f_152_2,plain,
! [U_400,U_399,U_398,U_397] :
( hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,fun(U_400,U_398)),fun(fun(U_399,bool),bool),inj_on(U_399,fun(U_400,U_398)),hAPP(fun(U_399,U_398),fun(U_399,fun(U_400,U_398)),hAPP(fun(U_398,fun(U_400,U_398)),fun(fun(U_399,U_398),fun(U_399,fun(U_400,U_398))),combb(U_398,fun(U_400,U_398),U_399),combk(U_398,U_400)),U_397)),top_top(fun(U_399,bool))))
| ~ hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,U_398),fun(fun(U_399,bool),bool),inj_on(U_399,U_398),U_397),top_top(fun(U_399,bool)))) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,fun(U_400,U_398)),fun(fun(U_399,bool),bool),inj_on(U_399,fun(U_400,U_398)),hAPP(fun(U_399,U_398),fun(U_399,fun(U_400,U_398)),hAPP(fun(U_398,fun(U_400,U_398)),fun(fun(U_399,U_398),fun(U_399,fun(U_400,U_398))),combb(U_398,fun(U_400,U_398),U_399),combk(U_398,U_400)),U_397)),top_top(fun(U_399,bool))))
| ~ hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,U_398),fun(fun(U_399,bool),bool),inj_on(U_399,U_398),U_397),top_top(fun(U_399,bool)))) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_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_90_order__refl]) ).
fof(f_153_2,plain,
! [U_402] :
( ! [U_401] : hBOOL(hAPP(U_402,bool,hAPP(U_402,fun(U_402,bool),ord_less_eq(U_402),U_401),U_401))
| ~ preorder(U_402) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
( hBOOL(hAPP(U_402,bool,hAPP(U_402,fun(U_402,bool),ord_less_eq(U_402),U_401),U_401))
| ~ preorder(U_402) ),
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_1,plain,
? [N] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))))),lab)),lba))))
& ! [M] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),M))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))) ),
inference(fof_nnf,[status(thm)],[fact_91__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_]) ).
fof(f_154_2,plain,
? [U_404] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_404),one_one(nat))))),lab)),lba))))
& ! [U_403] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),U_403))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_403),U_404)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_404),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK35),one_one(nat))))),lab)),lba))))
& ! [U_403] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),U_403))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_403),sK35)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK35),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_404,sK35)],[f_154_2]) ).
cnf(f_154_4,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK35),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
inference(clausify,[status(thm)],[f_154_3]) ).
cnf(f_154_5,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),U_403))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_403),sK35)) ),
inference(clausify,[status(thm)],[f_154_3]) ).
cnf(f_154_6,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK35),one_one(nat))))),lab)),lba)))),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_1,plain,
? [N] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))))),lab)),lba))))
& ! [M] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),M))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))) ),
inference(fof_nnf,[status(thm)],[fact_92__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O]) ).
fof(f_155_2,plain,
? [U_406] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_406),one_one(nat))))),lab)),lba))))
& ! [U_405] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),U_405))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_405),U_406)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_406),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK36),one_one(nat))))),lab)),lba))))
& ! [U_405] :
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),U_405))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_405),sK36)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK36),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_406,sK36)],[f_155_2]) ).
cnf(f_155_4,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK36),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_5,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),U_405))),lab)),lba))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_405),sK36)) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_6,plain,
hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_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_155_3]) ).
fof(f_156_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_93_linorder__le__cases]) ).
fof(f_156_2,plain,
! [U_409] :
( ! [U_408,U_407] :
( hBOOL(hAPP(U_409,bool,hAPP(U_409,fun(U_409,bool),ord_less_eq(U_409),U_407),U_408))
| hBOOL(hAPP(U_409,bool,hAPP(U_409,fun(U_409,bool),ord_less_eq(U_409),U_408),U_407)) )
| ~ linorder(U_409) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( hBOOL(hAPP(U_409,bool,hAPP(U_409,fun(U_409,bool),ord_less_eq(U_409),U_407),U_408))
| hBOOL(hAPP(U_409,bool,hAPP(U_409,fun(U_409,bool),ord_less_eq(U_409),U_408),U_407))
| ~ linorder(U_409) ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_1,plain,
! [X_a,X_b] :
( ! [X_1,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_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_94_le__funE]) ).
fof(f_157_2,plain,
! [U_414,U_413] :
( ! [U_412,U_411,U_410] :
( hBOOL(hAPP(U_413,bool,hAPP(U_413,fun(U_413,bool),ord_less_eq(U_413),hAPP(U_414,U_413,U_411,U_412)),hAPP(U_414,U_413,U_410,U_412)))
| ~ hBOOL(hAPP(fun(U_414,U_413),bool,hAPP(fun(U_414,U_413),fun(fun(U_414,U_413),bool),ord_less_eq(fun(U_414,U_413)),U_411),U_410)) )
| ~ ord(U_413) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( hBOOL(hAPP(U_413,bool,hAPP(U_413,fun(U_413,bool),ord_less_eq(U_413),hAPP(U_414,U_413,U_411,U_412)),hAPP(U_414,U_413,U_410,U_412)))
| ~ hBOOL(hAPP(fun(U_414,U_413),bool,hAPP(fun(U_414,U_413),fun(fun(U_414,U_413),bool),ord_less_eq(fun(U_414,U_413)),U_411),U_410))
| ~ ord(U_413) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
! [X_a] :
( ! [Z_1,Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),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_95_xt1_I6_J]) ).
fof(f_158_2,plain,
! [U_418] :
( ! [U_417,U_416,U_415] :
( hBOOL(hAPP(U_418,bool,hAPP(U_418,fun(U_418,bool),ord_less_eq(U_418),U_417),U_415))
| ~ hBOOL(hAPP(U_418,bool,hAPP(U_418,fun(U_418,bool),ord_less_eq(U_418),U_417),U_416))
| ~ hBOOL(hAPP(U_418,bool,hAPP(U_418,fun(U_418,bool),ord_less_eq(U_418),U_416),U_415)) )
| ~ order(U_418) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( hBOOL(hAPP(U_418,bool,hAPP(U_418,fun(U_418,bool),ord_less_eq(U_418),U_417),U_415))
| ~ hBOOL(hAPP(U_418,bool,hAPP(U_418,fun(U_418,bool),ord_less_eq(U_418),U_417),U_416))
| ~ hBOOL(hAPP(U_418,bool,hAPP(U_418,fun(U_418,bool),ord_less_eq(U_418),U_416),U_415))
| ~ order(U_418) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_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_96_xt1_I5_J]) ).
fof(f_159_2,plain,
! [U_421] :
( ! [U_420,U_419] :
( ti(U_421,U_419) = ti(U_421,U_420)
| ~ hBOOL(hAPP(U_421,bool,hAPP(U_421,fun(U_421,bool),ord_less_eq(U_421),U_419),U_420))
| ~ hBOOL(hAPP(U_421,bool,hAPP(U_421,fun(U_421,bool),ord_less_eq(U_421),U_420),U_419)) )
| ~ order(U_421) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( ti(U_421,U_419) = ti(U_421,U_420)
| ~ hBOOL(hAPP(U_421,bool,hAPP(U_421,fun(U_421,bool),ord_less_eq(U_421),U_419),U_420))
| ~ hBOOL(hAPP(U_421,bool,hAPP(U_421,fun(U_421,bool),ord_less_eq(U_421),U_420),U_419))
| ~ order(U_421) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
! [X_a] :
( ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))
| ~ 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_97_order__trans]) ).
fof(f_160_2,plain,
! [U_425] :
( ! [U_424,U_423,U_422] :
( hBOOL(hAPP(U_425,bool,hAPP(U_425,fun(U_425,bool),ord_less_eq(U_425),U_423),U_424))
| ~ hBOOL(hAPP(U_425,bool,hAPP(U_425,fun(U_425,bool),ord_less_eq(U_425),U_422),U_424))
| ~ hBOOL(hAPP(U_425,bool,hAPP(U_425,fun(U_425,bool),ord_less_eq(U_425),U_423),U_422)) )
| ~ preorder(U_425) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
( hBOOL(hAPP(U_425,bool,hAPP(U_425,fun(U_425,bool),ord_less_eq(U_425),U_423),U_424))
| ~ hBOOL(hAPP(U_425,bool,hAPP(U_425,fun(U_425,bool),ord_less_eq(U_425),U_422),U_424))
| ~ hBOOL(hAPP(U_425,bool,hAPP(U_425,fun(U_425,bool),ord_less_eq(U_425),U_423),U_422))
| ~ preorder(U_425) ),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_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_98_order__antisym]) ).
fof(f_161_2,plain,
! [U_428] :
( ! [U_427,U_426] :
( ti(U_428,U_427) = ti(U_428,U_426)
| ~ hBOOL(hAPP(U_428,bool,hAPP(U_428,fun(U_428,bool),ord_less_eq(U_428),U_426),U_427))
| ~ hBOOL(hAPP(U_428,bool,hAPP(U_428,fun(U_428,bool),ord_less_eq(U_428),U_427),U_426)) )
| ~ order(U_428) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( ti(U_428,U_427) = ti(U_428,U_426)
| ~ hBOOL(hAPP(U_428,bool,hAPP(U_428,fun(U_428,bool),ord_less_eq(U_428),U_426),U_427))
| ~ hBOOL(hAPP(U_428,bool,hAPP(U_428,fun(U_428,bool),ord_less_eq(U_428),U_427),U_426))
| ~ order(U_428) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_1,plain,
! [X_a] :
( ! [C,B_1,A_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_2))
| ti(X_a,B_1) != ti(X_a,C)
| ~ 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_99_xt1_I4_J]) ).
fof(f_162_2,plain,
! [U_432] :
( ! [U_431,U_430,U_429] :
( hBOOL(hAPP(U_432,bool,hAPP(U_432,fun(U_432,bool),ord_less_eq(U_432),U_431),U_429))
| ti(U_432,U_430) != ti(U_432,U_431)
| ~ hBOOL(hAPP(U_432,bool,hAPP(U_432,fun(U_432,bool),ord_less_eq(U_432),U_430),U_429)) )
| ~ order(U_432) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( hBOOL(hAPP(U_432,bool,hAPP(U_432,fun(U_432,bool),ord_less_eq(U_432),U_431),U_429))
| ti(U_432,U_430) != ti(U_432,U_431)
| ~ hBOOL(hAPP(U_432,bool,hAPP(U_432,fun(U_432,bool),ord_less_eq(U_432),U_430),U_429))
| ~ order(U_432) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_1,plain,
! [X_a] :
( ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C))
| B_1 != C
| ~ 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_100_ord__le__eq__trans]) ).
fof(f_163_2,plain,
! [U_436] :
( ! [U_435,U_434,U_433] :
( hBOOL(hAPP(U_436,bool,hAPP(U_436,fun(U_436,bool),ord_less_eq(U_436),U_434),U_435))
| U_433 != U_435
| ~ hBOOL(hAPP(U_436,bool,hAPP(U_436,fun(U_436,bool),ord_less_eq(U_436),U_434),U_433)) )
| ~ ord(U_436) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( hBOOL(hAPP(U_436,bool,hAPP(U_436,fun(U_436,bool),ord_less_eq(U_436),U_434),U_435))
| U_433 != U_435
| ~ hBOOL(hAPP(U_436,bool,hAPP(U_436,fun(U_436,bool),ord_less_eq(U_436),U_434),U_433))
| ~ ord(U_436) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_1,plain,
! [X_a] :
( ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_2))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B_1))
| ti(X_a,A_2) != ti(X_a,B_1) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_101_xt1_I3_J]) ).
fof(f_164_2,plain,
! [U_440] :
( ! [U_439,U_438,U_437] :
( hBOOL(hAPP(U_440,bool,hAPP(U_440,fun(U_440,bool),ord_less_eq(U_440),U_439),U_438))
| ~ hBOOL(hAPP(U_440,bool,hAPP(U_440,fun(U_440,bool),ord_less_eq(U_440),U_439),U_437))
| ti(U_440,U_438) != ti(U_440,U_437) )
| ~ order(U_440) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( hBOOL(hAPP(U_440,bool,hAPP(U_440,fun(U_440,bool),ord_less_eq(U_440),U_439),U_438))
| ~ hBOOL(hAPP(U_440,bool,hAPP(U_440,fun(U_440,bool),ord_less_eq(U_440),U_439),U_437))
| ti(U_440,U_438) != ti(U_440,U_437)
| ~ order(U_440) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
! [X_a] :
( ! [C,A_2,B_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C))
| A_2 != B_1 )
| ~ ord(X_a) ),
inference(fof_nnf,[status(thm)],[fact_102_ord__eq__le__trans]) ).
fof(f_165_2,plain,
! [U_444] :
( ! [U_443,U_442,U_441] :
( hBOOL(hAPP(U_444,bool,hAPP(U_444,fun(U_444,bool),ord_less_eq(U_444),U_442),U_443))
| ~ hBOOL(hAPP(U_444,bool,hAPP(U_444,fun(U_444,bool),ord_less_eq(U_444),U_441),U_443))
| U_442 != U_441 )
| ~ ord(U_444) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( hBOOL(hAPP(U_444,bool,hAPP(U_444,fun(U_444,bool),ord_less_eq(U_444),U_442),U_443))
| ~ hBOOL(hAPP(U_444,bool,hAPP(U_444,fun(U_444,bool),ord_less_eq(U_444),U_441),U_443))
| U_442 != U_441
| ~ ord(U_444) ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_1,plain,
! [X_a] :
( ! [Y_2,X_1] :
( ( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2))
| ti(X_a,X_1) != ti(X_a,Y_2) )
& ( ti(X_a,X_1) = ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_1)) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_103_order__antisym__conv]) ).
fof(f_166_2,plain,
! [U_447] :
( ! [U_446,U_445] :
( ( ( hBOOL(hAPP(U_447,bool,hAPP(U_447,fun(U_447,bool),ord_less_eq(U_447),U_445),U_446))
| ti(U_447,U_445) != ti(U_447,U_446) )
& ( ti(U_447,U_445) = ti(U_447,U_446)
| ~ hBOOL(hAPP(U_447,bool,hAPP(U_447,fun(U_447,bool),ord_less_eq(U_447),U_445),U_446)) ) )
| ~ hBOOL(hAPP(U_447,bool,hAPP(U_447,fun(U_447,bool),ord_less_eq(U_447),U_446),U_445)) )
| ~ order(U_447) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( ti(U_447,U_445) = ti(U_447,U_446)
| ~ hBOOL(hAPP(U_447,bool,hAPP(U_447,fun(U_447,bool),ord_less_eq(U_447),U_445),U_446))
| ~ hBOOL(hAPP(U_447,bool,hAPP(U_447,fun(U_447,bool),ord_less_eq(U_447),U_446),U_445))
| ~ order(U_447) ),
inference(clausify,[status(thm)],[f_166_2]) ).
cnf(f_166_4,plain,
( hBOOL(hAPP(U_447,bool,hAPP(U_447,fun(U_447,bool),ord_less_eq(U_447),U_445),U_446))
| ti(U_447,U_445) != ti(U_447,U_446)
| ~ hBOOL(hAPP(U_447,bool,hAPP(U_447,fun(U_447,bool),ord_less_eq(U_447),U_446),U_445))
| ~ order(U_447) ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
! [X_a,X_b] :
( ! [X_1,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_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_104_le__funD]) ).
fof(f_167_2,plain,
! [U_452,U_451] :
( ! [U_450,U_449,U_448] :
( hBOOL(hAPP(U_451,bool,hAPP(U_451,fun(U_451,bool),ord_less_eq(U_451),hAPP(U_452,U_451,U_449,U_450)),hAPP(U_452,U_451,U_448,U_450)))
| ~ hBOOL(hAPP(fun(U_452,U_451),bool,hAPP(fun(U_452,U_451),fun(fun(U_452,U_451),bool),ord_less_eq(fun(U_452,U_451)),U_449),U_448)) )
| ~ ord(U_451) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( hBOOL(hAPP(U_451,bool,hAPP(U_451,fun(U_451,bool),ord_less_eq(U_451),hAPP(U_452,U_451,U_449,U_450)),hAPP(U_452,U_451,U_448,U_450)))
| ~ hBOOL(hAPP(fun(U_452,U_451),bool,hAPP(fun(U_452,U_451),fun(fun(U_452,U_451),bool),ord_less_eq(fun(U_452,U_451)),U_449),U_448))
| ~ ord(U_451) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_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_105_order__eq__refl]) ).
fof(f_168_2,plain,
! [U_455] :
( ! [U_454,U_453] :
( hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),U_454),U_453))
| U_454 != U_453 )
| ~ preorder(U_455) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( hBOOL(hAPP(U_455,bool,hAPP(U_455,fun(U_455,bool),ord_less_eq(U_455),U_454),U_453))
| U_454 != U_453
| ~ preorder(U_455) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
! [X_a] :
( ! [X_1,Y_2] :
( ( ti(X_a,X_1) = ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2)) )
| ti(X_a,X_1) != ti(X_a,Y_2) ) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_106_order__eq__iff]) ).
fof(f_169_2,plain,
! [U_458] :
( ! [U_457,U_456] :
( ( ti(U_458,U_457) = ti(U_458,U_456)
| ~ hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_456),U_457))
| ~ hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_457),U_456)) )
& ( ( hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_456),U_457))
& hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_457),U_456)) )
| ti(U_458,U_457) != ti(U_458,U_456) ) )
| ~ order(U_458) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_458] :
( ( ! [U_462,U_460] :
( ti(U_458,U_462) = ti(U_458,U_460)
| ~ hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_460),U_462))
| ~ hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_462),U_460)) )
& ! [U_461,U_459] :
( ( hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_459),U_461))
& hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_461),U_459)) )
| ti(U_458,U_461) != ti(U_458,U_459) ) )
| ~ order(U_458) ),
inference(miniscope,[status(thm)],[f_169_2]) ).
cnf(f_169_4,plain,
( hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_461),U_459))
| ti(U_458,U_461) != ti(U_458,U_459)
| ~ order(U_458) ),
inference(clausify,[status(thm)],[f_169_3]) ).
cnf(f_169_5,plain,
( hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_459),U_461))
| ti(U_458,U_461) != ti(U_458,U_459)
| ~ order(U_458) ),
inference(clausify,[status(thm)],[f_169_3]) ).
cnf(f_169_6,plain,
( ti(U_458,U_462) = ti(U_458,U_460)
| ~ hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_460),U_462))
| ~ hBOOL(hAPP(U_458,bool,hAPP(U_458,fun(U_458,bool),ord_less_eq(U_458),U_462),U_460))
| ~ order(U_458) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_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_107_linorder__linear]) ).
fof(f_170_2,plain,
! [U_465] :
( ! [U_464,U_463] :
( hBOOL(hAPP(U_465,bool,hAPP(U_465,fun(U_465,bool),ord_less_eq(U_465),U_463),U_464))
| hBOOL(hAPP(U_465,bool,hAPP(U_465,fun(U_465,bool),ord_less_eq(U_465),U_464),U_463)) )
| ~ linorder(U_465) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( hBOOL(hAPP(U_465,bool,hAPP(U_465,fun(U_465,bool),ord_less_eq(U_465),U_463),U_464))
| hBOOL(hAPP(U_465,bool,hAPP(U_465,fun(U_465,bool),ord_less_eq(U_465),U_464),U_463))
| ~ linorder(U_465) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_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_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_2)),hAPP(X_a,X_b,G,X_2))) )
& ( ! [X_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_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_108_le__fun__def]) ).
fof(f_171_2,plain,
! [U_471,U_470] :
( ! [U_469,U_468] :
( ( hBOOL(hAPP(fun(U_471,U_470),bool,hAPP(fun(U_471,U_470),fun(fun(U_471,U_470),bool),ord_less_eq(fun(U_471,U_470)),U_469),U_468))
| ? [U_467] : ~ hBOOL(hAPP(U_470,bool,hAPP(U_470,fun(U_470,bool),ord_less_eq(U_470),hAPP(U_471,U_470,U_469,U_467)),hAPP(U_471,U_470,U_468,U_467))) )
& ( ! [U_466] : hBOOL(hAPP(U_470,bool,hAPP(U_470,fun(U_470,bool),ord_less_eq(U_470),hAPP(U_471,U_470,U_469,U_466)),hAPP(U_471,U_470,U_468,U_466)))
| ~ hBOOL(hAPP(fun(U_471,U_470),bool,hAPP(fun(U_471,U_470),fun(fun(U_471,U_470),bool),ord_less_eq(fun(U_471,U_470)),U_469),U_468)) ) )
| ~ ord(U_470) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_471,U_470] :
( ( ! [U_475,U_473] :
( hBOOL(hAPP(fun(U_471,U_470),bool,hAPP(fun(U_471,U_470),fun(fun(U_471,U_470),bool),ord_less_eq(fun(U_471,U_470)),U_475),U_473))
| ? [U_467] : ~ hBOOL(hAPP(U_470,bool,hAPP(U_470,fun(U_470,bool),ord_less_eq(U_470),hAPP(U_471,U_470,U_475,U_467)),hAPP(U_471,U_470,U_473,U_467))) )
& ! [U_474,U_472] :
( ! [U_466] : hBOOL(hAPP(U_470,bool,hAPP(U_470,fun(U_470,bool),ord_less_eq(U_470),hAPP(U_471,U_470,U_474,U_466)),hAPP(U_471,U_470,U_472,U_466)))
| ~ hBOOL(hAPP(fun(U_471,U_470),bool,hAPP(fun(U_471,U_470),fun(fun(U_471,U_470),bool),ord_less_eq(fun(U_471,U_470)),U_474),U_472)) ) )
| ~ ord(U_470) ),
inference(miniscope,[status(thm)],[f_171_2]) ).
fof(f_171_4,plain,
! [U_471,U_470] :
( ( ! [U_475,U_473] :
( hBOOL(hAPP(fun(U_471,U_470),bool,hAPP(fun(U_471,U_470),fun(fun(U_471,U_470),bool),ord_less_eq(fun(U_471,U_470)),U_475),U_473))
| ~ hBOOL(hAPP(U_470,bool,hAPP(U_470,fun(U_470,bool),ord_less_eq(U_470),hAPP(U_471,U_470,U_475,sK37(U_471,U_470,U_475,U_473))),hAPP(U_471,U_470,U_473,sK37(U_471,U_470,U_475,U_473)))) )
& ! [U_474,U_472] :
( ! [U_466] : hBOOL(hAPP(U_470,bool,hAPP(U_470,fun(U_470,bool),ord_less_eq(U_470),hAPP(U_471,U_470,U_474,U_466)),hAPP(U_471,U_470,U_472,U_466)))
| ~ hBOOL(hAPP(fun(U_471,U_470),bool,hAPP(fun(U_471,U_470),fun(fun(U_471,U_470),bool),ord_less_eq(fun(U_471,U_470)),U_474),U_472)) ) )
| ~ ord(U_470) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_467,sK37(U_471,U_470,U_475,U_473))],[f_171_3]) ).
cnf(f_171_5,plain,
( hBOOL(hAPP(U_470,bool,hAPP(U_470,fun(U_470,bool),ord_less_eq(U_470),hAPP(U_471,U_470,U_474,U_466)),hAPP(U_471,U_470,U_472,U_466)))
| ~ hBOOL(hAPP(fun(U_471,U_470),bool,hAPP(fun(U_471,U_470),fun(fun(U_471,U_470),bool),ord_less_eq(fun(U_471,U_470)),U_474),U_472))
| ~ ord(U_470) ),
inference(clausify,[status(thm)],[f_171_4]) ).
cnf(f_171_6,plain,
( hBOOL(hAPP(fun(U_471,U_470),bool,hAPP(fun(U_471,U_470),fun(fun(U_471,U_470),bool),ord_less_eq(fun(U_471,U_470)),U_475),U_473))
| ~ hBOOL(hAPP(U_470,bool,hAPP(U_470,fun(U_470,bool),ord_less_eq(U_470),hAPP(U_471,U_470,U_475,sK37(U_471,U_470,U_475,U_473))),hAPP(U_471,U_470,U_473,sK37(U_471,U_470,U_475,U_473))))
| ~ ord(U_470) ),
inference(clausify,[status(thm)],[f_171_4]) ).
fof(f_172_1,plain,
! [X_a] :
( ! [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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) ) )
| ~ linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_109_linorder__not__less]) ).
fof(f_172_2,plain,
! [U_478] :
( ! [U_477,U_476] :
( ( ~ hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less(U_478),U_477),U_476))
| ~ hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less_eq(U_478),U_476),U_477)) )
& ( hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less_eq(U_478),U_476),U_477))
| hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less(U_478),U_477),U_476)) ) )
| ~ linorder(U_478) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
! [U_478] :
( ( ! [U_482,U_480] :
( ~ hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less(U_478),U_482),U_480))
| ~ hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less_eq(U_478),U_480),U_482)) )
& ! [U_481,U_479] :
( hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less_eq(U_478),U_479),U_481))
| hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less(U_478),U_481),U_479)) ) )
| ~ linorder(U_478) ),
inference(miniscope,[status(thm)],[f_172_2]) ).
cnf(f_172_4,plain,
( hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less_eq(U_478),U_479),U_481))
| hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less(U_478),U_481),U_479))
| ~ linorder(U_478) ),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_5,plain,
( ~ hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less(U_478),U_482),U_480))
| ~ hBOOL(hAPP(U_478,bool,hAPP(U_478,fun(U_478,bool),ord_less_eq(U_478),U_480),U_482))
| ~ linorder(U_478) ),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_1,plain,
! [X_a] :
( ! [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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2)) ) )
| ~ linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_110_linorder__not__le]) ).
fof(f_173_2,plain,
! [U_485] :
( ! [U_484,U_483] :
( ( ~ hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less_eq(U_485),U_484),U_483))
| ~ hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less(U_485),U_483),U_484)) )
& ( hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less(U_485),U_483),U_484))
| hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less_eq(U_485),U_484),U_483)) ) )
| ~ linorder(U_485) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_485] :
( ( ! [U_489,U_487] :
( ~ hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less_eq(U_485),U_489),U_487))
| ~ hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less(U_485),U_487),U_489)) )
& ! [U_488,U_486] :
( hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less(U_485),U_486),U_488))
| hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less_eq(U_485),U_488),U_486)) ) )
| ~ linorder(U_485) ),
inference(miniscope,[status(thm)],[f_173_2]) ).
cnf(f_173_4,plain,
( hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less(U_485),U_486),U_488))
| hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less_eq(U_485),U_488),U_486))
| ~ linorder(U_485) ),
inference(clausify,[status(thm)],[f_173_3]) ).
cnf(f_173_5,plain,
( ~ hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less_eq(U_485),U_489),U_487))
| ~ hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less(U_485),U_487),U_489))
| ~ linorder(U_485) ),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_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_111_linorder__le__less__linear]) ).
fof(f_174_2,plain,
! [U_492] :
( ! [U_491,U_490] :
( hBOOL(hAPP(U_492,bool,hAPP(U_492,fun(U_492,bool),ord_less(U_492),U_490),U_491))
| hBOOL(hAPP(U_492,bool,hAPP(U_492,fun(U_492,bool),ord_less_eq(U_492),U_491),U_490)) )
| ~ linorder(U_492) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( hBOOL(hAPP(U_492,bool,hAPP(U_492,fun(U_492,bool),ord_less(U_492),U_490),U_491))
| hBOOL(hAPP(U_492,bool,hAPP(U_492,fun(U_492,bool),ord_less_eq(U_492),U_491),U_490))
| ~ linorder(U_492) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_1,plain,
! [X_a] :
( ! [X_1,Y_2] :
( ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
| ti(X_a,X_1) = ti(X_a,Y_2)
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2)) )
& ( ( ti(X_a,X_1) != ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) ) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_112_order__less__le]) ).
fof(f_175_2,plain,
! [U_495] :
( ! [U_494,U_493] :
( ( hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less(U_495),U_494),U_493))
| ti(U_495,U_494) = ti(U_495,U_493)
| ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_494),U_493)) )
& ( ( ti(U_495,U_494) != ti(U_495,U_493)
& hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_494),U_493)) )
| ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less(U_495),U_494),U_493)) ) )
| ~ order(U_495) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_495] :
( ( ! [U_499,U_497] :
( hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less(U_495),U_499),U_497))
| ti(U_495,U_499) = ti(U_495,U_497)
| ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_499),U_497)) )
& ! [U_498,U_496] :
( ( ti(U_495,U_498) != ti(U_495,U_496)
& hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_498),U_496)) )
| ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less(U_495),U_498),U_496)) ) )
| ~ order(U_495) ),
inference(miniscope,[status(thm)],[f_175_2]) ).
cnf(f_175_4,plain,
( hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_498),U_496))
| ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less(U_495),U_498),U_496))
| ~ order(U_495) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_5,plain,
( ti(U_495,U_498) != ti(U_495,U_496)
| ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less(U_495),U_498),U_496))
| ~ order(U_495) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_6,plain,
( hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less(U_495),U_499),U_497))
| ti(U_495,U_499) = ti(U_495,U_497)
| ~ hBOOL(hAPP(U_495,bool,hAPP(U_495,fun(U_495,bool),ord_less_eq(U_495),U_499),U_497))
| ~ order(U_495) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_1,plain,
! [X_a] :
( ! [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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_1))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2)) )
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) ) )
| ~ preorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_113_less__le__not__le]) ).
fof(f_176_2,plain,
! [U_502] :
( ! [U_501,U_500] :
( ( hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less(U_502),U_501),U_500))
| hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_500),U_501))
| ~ hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_501),U_500)) )
& ( ( ~ hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_500),U_501))
& hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_501),U_500)) )
| ~ hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less(U_502),U_501),U_500)) ) )
| ~ preorder(U_502) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_502] :
( ( ! [U_506,U_504] :
( hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less(U_502),U_506),U_504))
| hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_504),U_506))
| ~ hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_506),U_504)) )
& ! [U_505,U_503] :
( ( ~ hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_503),U_505))
& hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_505),U_503)) )
| ~ hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less(U_502),U_505),U_503)) ) )
| ~ preorder(U_502) ),
inference(miniscope,[status(thm)],[f_176_2]) ).
cnf(f_176_4,plain,
( hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_505),U_503))
| ~ hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less(U_502),U_505),U_503))
| ~ preorder(U_502) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_5,plain,
( ~ hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_503),U_505))
| ~ hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less(U_502),U_505),U_503))
| ~ preorder(U_502) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_6,plain,
( hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less(U_502),U_506),U_504))
| hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_504),U_506))
| ~ hBOOL(hAPP(U_502,bool,hAPP(U_502,fun(U_502,bool),ord_less_eq(U_502),U_506),U_504))
| ~ preorder(U_502) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [X_a] :
( ! [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))
| ( ti(X_a,X_1) != ti(X_a,Y_2)
& ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) ) )
& ( ti(X_a,X_1) = ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2)) ) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_114_order__le__less]) ).
fof(f_177_2,plain,
! [U_509] :
( ! [U_508,U_507] :
( ( hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less_eq(U_509),U_508),U_507))
| ( ti(U_509,U_508) != ti(U_509,U_507)
& ~ hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less(U_509),U_508),U_507)) ) )
& ( ti(U_509,U_508) = ti(U_509,U_507)
| hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less(U_509),U_508),U_507))
| ~ hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less_eq(U_509),U_508),U_507)) ) )
| ~ order(U_509) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_509] :
( ( ! [U_513,U_511] :
( hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less_eq(U_509),U_513),U_511))
| ( ti(U_509,U_513) != ti(U_509,U_511)
& ~ hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less(U_509),U_513),U_511)) ) )
& ! [U_512,U_510] :
( ti(U_509,U_512) = ti(U_509,U_510)
| hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less(U_509),U_512),U_510))
| ~ hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less_eq(U_509),U_512),U_510)) ) )
| ~ order(U_509) ),
inference(miniscope,[status(thm)],[f_177_2]) ).
cnf(f_177_4,plain,
( ti(U_509,U_512) = ti(U_509,U_510)
| hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less(U_509),U_512),U_510))
| ~ hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less_eq(U_509),U_512),U_510))
| ~ order(U_509) ),
inference(clausify,[status(thm)],[f_177_3]) ).
cnf(f_177_5,plain,
( ~ hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less(U_509),U_513),U_511))
| hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less_eq(U_509),U_513),U_511))
| ~ order(U_509) ),
inference(clausify,[status(thm)],[f_177_3]) ).
cnf(f_177_6,plain,
( ti(U_509,U_513) != ti(U_509,U_511)
| hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),ord_less_eq(U_509),U_513),U_511))
| ~ order(U_509) ),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_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_115_leI]) ).
fof(f_178_2,plain,
! [U_516] :
( ! [U_515,U_514] :
( hBOOL(hAPP(U_516,bool,hAPP(U_516,fun(U_516,bool),ord_less_eq(U_516),U_514),U_515))
| hBOOL(hAPP(U_516,bool,hAPP(U_516,fun(U_516,bool),ord_less(U_516),U_515),U_514)) )
| ~ linorder(U_516) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( hBOOL(hAPP(U_516,bool,hAPP(U_516,fun(U_516,bool),ord_less_eq(U_516),U_514),U_515))
| hBOOL(hAPP(U_516,bool,hAPP(U_516,fun(U_516,bool),ord_less(U_516),U_515),U_514))
| ~ linorder(U_516) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_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_116_not__leE]) ).
fof(f_179_2,plain,
! [U_519] :
( ! [U_518,U_517] :
( hBOOL(hAPP(U_519,bool,hAPP(U_519,fun(U_519,bool),ord_less(U_519),U_517),U_518))
| hBOOL(hAPP(U_519,bool,hAPP(U_519,fun(U_519,bool),ord_less_eq(U_519),U_518),U_517)) )
| ~ linorder(U_519) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( hBOOL(hAPP(U_519,bool,hAPP(U_519,fun(U_519,bool),ord_less(U_519),U_517),U_518))
| hBOOL(hAPP(U_519,bool,hAPP(U_519,fun(U_519,bool),ord_less_eq(U_519),U_518),U_517))
| ~ linorder(U_519) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_1,plain,
! [X_a] :
( ! [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))
| ti(X_a,X_1) != ti(X_a,Y_2) )
& ( ti(X_a,X_1) = ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)) )
| ~ linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_117_linorder__antisym__conv1]) ).
fof(f_180_2,plain,
! [U_522] :
( ! [U_521,U_520] :
( ( ( hBOOL(hAPP(U_522,bool,hAPP(U_522,fun(U_522,bool),ord_less_eq(U_522),U_521),U_520))
| ti(U_522,U_521) != ti(U_522,U_520) )
& ( ti(U_522,U_521) = ti(U_522,U_520)
| ~ hBOOL(hAPP(U_522,bool,hAPP(U_522,fun(U_522,bool),ord_less_eq(U_522),U_521),U_520)) ) )
| hBOOL(hAPP(U_522,bool,hAPP(U_522,fun(U_522,bool),ord_less(U_522),U_521),U_520)) )
| ~ linorder(U_522) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( ti(U_522,U_521) = ti(U_522,U_520)
| ~ hBOOL(hAPP(U_522,bool,hAPP(U_522,fun(U_522,bool),ord_less_eq(U_522),U_521),U_520))
| hBOOL(hAPP(U_522,bool,hAPP(U_522,fun(U_522,bool),ord_less(U_522),U_521),U_520))
| ~ linorder(U_522) ),
inference(clausify,[status(thm)],[f_180_2]) ).
cnf(f_180_4,plain,
( hBOOL(hAPP(U_522,bool,hAPP(U_522,fun(U_522,bool),ord_less_eq(U_522),U_521),U_520))
| ti(U_522,U_521) != ti(U_522,U_520)
| hBOOL(hAPP(U_522,bool,hAPP(U_522,fun(U_522,bool),ord_less(U_522),U_521),U_520))
| ~ linorder(U_522) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_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_118_order__neq__le__trans]) ).
fof(f_181_2,plain,
! [U_525] :
( ! [U_524,U_523] :
( hBOOL(hAPP(U_525,bool,hAPP(U_525,fun(U_525,bool),ord_less(U_525),U_524),U_523))
| ~ hBOOL(hAPP(U_525,bool,hAPP(U_525,fun(U_525,bool),ord_less_eq(U_525),U_524),U_523))
| ti(U_525,U_524) = ti(U_525,U_523) )
| ~ order(U_525) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
( hBOOL(hAPP(U_525,bool,hAPP(U_525,fun(U_525,bool),ord_less(U_525),U_524),U_523))
| ~ hBOOL(hAPP(U_525,bool,hAPP(U_525,fun(U_525,bool),ord_less_eq(U_525),U_524),U_523))
| ti(U_525,U_524) = ti(U_525,U_523)
| ~ order(U_525) ),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_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_119_xt1_I12_J]) ).
fof(f_182_2,plain,
! [U_528] :
( ! [U_527,U_526] :
( hBOOL(hAPP(U_528,bool,hAPP(U_528,fun(U_528,bool),ord_less(U_528),U_526),U_527))
| ~ hBOOL(hAPP(U_528,bool,hAPP(U_528,fun(U_528,bool),ord_less_eq(U_528),U_526),U_527))
| ti(U_528,U_527) = ti(U_528,U_526) )
| ~ order(U_528) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( hBOOL(hAPP(U_528,bool,hAPP(U_528,fun(U_528,bool),ord_less(U_528),U_526),U_527))
| ~ hBOOL(hAPP(U_528,bool,hAPP(U_528,fun(U_528,bool),ord_less_eq(U_528),U_526),U_527))
| ti(U_528,U_527) = ti(U_528,U_526)
| ~ order(U_528) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_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_120_leD]) ).
fof(f_183_2,plain,
! [U_531] :
( ! [U_530,U_529] :
( ~ hBOOL(hAPP(U_531,bool,hAPP(U_531,fun(U_531,bool),ord_less(U_531),U_529),U_530))
| ~ hBOOL(hAPP(U_531,bool,hAPP(U_531,fun(U_531,bool),ord_less_eq(U_531),U_530),U_529)) )
| ~ linorder(U_531) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
cnf(f_183_3,plain,
( ~ hBOOL(hAPP(U_531,bool,hAPP(U_531,fun(U_531,bool),ord_less(U_531),U_529),U_530))
| ~ hBOOL(hAPP(U_531,bool,hAPP(U_531,fun(U_531,bool),ord_less_eq(U_531),U_530),U_529))
| ~ linorder(U_531) ),
inference(clausify,[status(thm)],[f_183_2]) ).
fof(f_184_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_121_order__less__imp__le]) ).
fof(f_184_2,plain,
! [U_534] :
( ! [U_533,U_532] :
( hBOOL(hAPP(U_534,bool,hAPP(U_534,fun(U_534,bool),ord_less_eq(U_534),U_533),U_532))
| ~ hBOOL(hAPP(U_534,bool,hAPP(U_534,fun(U_534,bool),ord_less(U_534),U_533),U_532)) )
| ~ preorder(U_534) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( hBOOL(hAPP(U_534,bool,hAPP(U_534,fun(U_534,bool),ord_less_eq(U_534),U_533),U_532))
| ~ hBOOL(hAPP(U_534,bool,hAPP(U_534,fun(U_534,bool),ord_less(U_534),U_533),U_532))
| ~ preorder(U_534) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [X_a] :
( ! [X_1,Y_2] :
( ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))
| ti(X_a,X_1) != ti(X_a,Y_2) )
& ( ti(X_a,X_1) = ti(X_a,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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_2)) )
| ~ linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_122_linorder__antisym__conv2]) ).
fof(f_185_2,plain,
! [U_537] :
( ! [U_536,U_535] :
( ( ( ~ hBOOL(hAPP(U_537,bool,hAPP(U_537,fun(U_537,bool),ord_less(U_537),U_536),U_535))
| ti(U_537,U_536) != ti(U_537,U_535) )
& ( ti(U_537,U_536) = ti(U_537,U_535)
| hBOOL(hAPP(U_537,bool,hAPP(U_537,fun(U_537,bool),ord_less(U_537),U_536),U_535)) ) )
| ~ hBOOL(hAPP(U_537,bool,hAPP(U_537,fun(U_537,bool),ord_less_eq(U_537),U_536),U_535)) )
| ~ linorder(U_537) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( ti(U_537,U_536) = ti(U_537,U_535)
| hBOOL(hAPP(U_537,bool,hAPP(U_537,fun(U_537,bool),ord_less(U_537),U_536),U_535))
| ~ hBOOL(hAPP(U_537,bool,hAPP(U_537,fun(U_537,bool),ord_less_eq(U_537),U_536),U_535))
| ~ linorder(U_537) ),
inference(clausify,[status(thm)],[f_185_2]) ).
cnf(f_185_4,plain,
( ~ hBOOL(hAPP(U_537,bool,hAPP(U_537,fun(U_537,bool),ord_less(U_537),U_536),U_535))
| ti(U_537,U_536) != ti(U_537,U_535)
| ~ hBOOL(hAPP(U_537,bool,hAPP(U_537,fun(U_537,bool),ord_less_eq(U_537),U_536),U_535))
| ~ linorder(U_537) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_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_123_order__le__imp__less__or__eq]) ).
fof(f_186_2,plain,
! [U_540] :
( ! [U_539,U_538] :
( ti(U_540,U_539) = ti(U_540,U_538)
| hBOOL(hAPP(U_540,bool,hAPP(U_540,fun(U_540,bool),ord_less(U_540),U_539),U_538))
| ~ hBOOL(hAPP(U_540,bool,hAPP(U_540,fun(U_540,bool),ord_less_eq(U_540),U_539),U_538)) )
| ~ order(U_540) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( ti(U_540,U_539) = ti(U_540,U_538)
| hBOOL(hAPP(U_540,bool,hAPP(U_540,fun(U_540,bool),ord_less(U_540),U_539),U_538))
| ~ hBOOL(hAPP(U_540,bool,hAPP(U_540,fun(U_540,bool),ord_less_eq(U_540),U_539),U_538))
| ~ order(U_540) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_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_124_order__le__neq__trans]) ).
fof(f_187_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)) )
| ~ order(U_543) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( 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))
| ~ order(U_543) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_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_125_xt1_I11_J]) ).
fof(f_188_2,plain,
! [U_546] :
( ! [U_545,U_544] :
( hBOOL(hAPP(U_546,bool,hAPP(U_546,fun(U_546,bool),ord_less(U_546),U_545),U_544))
| ti(U_546,U_544) = ti(U_546,U_545)
| ~ hBOOL(hAPP(U_546,bool,hAPP(U_546,fun(U_546,bool),ord_less_eq(U_546),U_545),U_544)) )
| ~ order(U_546) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
( hBOOL(hAPP(U_546,bool,hAPP(U_546,fun(U_546,bool),ord_less(U_546),U_545),U_544))
| ti(U_546,U_544) = ti(U_546,U_545)
| ~ hBOOL(hAPP(U_546,bool,hAPP(U_546,fun(U_546,bool),ord_less_eq(U_546),U_545),U_544))
| ~ order(U_546) ),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_1,plain,
! [X_a] :
( ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))
| ~ 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_126_order__less__le__trans]) ).
fof(f_189_2,plain,
! [U_550] :
( ! [U_549,U_548,U_547] :
( hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_548),U_549))
| ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_547),U_549))
| ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_548),U_547)) )
| ~ preorder(U_550) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
( hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_548),U_549))
| ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less_eq(U_550),U_547),U_549))
| ~ hBOOL(hAPP(U_550,bool,hAPP(U_550,fun(U_550,bool),ord_less(U_550),U_548),U_547))
| ~ preorder(U_550) ),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_1,plain,
! [X_a] :
( ! [Z_1,Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),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_127_xt1_I7_J]) ).
fof(f_190_2,plain,
! [U_554] :
( ! [U_553,U_552,U_551] :
( hBOOL(hAPP(U_554,bool,hAPP(U_554,fun(U_554,bool),ord_less(U_554),U_553),U_551))
| ~ hBOOL(hAPP(U_554,bool,hAPP(U_554,fun(U_554,bool),ord_less_eq(U_554),U_553),U_552))
| ~ hBOOL(hAPP(U_554,bool,hAPP(U_554,fun(U_554,bool),ord_less(U_554),U_552),U_551)) )
| ~ order(U_554) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
( hBOOL(hAPP(U_554,bool,hAPP(U_554,fun(U_554,bool),ord_less(U_554),U_553),U_551))
| ~ hBOOL(hAPP(U_554,bool,hAPP(U_554,fun(U_554,bool),ord_less_eq(U_554),U_553),U_552))
| ~ hBOOL(hAPP(U_554,bool,hAPP(U_554,fun(U_554,bool),ord_less(U_554),U_552),U_551))
| ~ order(U_554) ),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_1,plain,
! [X_a] :
( ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1))
| ~ 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_128_order__le__less__trans]) ).
fof(f_191_2,plain,
! [U_558] :
( ! [U_557,U_556,U_555] :
( hBOOL(hAPP(U_558,bool,hAPP(U_558,fun(U_558,bool),ord_less(U_558),U_556),U_557))
| ~ hBOOL(hAPP(U_558,bool,hAPP(U_558,fun(U_558,bool),ord_less(U_558),U_555),U_557))
| ~ hBOOL(hAPP(U_558,bool,hAPP(U_558,fun(U_558,bool),ord_less_eq(U_558),U_556),U_555)) )
| ~ preorder(U_558) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( hBOOL(hAPP(U_558,bool,hAPP(U_558,fun(U_558,bool),ord_less(U_558),U_556),U_557))
| ~ hBOOL(hAPP(U_558,bool,hAPP(U_558,fun(U_558,bool),ord_less(U_558),U_555),U_557))
| ~ hBOOL(hAPP(U_558,bool,hAPP(U_558,fun(U_558,bool),ord_less_eq(U_558),U_556),U_555))
| ~ preorder(U_558) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_1,plain,
! [X_a] :
( ! [Z_1,Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),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_129_xt1_I8_J]) ).
fof(f_192_2,plain,
! [U_562] :
( ! [U_561,U_560,U_559] :
( hBOOL(hAPP(U_562,bool,hAPP(U_562,fun(U_562,bool),ord_less(U_562),U_561),U_559))
| ~ hBOOL(hAPP(U_562,bool,hAPP(U_562,fun(U_562,bool),ord_less(U_562),U_561),U_560))
| ~ hBOOL(hAPP(U_562,bool,hAPP(U_562,fun(U_562,bool),ord_less_eq(U_562),U_560),U_559)) )
| ~ order(U_562) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( hBOOL(hAPP(U_562,bool,hAPP(U_562,fun(U_562,bool),ord_less(U_562),U_561),U_559))
| ~ hBOOL(hAPP(U_562,bool,hAPP(U_562,fun(U_562,bool),ord_less(U_562),U_561),U_560))
| ~ hBOOL(hAPP(U_562,bool,hAPP(U_562,fun(U_562,bool),ord_less_eq(U_562),U_560),U_559))
| ~ order(U_562) ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_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_130_top__greatest]) ).
fof(f_193_2,plain,
! [U_564] :
( ! [U_563] : hBOOL(hAPP(U_564,bool,hAPP(U_564,fun(U_564,bool),ord_less_eq(U_564),U_563),top_top(U_564)))
| ~ top(U_564) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( hBOOL(hAPP(U_564,bool,hAPP(U_564,fun(U_564,bool),ord_less_eq(U_564),U_563),top_top(U_564)))
| ~ top(U_564) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_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_131_top__unique]) ).
fof(f_194_2,plain,
! [U_566] :
( ! [U_565] :
( ( hBOOL(hAPP(U_566,bool,hAPP(U_566,fun(U_566,bool),ord_less_eq(U_566),top_top(U_566)),U_565))
| ti(U_566,U_565) != top_top(U_566) )
& ( ti(U_566,U_565) = top_top(U_566)
| ~ hBOOL(hAPP(U_566,bool,hAPP(U_566,fun(U_566,bool),ord_less_eq(U_566),top_top(U_566)),U_565)) ) )
| ~ top(U_566) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_566] :
( ( ! [U_568] :
( hBOOL(hAPP(U_566,bool,hAPP(U_566,fun(U_566,bool),ord_less_eq(U_566),top_top(U_566)),U_568))
| ti(U_566,U_568) != top_top(U_566) )
& ! [U_567] :
( ti(U_566,U_567) = top_top(U_566)
| ~ hBOOL(hAPP(U_566,bool,hAPP(U_566,fun(U_566,bool),ord_less_eq(U_566),top_top(U_566)),U_567)) ) )
| ~ top(U_566) ),
inference(miniscope,[status(thm)],[f_194_2]) ).
cnf(f_194_4,plain,
( ti(U_566,U_567) = top_top(U_566)
| ~ hBOOL(hAPP(U_566,bool,hAPP(U_566,fun(U_566,bool),ord_less_eq(U_566),top_top(U_566)),U_567))
| ~ top(U_566) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_5,plain,
( hBOOL(hAPP(U_566,bool,hAPP(U_566,fun(U_566,bool),ord_less_eq(U_566),top_top(U_566)),U_568))
| ti(U_566,U_568) != top_top(U_566)
| ~ top(U_566) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_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_132_top__le]) ).
fof(f_195_2,plain,
! [U_570] :
( ! [U_569] :
( ti(U_570,U_569) = top_top(U_570)
| ~ hBOOL(hAPP(U_570,bool,hAPP(U_570,fun(U_570,bool),ord_less_eq(U_570),top_top(U_570)),U_569)) )
| ~ top(U_570) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
( ti(U_570,U_569) = top_top(U_570)
| ~ hBOOL(hAPP(U_570,bool,hAPP(U_570,fun(U_570,bool),ord_less_eq(U_570),top_top(U_570)),U_569))
| ~ top(U_570) ),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_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_2] :
( ? [Xa] :
( ti(X_a,X_2) != ti(X_a,Xa)
& hAPP(X_a,X_b,F,X_2) = 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_2),A_1)) ) )
& ( ! [X_2] :
( ! [Xa] :
( ti(X_a,X_2) = ti(X_a,Xa)
| hAPP(X_a,X_b,F,X_2) != 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_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_133_inj__on__def]) ).
fof(f_196_2,plain,
! [U_578,U_577,U_576,U_575] :
( ( hBOOL(hAPP(fun(U_578,bool),bool,hAPP(fun(U_578,U_577),fun(fun(U_578,bool),bool),inj_on(U_578,U_577),U_576),U_575))
| ? [U_574] :
( ? [U_573] :
( ti(U_578,U_574) != ti(U_578,U_573)
& hAPP(U_578,U_577,U_576,U_574) = hAPP(U_578,U_577,U_576,U_573)
& hBOOL(hAPP(fun(U_578,bool),bool,hAPP(U_578,fun(fun(U_578,bool),bool),member(U_578),U_573),U_575)) )
& hBOOL(hAPP(fun(U_578,bool),bool,hAPP(U_578,fun(fun(U_578,bool),bool),member(U_578),U_574),U_575)) ) )
& ( ! [U_572] :
( ! [U_571] :
( ti(U_578,U_572) = ti(U_578,U_571)
| hAPP(U_578,U_577,U_576,U_572) != hAPP(U_578,U_577,U_576,U_571)
| ~ hBOOL(hAPP(fun(U_578,bool),bool,hAPP(U_578,fun(fun(U_578,bool),bool),member(U_578),U_571),U_575)) )
| ~ hBOOL(hAPP(fun(U_578,bool),bool,hAPP(U_578,fun(fun(U_578,bool),bool),member(U_578),U_572),U_575)) )
| ~ hBOOL(hAPP(fun(U_578,bool),bool,hAPP(fun(U_578,U_577),fun(fun(U_578,bool),bool),inj_on(U_578,U_577),U_576),U_575)) ) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
( ! [U_586,U_584,U_582,U_580] :
( hBOOL(hAPP(fun(U_586,bool),bool,hAPP(fun(U_586,U_584),fun(fun(U_586,bool),bool),inj_on(U_586,U_584),U_582),U_580))
| ? [U_574] :
( ? [U_573] :
( ti(U_586,U_574) != ti(U_586,U_573)
& hAPP(U_586,U_584,U_582,U_574) = hAPP(U_586,U_584,U_582,U_573)
& hBOOL(hAPP(fun(U_586,bool),bool,hAPP(U_586,fun(fun(U_586,bool),bool),member(U_586),U_573),U_580)) )
& hBOOL(hAPP(fun(U_586,bool),bool,hAPP(U_586,fun(fun(U_586,bool),bool),member(U_586),U_574),U_580)) ) )
& ! [U_585,U_583,U_581,U_579] :
( ! [U_572] :
( ! [U_571] :
( ti(U_585,U_572) = ti(U_585,U_571)
| hAPP(U_585,U_583,U_581,U_572) != hAPP(U_585,U_583,U_581,U_571)
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(U_585,fun(fun(U_585,bool),bool),member(U_585),U_571),U_579)) )
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(U_585,fun(fun(U_585,bool),bool),member(U_585),U_572),U_579)) )
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(fun(U_585,U_583),fun(fun(U_585,bool),bool),inj_on(U_585,U_583),U_581),U_579)) ) ),
inference(miniscope,[status(thm)],[f_196_2]) ).
fof(f_196_4,plain,
( ! [U_586,U_584,U_582,U_580] :
( hBOOL(hAPP(fun(U_586,bool),bool,hAPP(fun(U_586,U_584),fun(fun(U_586,bool),bool),inj_on(U_586,U_584),U_582),U_580))
| ( ? [U_573] :
( ti(U_586,sK38(U_586,U_584,U_582,U_580)) != ti(U_586,U_573)
& hAPP(U_586,U_584,U_582,sK38(U_586,U_584,U_582,U_580)) = hAPP(U_586,U_584,U_582,U_573)
& hBOOL(hAPP(fun(U_586,bool),bool,hAPP(U_586,fun(fun(U_586,bool),bool),member(U_586),U_573),U_580)) )
& hBOOL(hAPP(fun(U_586,bool),bool,hAPP(U_586,fun(fun(U_586,bool),bool),member(U_586),sK38(U_586,U_584,U_582,U_580)),U_580)) ) )
& ! [U_585,U_583,U_581,U_579] :
( ! [U_572] :
( ! [U_571] :
( ti(U_585,U_572) = ti(U_585,U_571)
| hAPP(U_585,U_583,U_581,U_572) != hAPP(U_585,U_583,U_581,U_571)
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(U_585,fun(fun(U_585,bool),bool),member(U_585),U_571),U_579)) )
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(U_585,fun(fun(U_585,bool),bool),member(U_585),U_572),U_579)) )
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(fun(U_585,U_583),fun(fun(U_585,bool),bool),inj_on(U_585,U_583),U_581),U_579)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_574,sK38(U_586,U_584,U_582,U_580))],[f_196_3]) ).
fof(f_196_5,plain,
( ! [U_586,U_584,U_582,U_580] :
( hBOOL(hAPP(fun(U_586,bool),bool,hAPP(fun(U_586,U_584),fun(fun(U_586,bool),bool),inj_on(U_586,U_584),U_582),U_580))
| ( ti(U_586,sK38(U_586,U_584,U_582,U_580)) != ti(U_586,sK39(U_586,U_584,U_582,U_580))
& hAPP(U_586,U_584,U_582,sK38(U_586,U_584,U_582,U_580)) = hAPP(U_586,U_584,U_582,sK39(U_586,U_584,U_582,U_580))
& hBOOL(hAPP(fun(U_586,bool),bool,hAPP(U_586,fun(fun(U_586,bool),bool),member(U_586),sK39(U_586,U_584,U_582,U_580)),U_580))
& hBOOL(hAPP(fun(U_586,bool),bool,hAPP(U_586,fun(fun(U_586,bool),bool),member(U_586),sK38(U_586,U_584,U_582,U_580)),U_580)) ) )
& ! [U_585,U_583,U_581,U_579] :
( ! [U_572] :
( ! [U_571] :
( ti(U_585,U_572) = ti(U_585,U_571)
| hAPP(U_585,U_583,U_581,U_572) != hAPP(U_585,U_583,U_581,U_571)
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(U_585,fun(fun(U_585,bool),bool),member(U_585),U_571),U_579)) )
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(U_585,fun(fun(U_585,bool),bool),member(U_585),U_572),U_579)) )
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(fun(U_585,U_583),fun(fun(U_585,bool),bool),inj_on(U_585,U_583),U_581),U_579)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_573,sK39(U_586,U_584,U_582,U_580))],[f_196_4]) ).
cnf(f_196_6,plain,
( ti(U_585,U_572) = ti(U_585,U_571)
| hAPP(U_585,U_583,U_581,U_572) != hAPP(U_585,U_583,U_581,U_571)
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(U_585,fun(fun(U_585,bool),bool),member(U_585),U_571),U_579))
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(U_585,fun(fun(U_585,bool),bool),member(U_585),U_572),U_579))
| ~ hBOOL(hAPP(fun(U_585,bool),bool,hAPP(fun(U_585,U_583),fun(fun(U_585,bool),bool),inj_on(U_585,U_583),U_581),U_579)) ),
inference(clausify,[status(thm)],[f_196_5]) ).
cnf(f_196_7,plain,
( hBOOL(hAPP(fun(U_586,bool),bool,hAPP(U_586,fun(fun(U_586,bool),bool),member(U_586),sK38(U_586,U_584,U_582,U_580)),U_580))
| hBOOL(hAPP(fun(U_586,bool),bool,hAPP(fun(U_586,U_584),fun(fun(U_586,bool),bool),inj_on(U_586,U_584),U_582),U_580)) ),
inference(clausify,[status(thm)],[f_196_5]) ).
cnf(f_196_8,plain,
( hBOOL(hAPP(fun(U_586,bool),bool,hAPP(U_586,fun(fun(U_586,bool),bool),member(U_586),sK39(U_586,U_584,U_582,U_580)),U_580))
| hBOOL(hAPP(fun(U_586,bool),bool,hAPP(fun(U_586,U_584),fun(fun(U_586,bool),bool),inj_on(U_586,U_584),U_582),U_580)) ),
inference(clausify,[status(thm)],[f_196_5]) ).
cnf(f_196_9,plain,
( hAPP(U_586,U_584,U_582,sK38(U_586,U_584,U_582,U_580)) = hAPP(U_586,U_584,U_582,sK39(U_586,U_584,U_582,U_580))
| hBOOL(hAPP(fun(U_586,bool),bool,hAPP(fun(U_586,U_584),fun(fun(U_586,bool),bool),inj_on(U_586,U_584),U_582),U_580)) ),
inference(clausify,[status(thm)],[f_196_5]) ).
cnf(f_196_10,plain,
( ti(U_586,sK38(U_586,U_584,U_582,U_580)) != ti(U_586,sK39(U_586,U_584,U_582,U_580))
| hBOOL(hAPP(fun(U_586,bool),bool,hAPP(fun(U_586,U_584),fun(fun(U_586,bool),bool),inj_on(U_586,U_584),U_582),U_580)) ),
inference(clausify,[status(thm)],[f_196_5]) ).
fof(f_197_1,plain,
! [X_a,X_b,X_1,Y_2,F,A_1] :
( 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))
| 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)) ),
inference(fof_nnf,[status(thm)],[fact_134_inj__on__contraD]) ).
fof(f_197_2,plain,
! [U_592,U_591,U_590,U_589,U_588,U_587] :
( hAPP(U_592,U_591,U_588,U_590) != hAPP(U_592,U_591,U_588,U_589)
| ~ hBOOL(hAPP(fun(U_592,bool),bool,hAPP(U_592,fun(fun(U_592,bool),bool),member(U_592),U_589),U_587))
| ~ hBOOL(hAPP(fun(U_592,bool),bool,hAPP(U_592,fun(fun(U_592,bool),bool),member(U_592),U_590),U_587))
| ti(U_592,U_590) = ti(U_592,U_589)
| ~ hBOOL(hAPP(fun(U_592,bool),bool,hAPP(fun(U_592,U_591),fun(fun(U_592,bool),bool),inj_on(U_592,U_591),U_588),U_587)) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( hAPP(U_592,U_591,U_588,U_590) != hAPP(U_592,U_591,U_588,U_589)
| ~ hBOOL(hAPP(fun(U_592,bool),bool,hAPP(U_592,fun(fun(U_592,bool),bool),member(U_592),U_589),U_587))
| ~ hBOOL(hAPP(fun(U_592,bool),bool,hAPP(U_592,fun(fun(U_592,bool),bool),member(U_592),U_590),U_587))
| ti(U_592,U_590) = ti(U_592,U_589)
| ~ hBOOL(hAPP(fun(U_592,bool),bool,hAPP(fun(U_592,U_591),fun(fun(U_592,bool),bool),inj_on(U_592,U_591),U_588),U_587)) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_1,plain,
! [X_a,X_b,Y_2,X_1,F,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) )
& ( 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))
| ~ 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__iff]) ).
fof(f_198_2,plain,
! [U_598,U_597,U_596,U_595,U_594,U_593] :
( ( ( hAPP(U_598,U_597,U_594,U_595) = hAPP(U_598,U_597,U_594,U_596)
| ti(U_598,U_595) != ti(U_598,U_596) )
& ( ti(U_598,U_595) = ti(U_598,U_596)
| hAPP(U_598,U_597,U_594,U_595) != hAPP(U_598,U_597,U_594,U_596) ) )
| ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(U_598,fun(fun(U_598,bool),bool),member(U_598),U_596),U_593))
| ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(U_598,fun(fun(U_598,bool),bool),member(U_598),U_595),U_593))
| ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(fun(U_598,U_597),fun(fun(U_598,bool),bool),inj_on(U_598,U_597),U_594),U_593)) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( ti(U_598,U_595) = ti(U_598,U_596)
| hAPP(U_598,U_597,U_594,U_595) != hAPP(U_598,U_597,U_594,U_596)
| ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(U_598,fun(fun(U_598,bool),bool),member(U_598),U_596),U_593))
| ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(U_598,fun(fun(U_598,bool),bool),member(U_598),U_595),U_593))
| ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(fun(U_598,U_597),fun(fun(U_598,bool),bool),inj_on(U_598,U_597),U_594),U_593)) ),
inference(clausify,[status(thm)],[f_198_2]) ).
cnf(f_198_4,plain,
( hAPP(U_598,U_597,U_594,U_595) = hAPP(U_598,U_597,U_594,U_596)
| ti(U_598,U_595) != ti(U_598,U_596)
| ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(U_598,fun(fun(U_598,bool),bool),member(U_598),U_596),U_593))
| ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(U_598,fun(fun(U_598,bool),bool),member(U_598),U_595),U_593))
| ~ hBOOL(hAPP(fun(U_598,bool),bool,hAPP(fun(U_598,U_597),fun(fun(U_598,bool),bool),inj_on(U_598,U_597),U_594),U_593)) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_1,plain,
! [X_a,X_b,X_1,Y_2,F,A_1] :
( ti(X_a,X_1) = ti(X_a,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))
| hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,F,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)) ),
inference(fof_nnf,[status(thm)],[fact_136_inj__onD]) ).
fof(f_199_2,plain,
! [U_604,U_603,U_602,U_601,U_600,U_599] :
( ti(U_604,U_602) = ti(U_604,U_601)
| ~ hBOOL(hAPP(fun(U_604,bool),bool,hAPP(U_604,fun(fun(U_604,bool),bool),member(U_604),U_601),U_599))
| ~ hBOOL(hAPP(fun(U_604,bool),bool,hAPP(U_604,fun(fun(U_604,bool),bool),member(U_604),U_602),U_599))
| hAPP(U_604,U_603,U_600,U_602) != hAPP(U_604,U_603,U_600,U_601)
| ~ hBOOL(hAPP(fun(U_604,bool),bool,hAPP(fun(U_604,U_603),fun(fun(U_604,bool),bool),inj_on(U_604,U_603),U_600),U_599)) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( ti(U_604,U_602) = ti(U_604,U_601)
| ~ hBOOL(hAPP(fun(U_604,bool),bool,hAPP(U_604,fun(fun(U_604,bool),bool),member(U_604),U_601),U_599))
| ~ hBOOL(hAPP(fun(U_604,bool),bool,hAPP(U_604,fun(fun(U_604,bool),bool),member(U_604),U_602),U_599))
| hAPP(U_604,U_603,U_600,U_602) != hAPP(U_604,U_603,U_600,U_601)
| ~ hBOOL(hAPP(fun(U_604,bool),bool,hAPP(fun(U_604,U_603),fun(fun(U_604,bool),bool),inj_on(U_604,U_603),U_600),U_599)) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_1,plain,
! [X_a,X_b,X_1,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_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))
| ~ 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_137_Pi__mem]) ).
fof(f_200_2,plain,
! [U_610,U_609,U_608,U_607,U_606,U_605] :
( hBOOL(hAPP(fun(U_609,bool),bool,hAPP(U_609,fun(fun(U_609,bool),bool),member(U_609),hAPP(U_610,U_609,U_607,U_608)),hAPP(U_610,fun(U_609,bool),U_605,U_608)))
| ~ hBOOL(hAPP(fun(U_610,bool),bool,hAPP(U_610,fun(fun(U_610,bool),bool),member(U_610),U_608),U_606))
| ~ hBOOL(hAPP(fun(fun(U_610,U_609),bool),bool,hAPP(fun(U_610,U_609),fun(fun(fun(U_610,U_609),bool),bool),member(fun(U_610,U_609)),U_607),hAPP(fun(U_610,fun(U_609,bool)),fun(fun(U_610,U_609),bool),hAPP(fun(U_610,bool),fun(fun(U_610,fun(U_609,bool)),fun(fun(U_610,U_609),bool)),pi(U_610,U_609),U_606),U_605))) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( hBOOL(hAPP(fun(U_609,bool),bool,hAPP(U_609,fun(fun(U_609,bool),bool),member(U_609),hAPP(U_610,U_609,U_607,U_608)),hAPP(U_610,fun(U_609,bool),U_605,U_608)))
| ~ hBOOL(hAPP(fun(U_610,bool),bool,hAPP(U_610,fun(fun(U_610,bool),bool),member(U_610),U_608),U_606))
| ~ hBOOL(hAPP(fun(fun(U_610,U_609),bool),bool,hAPP(fun(U_610,U_609),fun(fun(fun(U_610,U_609),bool),bool),member(fun(U_610,U_609)),U_607),hAPP(fun(U_610,fun(U_609,bool)),fun(fun(U_610,U_609),bool),hAPP(fun(U_610,bool),fun(fun(U_610,fun(U_609,bool)),fun(fun(U_610,U_609),bool)),pi(U_610,U_609),U_606),U_605))) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_1,plain,
arrow_1111136790e_Prof = hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)),
inference(fof_nnf,[status(thm)],[fact_138_Prof__def]) ).
cnf(f_201_2,plain,
arrow_1111136790e_Prof = hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)),
inference(clausify,[status(thm)],[f_201_1]) ).
fof(f_202_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_139_inj__on__id2]) ).
fof(f_202_2,plain,
! [U_612,U_611] : hBOOL(hAPP(fun(U_612,bool),bool,hAPP(fun(U_612,U_612),fun(fun(U_612,bool),bool),inj_on(U_612,U_612),combi(U_612)),U_611)),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
hBOOL(hAPP(fun(U_612,bool),bool,hAPP(fun(U_612,U_612),fun(fun(U_612,bool),bool),inj_on(U_612,U_612),combi(U_612)),U_611)),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_1,plain,
! [X_a,X_b,X_1,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_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))
| ~ 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_140_funcset__mem]) ).
fof(f_203_2,plain,
! [U_618,U_617,U_616,U_615,U_614,U_613] :
( hBOOL(hAPP(fun(U_617,bool),bool,hAPP(U_617,fun(fun(U_617,bool),bool),member(U_617),hAPP(U_618,U_617,U_615,U_616)),U_613))
| ~ hBOOL(hAPP(fun(U_618,bool),bool,hAPP(U_618,fun(fun(U_618,bool),bool),member(U_618),U_616),U_614))
| ~ hBOOL(hAPP(fun(fun(U_618,U_617),bool),bool,hAPP(fun(U_618,U_617),fun(fun(fun(U_618,U_617),bool),bool),member(fun(U_618,U_617)),U_615),hAPP(fun(U_618,fun(U_617,bool)),fun(fun(U_618,U_617),bool),hAPP(fun(U_618,bool),fun(fun(U_618,fun(U_617,bool)),fun(fun(U_618,U_617),bool)),pi(U_618,U_617),U_614),hAPP(fun(U_617,bool),fun(U_618,fun(U_617,bool)),combk(fun(U_617,bool),U_618),U_613)))) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( hBOOL(hAPP(fun(U_617,bool),bool,hAPP(U_617,fun(fun(U_617,bool),bool),member(U_617),hAPP(U_618,U_617,U_615,U_616)),U_613))
| ~ hBOOL(hAPP(fun(U_618,bool),bool,hAPP(U_618,fun(fun(U_618,bool),bool),member(U_618),U_616),U_614))
| ~ hBOOL(hAPP(fun(fun(U_618,U_617),bool),bool,hAPP(fun(U_618,U_617),fun(fun(fun(U_618,U_617),bool),bool),member(fun(U_618,U_617)),U_615),hAPP(fun(U_618,fun(U_617,bool)),fun(fun(U_618,U_617),bool),hAPP(fun(U_618,bool),fun(fun(U_618,fun(U_617,bool)),fun(fun(U_618,U_617),bool)),pi(U_618,U_617),U_614),hAPP(fun(U_617,bool),fun(U_618,fun(U_617,bool)),combk(fun(U_617,bool),U_618),U_613)))) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_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_141_funcset__id]) ).
fof(f_204_2,plain,
! [U_620,U_619] : hBOOL(hAPP(fun(fun(U_620,U_620),bool),bool,hAPP(fun(U_620,U_620),fun(fun(fun(U_620,U_620),bool),bool),member(fun(U_620,U_620)),combi(U_620)),hAPP(fun(U_620,fun(U_620,bool)),fun(fun(U_620,U_620),bool),hAPP(fun(U_620,bool),fun(fun(U_620,fun(U_620,bool)),fun(fun(U_620,U_620),bool)),pi(U_620,U_620),U_619),hAPP(fun(U_620,bool),fun(U_620,fun(U_620,bool)),combk(fun(U_620,bool),U_620),U_619)))),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
hBOOL(hAPP(fun(fun(U_620,U_620),bool),bool,hAPP(fun(U_620,U_620),fun(fun(fun(U_620,U_620),bool),bool),member(fun(U_620,U_620)),combi(U_620)),hAPP(fun(U_620,fun(U_620,bool)),fun(fun(U_620,U_620),bool),hAPP(fun(U_620,bool),fun(fun(U_620,fun(U_620,bool)),fun(fun(U_620,U_620),bool)),pi(U_620,U_620),U_619),hAPP(fun(U_620,bool),fun(U_620,fun(U_620,bool)),combk(fun(U_620,bool),U_620),U_619)))),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_1,plain,
! [Fa,I_1] :
( ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_1))
| ? [X_2] :
( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_1)
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) ) )
& ( ! [X_2] :
( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_1)
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_142_dictator__def]) ).
fof(f_205_2,plain,
! [U_624,U_623] :
( ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_624),U_623))
| ? [U_622] :
( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_624,U_622) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_622,U_623)
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_622),arrow_1111136790e_Prof)) ) )
& ( ! [U_621] :
( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_624,U_621) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_621,U_623)
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_621),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_624),U_623)) ) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
( ! [U_628,U_626] :
( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_628),U_626))
| ? [U_622] :
( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_628,U_622) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_622,U_626)
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_622),arrow_1111136790e_Prof)) ) )
& ! [U_627,U_625] :
( ! [U_621] :
( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_627,U_621) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_621,U_625)
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_621),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_627),U_625)) ) ),
inference(miniscope,[status(thm)],[f_205_2]) ).
fof(f_205_4,plain,
( ! [U_628,U_626] :
( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_628),U_626))
| ( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_628,sK40(U_628,U_626)) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK40(U_628,U_626),U_626)
& hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK40(U_628,U_626)),arrow_1111136790e_Prof)) ) )
& ! [U_627,U_625] :
( ! [U_621] :
( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_627,U_621) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_621,U_625)
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_621),arrow_1111136790e_Prof)) )
| ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_627),U_625)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_622,sK40(U_628,U_626))],[f_205_3]) ).
cnf(f_205_5,plain,
( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_627,U_621) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_621,U_625)
| ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),U_621),arrow_1111136790e_Prof))
| ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_627),U_625)) ),
inference(clausify,[status(thm)],[f_205_4]) ).
cnf(f_205_6,plain,
( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sK40(U_628,U_626)),arrow_1111136790e_Prof))
| hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_628),U_626)) ),
inference(clausify,[status(thm)],[f_205_4]) ).
cnf(f_205_7,plain,
( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),U_628,sK40(U_628,U_626)) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sK40(U_628,U_626),U_626)
| hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,U_628),U_626)) ),
inference(clausify,[status(thm)],[f_205_4]) ).
fof(f_206_1,plain,
! [X_a,X_b,X_1,Y_2,F] :
( ( ( 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) )
& ( 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(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_143_inj__eq]) ).
fof(f_206_2,plain,
! [U_633,U_632,U_631,U_630,U_629] :
( ( ( hAPP(U_633,U_632,U_629,U_631) = hAPP(U_633,U_632,U_629,U_630)
| ti(U_633,U_631) != ti(U_633,U_630) )
& ( ti(U_633,U_631) = ti(U_633,U_630)
| hAPP(U_633,U_632,U_629,U_631) != hAPP(U_633,U_632,U_629,U_630) ) )
| ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(fun(U_633,U_632),fun(fun(U_633,bool),bool),inj_on(U_633,U_632),U_629),top_top(fun(U_633,bool)))) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( ti(U_633,U_631) = ti(U_633,U_630)
| hAPP(U_633,U_632,U_629,U_631) != hAPP(U_633,U_632,U_629,U_630)
| ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(fun(U_633,U_632),fun(fun(U_633,bool),bool),inj_on(U_633,U_632),U_629),top_top(fun(U_633,bool)))) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_4,plain,
( hAPP(U_633,U_632,U_629,U_631) = hAPP(U_633,U_632,U_629,U_630)
| ti(U_633,U_631) != ti(U_633,U_630)
| ~ hBOOL(hAPP(fun(U_633,bool),bool,hAPP(fun(U_633,U_632),fun(fun(U_633,bool),bool),inj_on(U_633,U_632),U_629),top_top(fun(U_633,bool)))) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_1,plain,
! [X_a,X_b,X_1,Y_2,F] :
( 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(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_144_injD]) ).
fof(f_207_2,plain,
! [U_638,U_637,U_636,U_635,U_634] :
( ti(U_638,U_636) = ti(U_638,U_635)
| hAPP(U_638,U_637,U_634,U_636) != hAPP(U_638,U_637,U_634,U_635)
| ~ hBOOL(hAPP(fun(U_638,bool),bool,hAPP(fun(U_638,U_637),fun(fun(U_638,bool),bool),inj_on(U_638,U_637),U_634),top_top(fun(U_638,bool)))) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( ti(U_638,U_636) = ti(U_638,U_635)
| hAPP(U_638,U_637,U_634,U_636) != hAPP(U_638,U_637,U_634,U_635)
| ~ hBOOL(hAPP(fun(U_638,bool),bool,hAPP(fun(U_638,U_637),fun(fun(U_638,bool),bool),inj_on(U_638,U_637),U_634),top_top(fun(U_638,bool)))) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_1,plain,
! [X_a,X_b,X_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)),hilbert_inv_into(X_a,X_b),A_1),F),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))
| ~ 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_145_inv__into__f__f]) ).
fof(f_208_2,plain,
! [U_643,U_642,U_641,U_640,U_639] :
( hAPP(U_642,U_643,hAPP(fun(U_643,U_642),fun(U_642,U_643),hAPP(fun(U_643,bool),fun(fun(U_643,U_642),fun(U_642,U_643)),hilbert_inv_into(U_643,U_642),U_639),U_640),hAPP(U_643,U_642,U_640,U_641)) = ti(U_643,U_641)
| ~ hBOOL(hAPP(fun(U_643,bool),bool,hAPP(U_643,fun(fun(U_643,bool),bool),member(U_643),U_641),U_639))
| ~ hBOOL(hAPP(fun(U_643,bool),bool,hAPP(fun(U_643,U_642),fun(fun(U_643,bool),bool),inj_on(U_643,U_642),U_640),U_639)) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( hAPP(U_642,U_643,hAPP(fun(U_643,U_642),fun(U_642,U_643),hAPP(fun(U_643,bool),fun(fun(U_643,U_642),fun(U_642,U_643)),hilbert_inv_into(U_643,U_642),U_639),U_640),hAPP(U_643,U_642,U_640,U_641)) = ti(U_643,U_641)
| ~ hBOOL(hAPP(fun(U_643,bool),bool,hAPP(U_643,fun(fun(U_643,bool),bool),member(U_643),U_641),U_639))
| ~ hBOOL(hAPP(fun(U_643,bool),bool,hAPP(fun(U_643,U_642),fun(fun(U_643,bool),bool),inj_on(U_643,U_642),U_640),U_639)) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [X_a,X_b,Y_2,X_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)),hilbert_inv_into(X_a,X_b),A_1),F),Y_2) = ti(X_a,X_1)
| hAPP(X_a,X_b,F,X_1) != ti(X_b,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(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_146_inv__into__f__eq]) ).
fof(f_209_2,plain,
! [U_649,U_648,U_647,U_646,U_645,U_644] :
( hAPP(U_648,U_649,hAPP(fun(U_649,U_648),fun(U_648,U_649),hAPP(fun(U_649,bool),fun(fun(U_649,U_648),fun(U_648,U_649)),hilbert_inv_into(U_649,U_648),U_644),U_645),U_647) = ti(U_649,U_646)
| hAPP(U_649,U_648,U_645,U_646) != ti(U_648,U_647)
| ~ hBOOL(hAPP(fun(U_649,bool),bool,hAPP(U_649,fun(fun(U_649,bool),bool),member(U_649),U_646),U_644))
| ~ hBOOL(hAPP(fun(U_649,bool),bool,hAPP(fun(U_649,U_648),fun(fun(U_649,bool),bool),inj_on(U_649,U_648),U_645),U_644)) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( hAPP(U_648,U_649,hAPP(fun(U_649,U_648),fun(U_648,U_649),hAPP(fun(U_649,bool),fun(fun(U_649,U_648),fun(U_648,U_649)),hilbert_inv_into(U_649,U_648),U_644),U_645),U_647) = ti(U_649,U_646)
| hAPP(U_649,U_648,U_645,U_646) != ti(U_648,U_647)
| ~ hBOOL(hAPP(fun(U_649,bool),bool,hAPP(U_649,fun(fun(U_649,bool),bool),member(U_649),U_646),U_644))
| ~ hBOOL(hAPP(fun(U_649,bool),bool,hAPP(fun(U_649,U_648),fun(fun(U_649,bool),bool),inj_on(U_649,U_648),U_645),U_644)) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_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_2] :
( ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_147_Pi__I]) ).
fof(f_210_2,plain,
! [U_655,U_654,U_653,U_652,U_651] :
( hBOOL(hAPP(fun(fun(U_654,U_655),bool),bool,hAPP(fun(U_654,U_655),fun(fun(fun(U_654,U_655),bool),bool),member(fun(U_654,U_655)),U_653),hAPP(fun(U_654,fun(U_655,bool)),fun(fun(U_654,U_655),bool),hAPP(fun(U_654,bool),fun(fun(U_654,fun(U_655,bool)),fun(fun(U_654,U_655),bool)),pi(U_654,U_655),U_651),U_652)))
| ? [U_650] :
( ~ hBOOL(hAPP(fun(U_655,bool),bool,hAPP(U_655,fun(fun(U_655,bool),bool),member(U_655),hAPP(U_654,U_655,U_653,U_650)),hAPP(U_654,fun(U_655,bool),U_652,U_650)))
& hBOOL(hAPP(fun(U_654,bool),bool,hAPP(U_654,fun(fun(U_654,bool),bool),member(U_654),U_650),U_651)) ) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_655,U_654,U_653,U_652,U_651] :
( hBOOL(hAPP(fun(fun(U_654,U_655),bool),bool,hAPP(fun(U_654,U_655),fun(fun(fun(U_654,U_655),bool),bool),member(fun(U_654,U_655)),U_653),hAPP(fun(U_654,fun(U_655,bool)),fun(fun(U_654,U_655),bool),hAPP(fun(U_654,bool),fun(fun(U_654,fun(U_655,bool)),fun(fun(U_654,U_655),bool)),pi(U_654,U_655),U_651),U_652)))
| ( ~ hBOOL(hAPP(fun(U_655,bool),bool,hAPP(U_655,fun(fun(U_655,bool),bool),member(U_655),hAPP(U_654,U_655,U_653,sK41(U_655,U_654,U_653,U_652,U_651))),hAPP(U_654,fun(U_655,bool),U_652,sK41(U_655,U_654,U_653,U_652,U_651))))
& hBOOL(hAPP(fun(U_654,bool),bool,hAPP(U_654,fun(fun(U_654,bool),bool),member(U_654),sK41(U_655,U_654,U_653,U_652,U_651)),U_651)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_650,sK41(U_655,U_654,U_653,U_652,U_651))],[f_210_2]) ).
cnf(f_210_4,plain,
( hBOOL(hAPP(fun(U_654,bool),bool,hAPP(U_654,fun(fun(U_654,bool),bool),member(U_654),sK41(U_655,U_654,U_653,U_652,U_651)),U_651))
| hBOOL(hAPP(fun(fun(U_654,U_655),bool),bool,hAPP(fun(U_654,U_655),fun(fun(fun(U_654,U_655),bool),bool),member(fun(U_654,U_655)),U_653),hAPP(fun(U_654,fun(U_655,bool)),fun(fun(U_654,U_655),bool),hAPP(fun(U_654,bool),fun(fun(U_654,fun(U_655,bool)),fun(fun(U_654,U_655),bool)),pi(U_654,U_655),U_651),U_652))) ),
inference(clausify,[status(thm)],[f_210_3]) ).
cnf(f_210_5,plain,
( ~ hBOOL(hAPP(fun(U_655,bool),bool,hAPP(U_655,fun(fun(U_655,bool),bool),member(U_655),hAPP(U_654,U_655,U_653,sK41(U_655,U_654,U_653,U_652,U_651))),hAPP(U_654,fun(U_655,bool),U_652,sK41(U_655,U_654,U_653,U_652,U_651))))
| hBOOL(hAPP(fun(fun(U_654,U_655),bool),bool,hAPP(fun(U_654,U_655),fun(fun(fun(U_654,U_655),bool),bool),member(fun(U_654,U_655)),U_653),hAPP(fun(U_654,fun(U_655,bool)),fun(fun(U_654,U_655),bool),hAPP(fun(U_654,bool),fun(fun(U_654,fun(U_655,bool)),fun(fun(U_654,U_655),bool)),pi(U_654,U_655),U_651),U_652))) ),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_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_2] : hAPP(X_a,X_b,F,hAPP(X_b,X_a,G,X_2)) != ti(X_b,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_148_inj__imp__inv__eq]) ).
fof(f_211_2,plain,
! [U_660,U_659,U_658,U_657] :
( hAPP(fun(U_660,U_659),fun(U_659,U_660),hAPP(fun(U_660,bool),fun(fun(U_660,U_659),fun(U_659,U_660)),hilbert_inv_into(U_660,U_659),top_top(fun(U_660,bool))),U_657) = ti(fun(U_659,U_660),U_658)
| ? [U_656] : hAPP(U_660,U_659,U_657,hAPP(U_659,U_660,U_658,U_656)) != ti(U_659,U_656)
| ~ hBOOL(hAPP(fun(U_660,bool),bool,hAPP(fun(U_660,U_659),fun(fun(U_660,bool),bool),inj_on(U_660,U_659),U_657),top_top(fun(U_660,bool)))) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_660,U_659,U_658,U_657] :
( hAPP(fun(U_660,U_659),fun(U_659,U_660),hAPP(fun(U_660,bool),fun(fun(U_660,U_659),fun(U_659,U_660)),hilbert_inv_into(U_660,U_659),top_top(fun(U_660,bool))),U_657) = ti(fun(U_659,U_660),U_658)
| hAPP(U_660,U_659,U_657,hAPP(U_659,U_660,U_658,sK42(U_660,U_659,U_658,U_657))) != ti(U_659,sK42(U_660,U_659,U_658,U_657))
| ~ hBOOL(hAPP(fun(U_660,bool),bool,hAPP(fun(U_660,U_659),fun(fun(U_660,bool),bool),inj_on(U_660,U_659),U_657),top_top(fun(U_660,bool)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_656,sK42(U_660,U_659,U_658,U_657))],[f_211_2]) ).
cnf(f_211_4,plain,
( hAPP(fun(U_660,U_659),fun(U_659,U_660),hAPP(fun(U_660,bool),fun(fun(U_660,U_659),fun(U_659,U_660)),hilbert_inv_into(U_660,U_659),top_top(fun(U_660,bool))),U_657) = ti(fun(U_659,U_660),U_658)
| hAPP(U_660,U_659,U_657,hAPP(U_659,U_660,U_658,sK42(U_660,U_659,U_658,U_657))) != ti(U_659,sK42(U_660,U_659,U_658,U_657))
| ~ hBOOL(hAPP(fun(U_660,bool),bool,hAPP(fun(U_660,U_659),fun(fun(U_660,bool),bool),inj_on(U_660,U_659),U_657),top_top(fun(U_660,bool)))) ),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_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_149_less__add__one]) ).
fof(f_212_2,plain,
! [U_662] :
( ! [U_661] : hBOOL(hAPP(U_662,bool,hAPP(U_662,fun(U_662,bool),ord_less(U_662),U_661),hAPP(U_662,U_662,hAPP(U_662,fun(U_662,U_662),plus_plus(U_662),U_661),one_one(U_662))))
| ~ linordered_semidom(U_662) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( hBOOL(hAPP(U_662,bool,hAPP(U_662,fun(U_662,bool),ord_less(U_662),U_661),hAPP(U_662,U_662,hAPP(U_662,fun(U_662,U_662),plus_plus(U_662),U_661),one_one(U_662))))
| ~ linordered_semidom(U_662) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_1,plain,
! [X_a] :
( ! [C,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)),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),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_150_add__less__le__mono]) ).
fof(f_213_2,plain,
! [U_667] :
( ! [U_666,U_665,U_664,U_663] :
( hBOOL(hAPP(U_667,bool,hAPP(U_667,fun(U_667,bool),ord_less(U_667),hAPP(U_667,U_667,hAPP(U_667,fun(U_667,U_667),plus_plus(U_667),U_664),U_666)),hAPP(U_667,U_667,hAPP(U_667,fun(U_667,U_667),plus_plus(U_667),U_663),U_665)))
| ~ hBOOL(hAPP(U_667,bool,hAPP(U_667,fun(U_667,bool),ord_less_eq(U_667),U_666),U_665))
| ~ hBOOL(hAPP(U_667,bool,hAPP(U_667,fun(U_667,bool),ord_less(U_667),U_664),U_663)) )
| ~ ordere223160158up_add(U_667) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( hBOOL(hAPP(U_667,bool,hAPP(U_667,fun(U_667,bool),ord_less(U_667),hAPP(U_667,U_667,hAPP(U_667,fun(U_667,U_667),plus_plus(U_667),U_664),U_666)),hAPP(U_667,U_667,hAPP(U_667,fun(U_667,U_667),plus_plus(U_667),U_663),U_665)))
| ~ hBOOL(hAPP(U_667,bool,hAPP(U_667,fun(U_667,bool),ord_less_eq(U_667),U_666),U_665))
| ~ hBOOL(hAPP(U_667,bool,hAPP(U_667,fun(U_667,bool),ord_less(U_667),U_664),U_663))
| ~ ordere223160158up_add(U_667) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_1,plain,
! [X_a] :
( ! [C,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)),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),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_151_add__le__less__mono]) ).
fof(f_214_2,plain,
! [U_672] :
( ! [U_671,U_670,U_669,U_668] :
( hBOOL(hAPP(U_672,bool,hAPP(U_672,fun(U_672,bool),ord_less(U_672),hAPP(U_672,U_672,hAPP(U_672,fun(U_672,U_672),plus_plus(U_672),U_669),U_671)),hAPP(U_672,U_672,hAPP(U_672,fun(U_672,U_672),plus_plus(U_672),U_668),U_670)))
| ~ hBOOL(hAPP(U_672,bool,hAPP(U_672,fun(U_672,bool),ord_less(U_672),U_671),U_670))
| ~ hBOOL(hAPP(U_672,bool,hAPP(U_672,fun(U_672,bool),ord_less_eq(U_672),U_669),U_668)) )
| ~ ordere223160158up_add(U_672) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( hBOOL(hAPP(U_672,bool,hAPP(U_672,fun(U_672,bool),ord_less(U_672),hAPP(U_672,U_672,hAPP(U_672,fun(U_672,U_672),plus_plus(U_672),U_669),U_671)),hAPP(U_672,U_672,hAPP(U_672,fun(U_672,U_672),plus_plus(U_672),U_668),U_670)))
| ~ hBOOL(hAPP(U_672,bool,hAPP(U_672,fun(U_672,bool),ord_less(U_672),U_671),U_670))
| ~ hBOOL(hAPP(U_672,bool,hAPP(U_672,fun(U_672,bool),ord_less_eq(U_672),U_669),U_668))
| ~ ordere223160158up_add(U_672) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_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_2,Y_3] :
( ti(X_a,X_2) != ti(X_a,Y_3)
& hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_3) ) ),
inference(fof_nnf,[status(thm)],[fact_152_injI]) ).
fof(f_215_2,plain,
! [U_677,U_676,U_675] :
( hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,U_676),fun(fun(U_677,bool),bool),inj_on(U_677,U_676),U_675),top_top(fun(U_677,bool))))
| ? [U_674,U_673] :
( ti(U_677,U_674) != ti(U_677,U_673)
& hAPP(U_677,U_676,U_675,U_674) = hAPP(U_677,U_676,U_675,U_673) ) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_677,U_676,U_675] :
( hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,U_676),fun(fun(U_677,bool),bool),inj_on(U_677,U_676),U_675),top_top(fun(U_677,bool))))
| ? [U_673] :
( ti(U_677,sK43(U_677,U_676,U_675)) != ti(U_677,U_673)
& hAPP(U_677,U_676,U_675,sK43(U_677,U_676,U_675)) = hAPP(U_677,U_676,U_675,U_673) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_674,sK43(U_677,U_676,U_675))],[f_215_2]) ).
fof(f_215_4,plain,
! [U_677,U_676,U_675] :
( hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,U_676),fun(fun(U_677,bool),bool),inj_on(U_677,U_676),U_675),top_top(fun(U_677,bool))))
| ( ti(U_677,sK43(U_677,U_676,U_675)) != ti(U_677,sK44(U_677,U_676,U_675))
& hAPP(U_677,U_676,U_675,sK43(U_677,U_676,U_675)) = hAPP(U_677,U_676,U_675,sK44(U_677,U_676,U_675)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_673,sK44(U_677,U_676,U_675))],[f_215_3]) ).
cnf(f_215_5,plain,
( hAPP(U_677,U_676,U_675,sK43(U_677,U_676,U_675)) = hAPP(U_677,U_676,U_675,sK44(U_677,U_676,U_675))
| hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,U_676),fun(fun(U_677,bool),bool),inj_on(U_677,U_676),U_675),top_top(fun(U_677,bool)))) ),
inference(clausify,[status(thm)],[f_215_4]) ).
cnf(f_215_6,plain,
( ti(U_677,sK43(U_677,U_676,U_675)) != ti(U_677,sK44(U_677,U_676,U_675))
| hBOOL(hAPP(fun(U_677,bool),bool,hAPP(fun(U_677,U_676),fun(fun(U_677,bool),bool),inj_on(U_677,U_676),U_675),top_top(fun(U_677,bool)))) ),
inference(clausify,[status(thm)],[f_215_4]) ).
fof(f_216_1,plain,
! [X_a] :
( ! [Z_1,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))
| ? [X_2] :
( ~ 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(X_a),X_2),Y)) ) )
| ~ dense_linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_153_dense__le]) ).
fof(f_216_2,plain,
! [U_681] :
( ! [U_680,U_679] :
( hBOOL(hAPP(U_681,bool,hAPP(U_681,fun(U_681,bool),ord_less_eq(U_681),U_679),U_680))
| ? [U_678] :
( ~ hBOOL(hAPP(U_681,bool,hAPP(U_681,fun(U_681,bool),ord_less_eq(U_681),U_678),U_680))
& hBOOL(hAPP(U_681,bool,hAPP(U_681,fun(U_681,bool),ord_less(U_681),U_678),U_679)) ) )
| ~ dense_linorder(U_681) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_681] :
( ! [U_680,U_679] :
( hBOOL(hAPP(U_681,bool,hAPP(U_681,fun(U_681,bool),ord_less_eq(U_681),U_679),U_680))
| ( ~ hBOOL(hAPP(U_681,bool,hAPP(U_681,fun(U_681,bool),ord_less_eq(U_681),sK45(U_681,U_680,U_679)),U_680))
& hBOOL(hAPP(U_681,bool,hAPP(U_681,fun(U_681,bool),ord_less(U_681),sK45(U_681,U_680,U_679)),U_679)) ) )
| ~ dense_linorder(U_681) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_678,sK45(U_681,U_680,U_679))],[f_216_2]) ).
cnf(f_216_4,plain,
( hBOOL(hAPP(U_681,bool,hAPP(U_681,fun(U_681,bool),ord_less(U_681),sK45(U_681,U_680,U_679)),U_679))
| hBOOL(hAPP(U_681,bool,hAPP(U_681,fun(U_681,bool),ord_less_eq(U_681),U_679),U_680))
| ~ dense_linorder(U_681) ),
inference(clausify,[status(thm)],[f_216_3]) ).
cnf(f_216_5,plain,
( ~ hBOOL(hAPP(U_681,bool,hAPP(U_681,fun(U_681,bool),ord_less_eq(U_681),sK45(U_681,U_680,U_679)),U_680))
| hBOOL(hAPP(U_681,bool,hAPP(U_681,fun(U_681,bool),ord_less_eq(U_681),U_679),U_680))
| ~ dense_linorder(U_681) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_1,plain,
! [X_a] :
( ! [Z_1,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))
| ? [W] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1))
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y))
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W)) )
| ~ 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_154_dense__le__bounded]) ).
fof(f_217_2,plain,
! [U_686] :
( ! [U_685,U_684,U_683] :
( hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less_eq(U_686),U_683),U_685))
| ? [U_682] :
( ~ hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less_eq(U_686),U_682),U_685))
& hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),U_682),U_683))
& hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),U_684),U_682)) )
| ~ hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),U_684),U_683)) )
| ~ dense_linorder(U_686) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_686] :
( ! [U_685,U_684,U_683] :
( hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less_eq(U_686),U_683),U_685))
| ( ~ hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less_eq(U_686),sK46(U_686,U_685,U_684,U_683)),U_685))
& hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),sK46(U_686,U_685,U_684,U_683)),U_683))
& hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),U_684),sK46(U_686,U_685,U_684,U_683))) )
| ~ hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),U_684),U_683)) )
| ~ dense_linorder(U_686) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_682,sK46(U_686,U_685,U_684,U_683))],[f_217_2]) ).
cnf(f_217_4,plain,
( hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),U_684),sK46(U_686,U_685,U_684,U_683)))
| hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less_eq(U_686),U_683),U_685))
| ~ hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),U_684),U_683))
| ~ dense_linorder(U_686) ),
inference(clausify,[status(thm)],[f_217_3]) ).
cnf(f_217_5,plain,
( hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),sK46(U_686,U_685,U_684,U_683)),U_683))
| hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less_eq(U_686),U_683),U_685))
| ~ hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),U_684),U_683))
| ~ dense_linorder(U_686) ),
inference(clausify,[status(thm)],[f_217_3]) ).
cnf(f_217_6,plain,
( ~ hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less_eq(U_686),sK46(U_686,U_685,U_684,U_683)),U_685))
| hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less_eq(U_686),U_683),U_685))
| ~ hBOOL(hAPP(U_686,bool,hAPP(U_686,fun(U_686,bool),ord_less(U_686),U_684),U_683))
| ~ dense_linorder(U_686) ),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_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_155_less__fun__def]) ).
fof(f_218_2,plain,
! [U_690,U_689] :
( ! [U_688,U_687] :
( ( hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less(fun(U_690,U_689)),U_688),U_687))
| hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_687),U_688))
| ~ hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_688),U_687)) )
& ( ( ~ hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_687),U_688))
& hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_688),U_687)) )
| ~ hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less(fun(U_690,U_689)),U_688),U_687)) ) )
| ~ ord(U_689) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_690,U_689] :
( ( ! [U_694,U_692] :
( hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less(fun(U_690,U_689)),U_694),U_692))
| hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_692),U_694))
| ~ hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_694),U_692)) )
& ! [U_693,U_691] :
( ( ~ hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_691),U_693))
& hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_693),U_691)) )
| ~ hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less(fun(U_690,U_689)),U_693),U_691)) ) )
| ~ ord(U_689) ),
inference(miniscope,[status(thm)],[f_218_2]) ).
cnf(f_218_4,plain,
( hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_693),U_691))
| ~ hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less(fun(U_690,U_689)),U_693),U_691))
| ~ ord(U_689) ),
inference(clausify,[status(thm)],[f_218_3]) ).
cnf(f_218_5,plain,
( ~ hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_691),U_693))
| ~ hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less(fun(U_690,U_689)),U_693),U_691))
| ~ ord(U_689) ),
inference(clausify,[status(thm)],[f_218_3]) ).
cnf(f_218_6,plain,
( hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less(fun(U_690,U_689)),U_694),U_692))
| hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_692),U_694))
| ~ hBOOL(hAPP(fun(U_690,U_689),bool,hAPP(fun(U_690,U_689),fun(fun(U_690,U_689),bool),ord_less_eq(fun(U_690,U_689)),U_694),U_692))
| ~ ord(U_689) ),
inference(clausify,[status(thm)],[f_218_3]) ).
fof(f_219_1,plain,
! [X_b,X_a,B,A_4,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_4),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_4),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_156_Pi__anti__mono]) ).
fof(f_219_2,plain,
! [U_699,U_698,U_697,U_696,U_695] :
( hBOOL(hAPP(fun(fun(U_698,U_699),bool),bool,hAPP(fun(fun(U_698,U_699),bool),fun(fun(fun(U_698,U_699),bool),bool),ord_less_eq(fun(fun(U_698,U_699),bool)),hAPP(fun(U_698,fun(U_699,bool)),fun(fun(U_698,U_699),bool),hAPP(fun(U_698,bool),fun(fun(U_698,fun(U_699,bool)),fun(fun(U_698,U_699),bool)),pi(U_698,U_699),U_695),U_697)),hAPP(fun(U_698,fun(U_699,bool)),fun(fun(U_698,U_699),bool),hAPP(fun(U_698,bool),fun(fun(U_698,fun(U_699,bool)),fun(fun(U_698,U_699),bool)),pi(U_698,U_699),U_696),U_697)))
| ~ hBOOL(hAPP(fun(U_698,bool),bool,hAPP(fun(U_698,bool),fun(fun(U_698,bool),bool),ord_less_eq(fun(U_698,bool)),U_696),U_695)) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( hBOOL(hAPP(fun(fun(U_698,U_699),bool),bool,hAPP(fun(fun(U_698,U_699),bool),fun(fun(fun(U_698,U_699),bool),bool),ord_less_eq(fun(fun(U_698,U_699),bool)),hAPP(fun(U_698,fun(U_699,bool)),fun(fun(U_698,U_699),bool),hAPP(fun(U_698,bool),fun(fun(U_698,fun(U_699,bool)),fun(fun(U_698,U_699),bool)),pi(U_698,U_699),U_695),U_697)),hAPP(fun(U_698,fun(U_699,bool)),fun(fun(U_698,U_699),bool),hAPP(fun(U_698,bool),fun(fun(U_698,fun(U_699,bool)),fun(fun(U_698,U_699),bool)),pi(U_698,U_699),U_696),U_697)))
| ~ hBOOL(hAPP(fun(U_698,bool),bool,hAPP(fun(U_698,bool),fun(fun(U_698,bool),bool),ord_less_eq(fun(U_698,bool)),U_696),U_695)) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_1,plain,
! [X_a,X_b,R_1,S_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))),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_1)),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_1)))
| ~ 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_1),S_1)) )
& ( 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_1),S_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))),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_1)),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_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_157_pred__subset__eq2]) ).
fof(f_220_2,plain,
! [U_703,U_702,U_701,U_700] :
( ( hBOOL(hAPP(fun(U_703,fun(U_702,bool)),bool,hAPP(fun(U_703,fun(U_702,bool)),fun(fun(U_703,fun(U_702,bool)),bool),ord_less_eq(fun(U_703,fun(U_702,bool))),hAPP(fun(product_prod(U_703,U_702),bool),fun(U_703,fun(U_702,bool)),hAPP(fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),fun(fun(product_prod(U_703,U_702),bool),fun(U_703,fun(U_702,bool))),combc(U_703,fun(product_prod(U_703,U_702),bool),fun(U_702,bool)),hAPP(fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),hAPP(fun(fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),fun(fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool)))),combb(fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool)),U_703),combc(U_702,fun(product_prod(U_703,U_702),bool),bool)),hAPP(fun(U_703,fun(U_702,product_prod(U_703,U_702))),fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),hAPP(fun(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(fun(U_703,fun(U_702,product_prod(U_703,U_702))),fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)))),combb(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),U_703),hAPP(fun(product_prod(U_703,U_702),fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),combb(product_prod(U_703,U_702),fun(fun(product_prod(U_703,U_702),bool),bool),U_702),member(product_prod(U_703,U_702)))),product_Pair(U_703,U_702)))),U_701)),hAPP(fun(product_prod(U_703,U_702),bool),fun(U_703,fun(U_702,bool)),hAPP(fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),fun(fun(product_prod(U_703,U_702),bool),fun(U_703,fun(U_702,bool))),combc(U_703,fun(product_prod(U_703,U_702),bool),fun(U_702,bool)),hAPP(fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),hAPP(fun(fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),fun(fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool)))),combb(fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool)),U_703),combc(U_702,fun(product_prod(U_703,U_702),bool),bool)),hAPP(fun(U_703,fun(U_702,product_prod(U_703,U_702))),fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),hAPP(fun(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(fun(U_703,fun(U_702,product_prod(U_703,U_702))),fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)))),combb(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),U_703),hAPP(fun(product_prod(U_703,U_702),fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),combb(product_prod(U_703,U_702),fun(fun(product_prod(U_703,U_702),bool),bool),U_702),member(product_prod(U_703,U_702)))),product_Pair(U_703,U_702)))),U_700)))
| ~ hBOOL(hAPP(fun(product_prod(U_703,U_702),bool),bool,hAPP(fun(product_prod(U_703,U_702),bool),fun(fun(product_prod(U_703,U_702),bool),bool),ord_less_eq(fun(product_prod(U_703,U_702),bool)),U_701),U_700)) )
& ( hBOOL(hAPP(fun(product_prod(U_703,U_702),bool),bool,hAPP(fun(product_prod(U_703,U_702),bool),fun(fun(product_prod(U_703,U_702),bool),bool),ord_less_eq(fun(product_prod(U_703,U_702),bool)),U_701),U_700))
| ~ hBOOL(hAPP(fun(U_703,fun(U_702,bool)),bool,hAPP(fun(U_703,fun(U_702,bool)),fun(fun(U_703,fun(U_702,bool)),bool),ord_less_eq(fun(U_703,fun(U_702,bool))),hAPP(fun(product_prod(U_703,U_702),bool),fun(U_703,fun(U_702,bool)),hAPP(fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),fun(fun(product_prod(U_703,U_702),bool),fun(U_703,fun(U_702,bool))),combc(U_703,fun(product_prod(U_703,U_702),bool),fun(U_702,bool)),hAPP(fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),hAPP(fun(fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),fun(fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool)))),combb(fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool)),U_703),combc(U_702,fun(product_prod(U_703,U_702),bool),bool)),hAPP(fun(U_703,fun(U_702,product_prod(U_703,U_702))),fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),hAPP(fun(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(fun(U_703,fun(U_702,product_prod(U_703,U_702))),fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)))),combb(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),U_703),hAPP(fun(product_prod(U_703,U_702),fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),combb(product_prod(U_703,U_702),fun(fun(product_prod(U_703,U_702),bool),bool),U_702),member(product_prod(U_703,U_702)))),product_Pair(U_703,U_702)))),U_701)),hAPP(fun(product_prod(U_703,U_702),bool),fun(U_703,fun(U_702,bool)),hAPP(fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),fun(fun(product_prod(U_703,U_702),bool),fun(U_703,fun(U_702,bool))),combc(U_703,fun(product_prod(U_703,U_702),bool),fun(U_702,bool)),hAPP(fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),hAPP(fun(fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool))),fun(fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(U_703,fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool)))),combb(fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(product_prod(U_703,U_702),bool),fun(U_702,bool)),U_703),combc(U_702,fun(product_prod(U_703,U_702),bool),bool)),hAPP(fun(U_703,fun(U_702,product_prod(U_703,U_702))),fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),hAPP(fun(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),fun(fun(U_703,fun(U_702,product_prod(U_703,U_702))),fun(U_703,fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)))),combb(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool)),U_703),hAPP(fun(product_prod(U_703,U_702),fun(fun(product_prod(U_703,U_702),bool),bool)),fun(fun(U_702,product_prod(U_703,U_702)),fun(U_702,fun(fun(product_prod(U_703,U_702),bool),bool))),combb(product_prod(U_703,U_702),fun(fun(product_prod(U_703,U_702),bool),bool),U_702),member(product_prod(U_703,U_702)))),product_Pair(U_703,U_702)))),U_700))) ) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
( ! [U_711,U_709,U_707,U_705] :
( hBOOL(hAPP(fun(U_711,fun(U_709,bool)),bool,hAPP(fun(U_711,fun(U_709,bool)),fun(fun(U_711,fun(U_709,bool)),bool),ord_less_eq(fun(U_711,fun(U_709,bool))),hAPP(fun(product_prod(U_711,U_709),bool),fun(U_711,fun(U_709,bool)),hAPP(fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),fun(fun(product_prod(U_711,U_709),bool),fun(U_711,fun(U_709,bool))),combc(U_711,fun(product_prod(U_711,U_709),bool),fun(U_709,bool)),hAPP(fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),hAPP(fun(fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),fun(fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool)))),combb(fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool)),U_711),combc(U_709,fun(product_prod(U_711,U_709),bool),bool)),hAPP(fun(U_711,fun(U_709,product_prod(U_711,U_709))),fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),hAPP(fun(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(fun(U_711,fun(U_709,product_prod(U_711,U_709))),fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)))),combb(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),U_711),hAPP(fun(product_prod(U_711,U_709),fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),combb(product_prod(U_711,U_709),fun(fun(product_prod(U_711,U_709),bool),bool),U_709),member(product_prod(U_711,U_709)))),product_Pair(U_711,U_709)))),U_707)),hAPP(fun(product_prod(U_711,U_709),bool),fun(U_711,fun(U_709,bool)),hAPP(fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),fun(fun(product_prod(U_711,U_709),bool),fun(U_711,fun(U_709,bool))),combc(U_711,fun(product_prod(U_711,U_709),bool),fun(U_709,bool)),hAPP(fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),hAPP(fun(fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),fun(fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool)))),combb(fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool)),U_711),combc(U_709,fun(product_prod(U_711,U_709),bool),bool)),hAPP(fun(U_711,fun(U_709,product_prod(U_711,U_709))),fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),hAPP(fun(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(fun(U_711,fun(U_709,product_prod(U_711,U_709))),fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)))),combb(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),U_711),hAPP(fun(product_prod(U_711,U_709),fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),combb(product_prod(U_711,U_709),fun(fun(product_prod(U_711,U_709),bool),bool),U_709),member(product_prod(U_711,U_709)))),product_Pair(U_711,U_709)))),U_705)))
| ~ hBOOL(hAPP(fun(product_prod(U_711,U_709),bool),bool,hAPP(fun(product_prod(U_711,U_709),bool),fun(fun(product_prod(U_711,U_709),bool),bool),ord_less_eq(fun(product_prod(U_711,U_709),bool)),U_707),U_705)) )
& ! [U_710,U_708,U_706,U_704] :
( hBOOL(hAPP(fun(product_prod(U_710,U_708),bool),bool,hAPP(fun(product_prod(U_710,U_708),bool),fun(fun(product_prod(U_710,U_708),bool),bool),ord_less_eq(fun(product_prod(U_710,U_708),bool)),U_706),U_704))
| ~ hBOOL(hAPP(fun(U_710,fun(U_708,bool)),bool,hAPP(fun(U_710,fun(U_708,bool)),fun(fun(U_710,fun(U_708,bool)),bool),ord_less_eq(fun(U_710,fun(U_708,bool))),hAPP(fun(product_prod(U_710,U_708),bool),fun(U_710,fun(U_708,bool)),hAPP(fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),fun(fun(product_prod(U_710,U_708),bool),fun(U_710,fun(U_708,bool))),combc(U_710,fun(product_prod(U_710,U_708),bool),fun(U_708,bool)),hAPP(fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),hAPP(fun(fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),fun(fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool)))),combb(fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool)),U_710),combc(U_708,fun(product_prod(U_710,U_708),bool),bool)),hAPP(fun(U_710,fun(U_708,product_prod(U_710,U_708))),fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),hAPP(fun(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(fun(U_710,fun(U_708,product_prod(U_710,U_708))),fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)))),combb(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),U_710),hAPP(fun(product_prod(U_710,U_708),fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),combb(product_prod(U_710,U_708),fun(fun(product_prod(U_710,U_708),bool),bool),U_708),member(product_prod(U_710,U_708)))),product_Pair(U_710,U_708)))),U_706)),hAPP(fun(product_prod(U_710,U_708),bool),fun(U_710,fun(U_708,bool)),hAPP(fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),fun(fun(product_prod(U_710,U_708),bool),fun(U_710,fun(U_708,bool))),combc(U_710,fun(product_prod(U_710,U_708),bool),fun(U_708,bool)),hAPP(fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),hAPP(fun(fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),fun(fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool)))),combb(fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool)),U_710),combc(U_708,fun(product_prod(U_710,U_708),bool),bool)),hAPP(fun(U_710,fun(U_708,product_prod(U_710,U_708))),fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),hAPP(fun(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(fun(U_710,fun(U_708,product_prod(U_710,U_708))),fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)))),combb(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),U_710),hAPP(fun(product_prod(U_710,U_708),fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),combb(product_prod(U_710,U_708),fun(fun(product_prod(U_710,U_708),bool),bool),U_708),member(product_prod(U_710,U_708)))),product_Pair(U_710,U_708)))),U_704))) ) ),
inference(miniscope,[status(thm)],[f_220_2]) ).
cnf(f_220_4,plain,
( hBOOL(hAPP(fun(product_prod(U_710,U_708),bool),bool,hAPP(fun(product_prod(U_710,U_708),bool),fun(fun(product_prod(U_710,U_708),bool),bool),ord_less_eq(fun(product_prod(U_710,U_708),bool)),U_706),U_704))
| ~ hBOOL(hAPP(fun(U_710,fun(U_708,bool)),bool,hAPP(fun(U_710,fun(U_708,bool)),fun(fun(U_710,fun(U_708,bool)),bool),ord_less_eq(fun(U_710,fun(U_708,bool))),hAPP(fun(product_prod(U_710,U_708),bool),fun(U_710,fun(U_708,bool)),hAPP(fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),fun(fun(product_prod(U_710,U_708),bool),fun(U_710,fun(U_708,bool))),combc(U_710,fun(product_prod(U_710,U_708),bool),fun(U_708,bool)),hAPP(fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),hAPP(fun(fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),fun(fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool)))),combb(fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool)),U_710),combc(U_708,fun(product_prod(U_710,U_708),bool),bool)),hAPP(fun(U_710,fun(U_708,product_prod(U_710,U_708))),fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),hAPP(fun(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(fun(U_710,fun(U_708,product_prod(U_710,U_708))),fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)))),combb(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),U_710),hAPP(fun(product_prod(U_710,U_708),fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),combb(product_prod(U_710,U_708),fun(fun(product_prod(U_710,U_708),bool),bool),U_708),member(product_prod(U_710,U_708)))),product_Pair(U_710,U_708)))),U_706)),hAPP(fun(product_prod(U_710,U_708),bool),fun(U_710,fun(U_708,bool)),hAPP(fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),fun(fun(product_prod(U_710,U_708),bool),fun(U_710,fun(U_708,bool))),combc(U_710,fun(product_prod(U_710,U_708),bool),fun(U_708,bool)),hAPP(fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),hAPP(fun(fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool))),fun(fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(U_710,fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool)))),combb(fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(product_prod(U_710,U_708),bool),fun(U_708,bool)),U_710),combc(U_708,fun(product_prod(U_710,U_708),bool),bool)),hAPP(fun(U_710,fun(U_708,product_prod(U_710,U_708))),fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),hAPP(fun(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),fun(fun(U_710,fun(U_708,product_prod(U_710,U_708))),fun(U_710,fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)))),combb(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool)),U_710),hAPP(fun(product_prod(U_710,U_708),fun(fun(product_prod(U_710,U_708),bool),bool)),fun(fun(U_708,product_prod(U_710,U_708)),fun(U_708,fun(fun(product_prod(U_710,U_708),bool),bool))),combb(product_prod(U_710,U_708),fun(fun(product_prod(U_710,U_708),bool),bool),U_708),member(product_prod(U_710,U_708)))),product_Pair(U_710,U_708)))),U_704))) ),
inference(clausify,[status(thm)],[f_220_3]) ).
cnf(f_220_5,plain,
( hBOOL(hAPP(fun(U_711,fun(U_709,bool)),bool,hAPP(fun(U_711,fun(U_709,bool)),fun(fun(U_711,fun(U_709,bool)),bool),ord_less_eq(fun(U_711,fun(U_709,bool))),hAPP(fun(product_prod(U_711,U_709),bool),fun(U_711,fun(U_709,bool)),hAPP(fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),fun(fun(product_prod(U_711,U_709),bool),fun(U_711,fun(U_709,bool))),combc(U_711,fun(product_prod(U_711,U_709),bool),fun(U_709,bool)),hAPP(fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),hAPP(fun(fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),fun(fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool)))),combb(fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool)),U_711),combc(U_709,fun(product_prod(U_711,U_709),bool),bool)),hAPP(fun(U_711,fun(U_709,product_prod(U_711,U_709))),fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),hAPP(fun(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(fun(U_711,fun(U_709,product_prod(U_711,U_709))),fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)))),combb(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),U_711),hAPP(fun(product_prod(U_711,U_709),fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),combb(product_prod(U_711,U_709),fun(fun(product_prod(U_711,U_709),bool),bool),U_709),member(product_prod(U_711,U_709)))),product_Pair(U_711,U_709)))),U_707)),hAPP(fun(product_prod(U_711,U_709),bool),fun(U_711,fun(U_709,bool)),hAPP(fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),fun(fun(product_prod(U_711,U_709),bool),fun(U_711,fun(U_709,bool))),combc(U_711,fun(product_prod(U_711,U_709),bool),fun(U_709,bool)),hAPP(fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),hAPP(fun(fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool))),fun(fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(U_711,fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool)))),combb(fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(product_prod(U_711,U_709),bool),fun(U_709,bool)),U_711),combc(U_709,fun(product_prod(U_711,U_709),bool),bool)),hAPP(fun(U_711,fun(U_709,product_prod(U_711,U_709))),fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),hAPP(fun(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),fun(fun(U_711,fun(U_709,product_prod(U_711,U_709))),fun(U_711,fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)))),combb(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool)),U_711),hAPP(fun(product_prod(U_711,U_709),fun(fun(product_prod(U_711,U_709),bool),bool)),fun(fun(U_709,product_prod(U_711,U_709)),fun(U_709,fun(fun(product_prod(U_711,U_709),bool),bool))),combb(product_prod(U_711,U_709),fun(fun(product_prod(U_711,U_709),bool),bool),U_709),member(product_prod(U_711,U_709)))),product_Pair(U_711,U_709)))),U_705)))
| ~ hBOOL(hAPP(fun(product_prod(U_711,U_709),bool),bool,hAPP(fun(product_prod(U_711,U_709),bool),fun(fun(product_prod(U_711,U_709),bool),bool),ord_less_eq(fun(product_prod(U_711,U_709),bool)),U_707),U_705)) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_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_158_subset__UNIV]) ).
fof(f_221_2,plain,
! [U_713,U_712] : hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),U_712),top_top(fun(U_713,bool)))),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
hBOOL(hAPP(fun(U_713,bool),bool,hAPP(fun(U_713,bool),fun(fun(U_713,bool),bool),ord_less_eq(fun(U_713,bool)),U_712),top_top(fun(U_713,bool)))),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_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_159_subset__inj__on]) ).
fof(f_222_2,plain,
! [U_718,U_717,U_716,U_715,U_714] :
( hBOOL(hAPP(fun(U_718,bool),bool,hAPP(fun(U_718,U_717),fun(fun(U_718,bool),bool),inj_on(U_718,U_717),U_715),U_716))
| ~ hBOOL(hAPP(fun(U_718,bool),bool,hAPP(fun(U_718,bool),fun(fun(U_718,bool),bool),ord_less_eq(fun(U_718,bool)),U_716),U_714))
| ~ hBOOL(hAPP(fun(U_718,bool),bool,hAPP(fun(U_718,U_717),fun(fun(U_718,bool),bool),inj_on(U_718,U_717),U_715),U_714)) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
( hBOOL(hAPP(fun(U_718,bool),bool,hAPP(fun(U_718,U_717),fun(fun(U_718,bool),bool),inj_on(U_718,U_717),U_715),U_716))
| ~ hBOOL(hAPP(fun(U_718,bool),bool,hAPP(fun(U_718,bool),fun(fun(U_718,bool),bool),ord_less_eq(fun(U_718,bool)),U_716),U_714))
| ~ hBOOL(hAPP(fun(U_718,bool),bool,hAPP(fun(U_718,U_717),fun(fun(U_718,bool),bool),inj_on(U_718,U_717),U_715),U_714)) ),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_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_160_linorder__neqE__linordered__idom]) ).
fof(f_223_2,plain,
! [U_721] :
( ! [U_720,U_719] :
( hBOOL(hAPP(U_721,bool,hAPP(U_721,fun(U_721,bool),ord_less(U_721),U_719),U_720))
| hBOOL(hAPP(U_721,bool,hAPP(U_721,fun(U_721,bool),ord_less(U_721),U_720),U_719))
| ti(U_721,U_720) = ti(U_721,U_719) )
| ~ linordered_idom(U_721) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( hBOOL(hAPP(U_721,bool,hAPP(U_721,fun(U_721,bool),ord_less(U_721),U_719),U_720))
| hBOOL(hAPP(U_721,bool,hAPP(U_721,fun(U_721,bool),ord_less(U_721),U_720),U_719))
| ti(U_721,U_720) = ti(U_721,U_719)
| ~ linordered_idom(U_721) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_1,plain,
! [X_a] :
( ! [B_1,A_2,C] :
( ti(X_a,B_1) = ti(X_a,C)
| 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),A_2) )
| ~ cancel_semigroup_add(X_a) ),
inference(fof_nnf,[status(thm)],[fact_161_add__right__imp__eq]) ).
fof(f_224_2,plain,
! [U_725] :
( ! [U_724,U_723,U_722] :
( ti(U_725,U_724) = ti(U_725,U_722)
| hAPP(U_725,U_725,hAPP(U_725,fun(U_725,U_725),plus_plus(U_725),U_724),U_723) != hAPP(U_725,U_725,hAPP(U_725,fun(U_725,U_725),plus_plus(U_725),U_722),U_723) )
| ~ cancel_semigroup_add(U_725) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
( ti(U_725,U_724) = ti(U_725,U_722)
| hAPP(U_725,U_725,hAPP(U_725,fun(U_725,U_725),plus_plus(U_725),U_724),U_723) != hAPP(U_725,U_725,hAPP(U_725,fun(U_725,U_725),plus_plus(U_725),U_722),U_723)
| ~ cancel_semigroup_add(U_725) ),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_1,plain,
! [X_a] :
( ! [A_2,B_1,C] :
( ti(X_a,B_1) = ti(X_a,C)
| 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) )
| ~ cancel146912293up_add(X_a) ),
inference(fof_nnf,[status(thm)],[fact_162_add__imp__eq]) ).
fof(f_225_2,plain,
! [U_729] :
( ! [U_728,U_727,U_726] :
( ti(U_729,U_727) = ti(U_729,U_726)
| hAPP(U_729,U_729,hAPP(U_729,fun(U_729,U_729),plus_plus(U_729),U_728),U_727) != hAPP(U_729,U_729,hAPP(U_729,fun(U_729,U_729),plus_plus(U_729),U_728),U_726) )
| ~ cancel146912293up_add(U_729) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( ti(U_729,U_727) = ti(U_729,U_726)
| hAPP(U_729,U_729,hAPP(U_729,fun(U_729,U_729),plus_plus(U_729),U_728),U_727) != hAPP(U_729,U_729,hAPP(U_729,fun(U_729,U_729),plus_plus(U_729),U_728),U_726)
| ~ cancel146912293up_add(U_729) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_1,plain,
! [X_a] :
( ! [A_2,B_1,C] :
( ti(X_a,B_1) = ti(X_a,C)
| 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) )
| ~ cancel_semigroup_add(X_a) ),
inference(fof_nnf,[status(thm)],[fact_163_add__left__imp__eq]) ).
fof(f_226_2,plain,
! [U_733] :
( ! [U_732,U_731,U_730] :
( ti(U_733,U_731) = ti(U_733,U_730)
| hAPP(U_733,U_733,hAPP(U_733,fun(U_733,U_733),plus_plus(U_733),U_732),U_731) != hAPP(U_733,U_733,hAPP(U_733,fun(U_733,U_733),plus_plus(U_733),U_732),U_730) )
| ~ cancel_semigroup_add(U_733) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
cnf(f_226_3,plain,
( ti(U_733,U_731) = ti(U_733,U_730)
| hAPP(U_733,U_733,hAPP(U_733,fun(U_733,U_733),plus_plus(U_733),U_732),U_731) != hAPP(U_733,U_733,hAPP(U_733,fun(U_733,U_733),plus_plus(U_733),U_732),U_730)
| ~ cancel_semigroup_add(U_733) ),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_227_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_164_add__right__cancel]) ).
fof(f_227_2,plain,
! [U_737] :
( ! [U_736,U_735,U_734] :
( ( hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_736),U_735) = hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_734),U_735)
| ti(U_737,U_736) != ti(U_737,U_734) )
& ( ti(U_737,U_736) = ti(U_737,U_734)
| hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_736),U_735) != hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_734),U_735) ) )
| ~ cancel_semigroup_add(U_737) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
! [U_737] :
( ( ! [U_743,U_741,U_739] :
( hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_743),U_741) = hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_739),U_741)
| ti(U_737,U_743) != ti(U_737,U_739) )
& ! [U_742,U_740,U_738] :
( ti(U_737,U_742) = ti(U_737,U_738)
| hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_742),U_740) != hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_738),U_740) ) )
| ~ cancel_semigroup_add(U_737) ),
inference(miniscope,[status(thm)],[f_227_2]) ).
cnf(f_227_4,plain,
( ti(U_737,U_742) = ti(U_737,U_738)
| hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_742),U_740) != hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_738),U_740)
| ~ cancel_semigroup_add(U_737) ),
inference(clausify,[status(thm)],[f_227_3]) ).
cnf(f_227_5,plain,
( hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_743),U_741) = hAPP(U_737,U_737,hAPP(U_737,fun(U_737,U_737),plus_plus(U_737),U_739),U_741)
| ti(U_737,U_743) != ti(U_737,U_739)
| ~ cancel_semigroup_add(U_737) ),
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_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_165_add__left__cancel]) ).
fof(f_228_2,plain,
! [U_747] :
( ! [U_746,U_745,U_744] :
( ( hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_746),U_745) = hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_746),U_744)
| ti(U_747,U_745) != ti(U_747,U_744) )
& ( ti(U_747,U_745) = ti(U_747,U_744)
| hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_746),U_745) != hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_746),U_744) ) )
| ~ cancel_semigroup_add(U_747) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_747] :
( ( ! [U_753,U_751,U_749] :
( hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_753),U_751) = hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_753),U_749)
| ti(U_747,U_751) != ti(U_747,U_749) )
& ! [U_752,U_750,U_748] :
( ti(U_747,U_750) = ti(U_747,U_748)
| hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_752),U_750) != hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_752),U_748) ) )
| ~ cancel_semigroup_add(U_747) ),
inference(miniscope,[status(thm)],[f_228_2]) ).
cnf(f_228_4,plain,
( ti(U_747,U_750) = ti(U_747,U_748)
| hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_752),U_750) != hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_752),U_748)
| ~ cancel_semigroup_add(U_747) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_5,plain,
( hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_753),U_751) = hAPP(U_747,U_747,hAPP(U_747,fun(U_747,U_747),plus_plus(U_747),U_753),U_749)
| ti(U_747,U_751) != ti(U_747,U_749)
| ~ cancel_semigroup_add(U_747) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_1,plain,
! [X_a] :
( ! [A_2,B_1,C] : 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) = 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))
| ~ ab_semigroup_add(X_a) ),
inference(fof_nnf,[status(thm)],[fact_166_ab__semigroup__add__class_Oadd__ac_I1_J]) ).
fof(f_229_2,plain,
! [U_757] :
( ! [U_756,U_755,U_754] : hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),plus_plus(U_757),hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),plus_plus(U_757),U_756),U_755)),U_754) = hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),plus_plus(U_757),U_756),hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),plus_plus(U_757),U_755),U_754))
| ~ ab_semigroup_add(U_757) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
( hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),plus_plus(U_757),hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),plus_plus(U_757),U_756),U_755)),U_754) = hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),plus_plus(U_757),U_756),hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),plus_plus(U_757),U_755),U_754))
| ~ ab_semigroup_add(U_757) ),
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_1,plain,
! [X_a] :
( ! [X_1] :
( ( one_one(X_a) = ti(X_a,X_1)
| ti(X_a,X_1) != one_one(X_a) )
& ( ti(X_a,X_1) = one_one(X_a)
| one_one(X_a) != ti(X_a,X_1) ) )
| ~ one(X_a) ),
inference(fof_nnf,[status(thm)],[fact_167_one__reorient]) ).
fof(f_230_2,plain,
! [U_759] :
( ! [U_758] :
( ( one_one(U_759) = ti(U_759,U_758)
| ti(U_759,U_758) != one_one(U_759) )
& ( ti(U_759,U_758) = one_one(U_759)
| one_one(U_759) != ti(U_759,U_758) ) )
| ~ one(U_759) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_759] :
( ( ! [U_761] :
( one_one(U_759) = ti(U_759,U_761)
| ti(U_759,U_761) != one_one(U_759) )
& ! [U_760] :
( ti(U_759,U_760) = one_one(U_759)
| one_one(U_759) != ti(U_759,U_760) ) )
| ~ one(U_759) ),
inference(miniscope,[status(thm)],[f_230_2]) ).
cnf(f_230_4,plain,
( ti(U_759,U_760) = one_one(U_759)
| one_one(U_759) != ti(U_759,U_760)
| ~ one(U_759) ),
inference(clausify,[status(thm)],[f_230_3]) ).
cnf(f_230_5,plain,
( one_one(U_759) = ti(U_759,U_761)
| ti(U_759,U_761) != one_one(U_759)
| ~ one(U_759) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_1,plain,
! [X_a] :
( ! [C,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),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) )
| ~ ordere236663937imp_le(X_a) ),
inference(fof_nnf,[status(thm)],[fact_168_add__le__imp__le__left]) ).
fof(f_231_2,plain,
! [U_765] :
( ! [U_764,U_763,U_762] :
( hBOOL(hAPP(U_765,bool,hAPP(U_765,fun(U_765,bool),ord_less_eq(U_765),U_763),U_762))
| ~ hBOOL(hAPP(U_765,bool,hAPP(U_765,fun(U_765,bool),ord_less_eq(U_765),hAPP(U_765,U_765,hAPP(U_765,fun(U_765,U_765),plus_plus(U_765),U_764),U_763)),hAPP(U_765,U_765,hAPP(U_765,fun(U_765,U_765),plus_plus(U_765),U_764),U_762))) )
| ~ ordere236663937imp_le(U_765) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( hBOOL(hAPP(U_765,bool,hAPP(U_765,fun(U_765,bool),ord_less_eq(U_765),U_763),U_762))
| ~ hBOOL(hAPP(U_765,bool,hAPP(U_765,fun(U_765,bool),ord_less_eq(U_765),hAPP(U_765,U_765,hAPP(U_765,fun(U_765,U_765),plus_plus(U_765),U_764),U_763)),hAPP(U_765,U_765,hAPP(U_765,fun(U_765,U_765),plus_plus(U_765),U_764),U_762)))
| ~ ordere236663937imp_le(U_765) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_1,plain,
! [X_a] :
( ! [A_2,C,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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))) )
| ~ ordere236663937imp_le(X_a) ),
inference(fof_nnf,[status(thm)],[fact_169_add__le__imp__le__right]) ).
fof(f_232_2,plain,
! [U_769] :
( ! [U_768,U_767,U_766] :
( hBOOL(hAPP(U_769,bool,hAPP(U_769,fun(U_769,bool),ord_less_eq(U_769),U_768),U_766))
| ~ hBOOL(hAPP(U_769,bool,hAPP(U_769,fun(U_769,bool),ord_less_eq(U_769),hAPP(U_769,U_769,hAPP(U_769,fun(U_769,U_769),plus_plus(U_769),U_768),U_767)),hAPP(U_769,U_769,hAPP(U_769,fun(U_769,U_769),plus_plus(U_769),U_766),U_767))) )
| ~ ordere236663937imp_le(U_769) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
cnf(f_232_3,plain,
( hBOOL(hAPP(U_769,bool,hAPP(U_769,fun(U_769,bool),ord_less_eq(U_769),U_768),U_766))
| ~ hBOOL(hAPP(U_769,bool,hAPP(U_769,fun(U_769,bool),ord_less_eq(U_769),hAPP(U_769,U_769,hAPP(U_769,fun(U_769,U_769),plus_plus(U_769),U_768),U_767)),hAPP(U_769,U_769,hAPP(U_769,fun(U_769,U_769),plus_plus(U_769),U_766),U_767)))
| ~ ordere236663937imp_le(U_769) ),
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_1,plain,
! [X_a] :
( ! [C,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)),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),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_170_add__mono]) ).
fof(f_233_2,plain,
! [U_774] :
( ! [U_773,U_772,U_771,U_770] :
( hBOOL(hAPP(U_774,bool,hAPP(U_774,fun(U_774,bool),ord_less_eq(U_774),hAPP(U_774,U_774,hAPP(U_774,fun(U_774,U_774),plus_plus(U_774),U_771),U_773)),hAPP(U_774,U_774,hAPP(U_774,fun(U_774,U_774),plus_plus(U_774),U_770),U_772)))
| ~ hBOOL(hAPP(U_774,bool,hAPP(U_774,fun(U_774,bool),ord_less_eq(U_774),U_773),U_772))
| ~ hBOOL(hAPP(U_774,bool,hAPP(U_774,fun(U_774,bool),ord_less_eq(U_774),U_771),U_770)) )
| ~ ordere779506340up_add(U_774) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( hBOOL(hAPP(U_774,bool,hAPP(U_774,fun(U_774,bool),ord_less_eq(U_774),hAPP(U_774,U_774,hAPP(U_774,fun(U_774,U_774),plus_plus(U_774),U_771),U_773)),hAPP(U_774,U_774,hAPP(U_774,fun(U_774,U_774),plus_plus(U_774),U_770),U_772)))
| ~ hBOOL(hAPP(U_774,bool,hAPP(U_774,fun(U_774,bool),ord_less_eq(U_774),U_773),U_772))
| ~ hBOOL(hAPP(U_774,bool,hAPP(U_774,fun(U_774,bool),ord_less_eq(U_774),U_771),U_770))
| ~ ordere779506340up_add(U_774) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_1,plain,
! [X_a] :
( ! [C,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),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),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_171_add__left__mono]) ).
fof(f_234_2,plain,
! [U_778] :
( ! [U_777,U_776,U_775] :
( hBOOL(hAPP(U_778,bool,hAPP(U_778,fun(U_778,bool),ord_less_eq(U_778),hAPP(U_778,U_778,hAPP(U_778,fun(U_778,U_778),plus_plus(U_778),U_777),U_776)),hAPP(U_778,U_778,hAPP(U_778,fun(U_778,U_778),plus_plus(U_778),U_777),U_775)))
| ~ hBOOL(hAPP(U_778,bool,hAPP(U_778,fun(U_778,bool),ord_less_eq(U_778),U_776),U_775)) )
| ~ ordere779506340up_add(U_778) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( hBOOL(hAPP(U_778,bool,hAPP(U_778,fun(U_778,bool),ord_less_eq(U_778),hAPP(U_778,U_778,hAPP(U_778,fun(U_778,U_778),plus_plus(U_778),U_777),U_776)),hAPP(U_778,U_778,hAPP(U_778,fun(U_778,U_778),plus_plus(U_778),U_777),U_775)))
| ~ hBOOL(hAPP(U_778,bool,hAPP(U_778,fun(U_778,bool),ord_less_eq(U_778),U_776),U_775))
| ~ ordere779506340up_add(U_778) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_1,plain,
! [X_a] :
( ! [C,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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)))
| ~ 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_172_add__right__mono]) ).
fof(f_235_2,plain,
! [U_782] :
( ! [U_781,U_780,U_779] :
( hBOOL(hAPP(U_782,bool,hAPP(U_782,fun(U_782,bool),ord_less_eq(U_782),hAPP(U_782,U_782,hAPP(U_782,fun(U_782,U_782),plus_plus(U_782),U_780),U_781)),hAPP(U_782,U_782,hAPP(U_782,fun(U_782,U_782),plus_plus(U_782),U_779),U_781)))
| ~ hBOOL(hAPP(U_782,bool,hAPP(U_782,fun(U_782,bool),ord_less_eq(U_782),U_780),U_779)) )
| ~ ordere779506340up_add(U_782) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
( hBOOL(hAPP(U_782,bool,hAPP(U_782,fun(U_782,bool),ord_less_eq(U_782),hAPP(U_782,U_782,hAPP(U_782,fun(U_782,U_782),plus_plus(U_782),U_780),U_781)),hAPP(U_782,U_782,hAPP(U_782,fun(U_782,U_782),plus_plus(U_782),U_779),U_781)))
| ~ hBOOL(hAPP(U_782,bool,hAPP(U_782,fun(U_782,bool),ord_less_eq(U_782),U_780),U_779))
| ~ ordere779506340up_add(U_782) ),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_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_173_add__le__cancel__left]) ).
fof(f_236_2,plain,
! [U_786] :
( ! [U_785,U_784,U_783] :
( ( hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_785),U_784)),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_785),U_783)))
| ~ hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),U_784),U_783)) )
& ( hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),U_784),U_783))
| ~ hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_785),U_784)),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_785),U_783))) ) )
| ~ ordere236663937imp_le(U_786) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_786] :
( ( ! [U_792,U_790,U_788] :
( hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_792),U_790)),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_792),U_788)))
| ~ hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),U_790),U_788)) )
& ! [U_791,U_789,U_787] :
( hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),U_789),U_787))
| ~ hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_791),U_789)),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_791),U_787))) ) )
| ~ ordere236663937imp_le(U_786) ),
inference(miniscope,[status(thm)],[f_236_2]) ).
cnf(f_236_4,plain,
( hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),U_789),U_787))
| ~ hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_791),U_789)),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_791),U_787)))
| ~ ordere236663937imp_le(U_786) ),
inference(clausify,[status(thm)],[f_236_3]) ).
cnf(f_236_5,plain,
( hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_792),U_790)),hAPP(U_786,U_786,hAPP(U_786,fun(U_786,U_786),plus_plus(U_786),U_792),U_788)))
| ~ hBOOL(hAPP(U_786,bool,hAPP(U_786,fun(U_786,bool),ord_less_eq(U_786),U_790),U_788))
| ~ ordere236663937imp_le(U_786) ),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_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_174_add__le__cancel__right]) ).
fof(f_237_2,plain,
! [U_796] :
( ! [U_795,U_794,U_793] :
( ( hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),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)))
| ~ hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),U_795),U_793)) )
& ( hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),U_795),U_793))
| ~ hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),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))) ) )
| ~ ordere236663937imp_le(U_796) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_796] :
( ( ! [U_802,U_800,U_798] :
( hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),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)))
| ~ hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),U_802),U_798)) )
& ! [U_801,U_799,U_797] :
( hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),U_801),U_797))
| ~ hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),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))) ) )
| ~ ordere236663937imp_le(U_796) ),
inference(miniscope,[status(thm)],[f_237_2]) ).
cnf(f_237_4,plain,
( hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),U_801),U_797))
| ~ hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),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)))
| ~ ordere236663937imp_le(U_796) ),
inference(clausify,[status(thm)],[f_237_3]) ).
cnf(f_237_5,plain,
( hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),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)))
| ~ hBOOL(hAPP(U_796,bool,hAPP(U_796,fun(U_796,bool),ord_less_eq(U_796),U_802),U_798))
| ~ ordere236663937imp_le(U_796) ),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_1,plain,
! [X_a] :
( ! [C,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),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) )
| ~ ordere236663937imp_le(X_a) ),
inference(fof_nnf,[status(thm)],[fact_175_add__less__imp__less__left]) ).
fof(f_238_2,plain,
! [U_806] :
( ! [U_805,U_804,U_803] :
( hBOOL(hAPP(U_806,bool,hAPP(U_806,fun(U_806,bool),ord_less(U_806),U_804),U_803))
| ~ hBOOL(hAPP(U_806,bool,hAPP(U_806,fun(U_806,bool),ord_less(U_806),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))) )
| ~ ordere236663937imp_le(U_806) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
( hBOOL(hAPP(U_806,bool,hAPP(U_806,fun(U_806,bool),ord_less(U_806),U_804),U_803))
| ~ hBOOL(hAPP(U_806,bool,hAPP(U_806,fun(U_806,bool),ord_less(U_806),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)))
| ~ ordere236663937imp_le(U_806) ),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_1,plain,
! [X_a] :
( ! [A_2,C,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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))) )
| ~ ordere236663937imp_le(X_a) ),
inference(fof_nnf,[status(thm)],[fact_176_add__less__imp__less__right]) ).
fof(f_239_2,plain,
! [U_810] :
( ! [U_809,U_808,U_807] :
( hBOOL(hAPP(U_810,bool,hAPP(U_810,fun(U_810,bool),ord_less(U_810),U_809),U_807))
| ~ hBOOL(hAPP(U_810,bool,hAPP(U_810,fun(U_810,bool),ord_less(U_810),hAPP(U_810,U_810,hAPP(U_810,fun(U_810,U_810),plus_plus(U_810),U_809),U_808)),hAPP(U_810,U_810,hAPP(U_810,fun(U_810,U_810),plus_plus(U_810),U_807),U_808))) )
| ~ ordere236663937imp_le(U_810) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( hBOOL(hAPP(U_810,bool,hAPP(U_810,fun(U_810,bool),ord_less(U_810),U_809),U_807))
| ~ hBOOL(hAPP(U_810,bool,hAPP(U_810,fun(U_810,bool),ord_less(U_810),hAPP(U_810,U_810,hAPP(U_810,fun(U_810,U_810),plus_plus(U_810),U_809),U_808)),hAPP(U_810,U_810,hAPP(U_810,fun(U_810,U_810),plus_plus(U_810),U_807),U_808)))
| ~ ordere236663937imp_le(U_810) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_1,plain,
! [X_a] :
( ! [C,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)),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),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_177_add__strict__mono]) ).
fof(f_240_2,plain,
! [U_815] :
( ! [U_814,U_813,U_812,U_811] :
( hBOOL(hAPP(U_815,bool,hAPP(U_815,fun(U_815,bool),ord_less(U_815),hAPP(U_815,U_815,hAPP(U_815,fun(U_815,U_815),plus_plus(U_815),U_812),U_814)),hAPP(U_815,U_815,hAPP(U_815,fun(U_815,U_815),plus_plus(U_815),U_811),U_813)))
| ~ hBOOL(hAPP(U_815,bool,hAPP(U_815,fun(U_815,bool),ord_less(U_815),U_814),U_813))
| ~ hBOOL(hAPP(U_815,bool,hAPP(U_815,fun(U_815,bool),ord_less(U_815),U_812),U_811)) )
| ~ ordere223160158up_add(U_815) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
cnf(f_240_3,plain,
( hBOOL(hAPP(U_815,bool,hAPP(U_815,fun(U_815,bool),ord_less(U_815),hAPP(U_815,U_815,hAPP(U_815,fun(U_815,U_815),plus_plus(U_815),U_812),U_814)),hAPP(U_815,U_815,hAPP(U_815,fun(U_815,U_815),plus_plus(U_815),U_811),U_813)))
| ~ hBOOL(hAPP(U_815,bool,hAPP(U_815,fun(U_815,bool),ord_less(U_815),U_814),U_813))
| ~ hBOOL(hAPP(U_815,bool,hAPP(U_815,fun(U_815,bool),ord_less(U_815),U_812),U_811))
| ~ ordere223160158up_add(U_815) ),
inference(clausify,[status(thm)],[f_240_2]) ).
fof(f_241_1,plain,
! [X_a] :
( ! [C,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),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),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_178_add__strict__left__mono]) ).
fof(f_241_2,plain,
! [U_819] :
( ! [U_818,U_817,U_816] :
( hBOOL(hAPP(U_819,bool,hAPP(U_819,fun(U_819,bool),ord_less(U_819),hAPP(U_819,U_819,hAPP(U_819,fun(U_819,U_819),plus_plus(U_819),U_818),U_817)),hAPP(U_819,U_819,hAPP(U_819,fun(U_819,U_819),plus_plus(U_819),U_818),U_816)))
| ~ hBOOL(hAPP(U_819,bool,hAPP(U_819,fun(U_819,bool),ord_less(U_819),U_817),U_816)) )
| ~ ordere223160158up_add(U_819) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( hBOOL(hAPP(U_819,bool,hAPP(U_819,fun(U_819,bool),ord_less(U_819),hAPP(U_819,U_819,hAPP(U_819,fun(U_819,U_819),plus_plus(U_819),U_818),U_817)),hAPP(U_819,U_819,hAPP(U_819,fun(U_819,U_819),plus_plus(U_819),U_818),U_816)))
| ~ hBOOL(hAPP(U_819,bool,hAPP(U_819,fun(U_819,bool),ord_less(U_819),U_817),U_816))
| ~ ordere223160158up_add(U_819) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_1,plain,
! [X_a] :
( ! [C,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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)))
| ~ 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_179_add__strict__right__mono]) ).
fof(f_242_2,plain,
! [U_823] :
( ! [U_822,U_821,U_820] :
( hBOOL(hAPP(U_823,bool,hAPP(U_823,fun(U_823,bool),ord_less(U_823),hAPP(U_823,U_823,hAPP(U_823,fun(U_823,U_823),plus_plus(U_823),U_821),U_822)),hAPP(U_823,U_823,hAPP(U_823,fun(U_823,U_823),plus_plus(U_823),U_820),U_822)))
| ~ hBOOL(hAPP(U_823,bool,hAPP(U_823,fun(U_823,bool),ord_less(U_823),U_821),U_820)) )
| ~ ordere223160158up_add(U_823) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
( hBOOL(hAPP(U_823,bool,hAPP(U_823,fun(U_823,bool),ord_less(U_823),hAPP(U_823,U_823,hAPP(U_823,fun(U_823,U_823),plus_plus(U_823),U_821),U_822)),hAPP(U_823,U_823,hAPP(U_823,fun(U_823,U_823),plus_plus(U_823),U_820),U_822)))
| ~ hBOOL(hAPP(U_823,bool,hAPP(U_823,fun(U_823,bool),ord_less(U_823),U_821),U_820))
| ~ ordere223160158up_add(U_823) ),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_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_180_add__less__cancel__left]) ).
fof(f_243_2,plain,
! [U_827] :
( ! [U_826,U_825,U_824] :
( ( hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_826),U_825)),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_826),U_824)))
| ~ hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),U_825),U_824)) )
& ( hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),U_825),U_824))
| ~ hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_826),U_825)),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_826),U_824))) ) )
| ~ ordere236663937imp_le(U_827) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_827] :
( ( ! [U_833,U_831,U_829] :
( hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_833),U_831)),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_833),U_829)))
| ~ hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),U_831),U_829)) )
& ! [U_832,U_830,U_828] :
( hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),U_830),U_828))
| ~ hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_832),U_830)),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_832),U_828))) ) )
| ~ ordere236663937imp_le(U_827) ),
inference(miniscope,[status(thm)],[f_243_2]) ).
cnf(f_243_4,plain,
( hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),U_830),U_828))
| ~ hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_832),U_830)),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_832),U_828)))
| ~ ordere236663937imp_le(U_827) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_5,plain,
( hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_833),U_831)),hAPP(U_827,U_827,hAPP(U_827,fun(U_827,U_827),plus_plus(U_827),U_833),U_829)))
| ~ hBOOL(hAPP(U_827,bool,hAPP(U_827,fun(U_827,bool),ord_less(U_827),U_831),U_829))
| ~ ordere236663937imp_le(U_827) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_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_181_add__less__cancel__right]) ).
fof(f_244_2,plain,
! [U_837] :
( ! [U_836,U_835,U_834] :
( ( hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(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_834),U_835)))
| ~ hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(U_837),U_836),U_834)) )
& ( hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(U_837),U_836),U_834))
| ~ hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(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_834),U_835))) ) )
| ~ ordere236663937imp_le(U_837) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
! [U_837] :
( ( ! [U_843,U_841,U_839] :
( hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(U_837),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_843),U_841)),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_839),U_841)))
| ~ hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(U_837),U_843),U_839)) )
& ! [U_842,U_840,U_838] :
( hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(U_837),U_842),U_838))
| ~ hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(U_837),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_842),U_840)),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_838),U_840))) ) )
| ~ ordere236663937imp_le(U_837) ),
inference(miniscope,[status(thm)],[f_244_2]) ).
cnf(f_244_4,plain,
( hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(U_837),U_842),U_838))
| ~ hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(U_837),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_842),U_840)),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_838),U_840)))
| ~ ordere236663937imp_le(U_837) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_5,plain,
( hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(U_837),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_843),U_841)),hAPP(U_837,U_837,hAPP(U_837,fun(U_837,U_837),plus_plus(U_837),U_839),U_841)))
| ~ hBOOL(hAPP(U_837,bool,hAPP(U_837,fun(U_837,bool),ord_less(U_837),U_843),U_839))
| ~ ordere236663937imp_le(U_837) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_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_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_2)),hAPP(X_a,X_b,G,X_2))) )
| ~ ord(X_b) ),
inference(fof_nnf,[status(thm)],[fact_182_le__funI]) ).
fof(f_245_2,plain,
! [U_848,U_847] :
( ! [U_846,U_845] :
( hBOOL(hAPP(fun(U_848,U_847),bool,hAPP(fun(U_848,U_847),fun(fun(U_848,U_847),bool),ord_less_eq(fun(U_848,U_847)),U_846),U_845))
| ? [U_844] : ~ hBOOL(hAPP(U_847,bool,hAPP(U_847,fun(U_847,bool),ord_less_eq(U_847),hAPP(U_848,U_847,U_846,U_844)),hAPP(U_848,U_847,U_845,U_844))) )
| ~ ord(U_847) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_848,U_847] :
( ! [U_846,U_845] :
( hBOOL(hAPP(fun(U_848,U_847),bool,hAPP(fun(U_848,U_847),fun(fun(U_848,U_847),bool),ord_less_eq(fun(U_848,U_847)),U_846),U_845))
| ~ hBOOL(hAPP(U_847,bool,hAPP(U_847,fun(U_847,bool),ord_less_eq(U_847),hAPP(U_848,U_847,U_846,sK47(U_848,U_847,U_846,U_845))),hAPP(U_848,U_847,U_845,sK47(U_848,U_847,U_846,U_845)))) )
| ~ ord(U_847) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_844,sK47(U_848,U_847,U_846,U_845))],[f_245_2]) ).
cnf(f_245_4,plain,
( hBOOL(hAPP(fun(U_848,U_847),bool,hAPP(fun(U_848,U_847),fun(fun(U_848,U_847),bool),ord_less_eq(fun(U_848,U_847)),U_846),U_845))
| ~ hBOOL(hAPP(U_847,bool,hAPP(U_847,fun(U_847,bool),ord_less_eq(U_847),hAPP(U_848,U_847,U_846,sK47(U_848,U_847,U_846,U_845))),hAPP(U_848,U_847,U_845,sK47(U_848,U_847,U_846,U_845))))
| ~ ord(U_847) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_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_2,Y_3] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_3)),hAPP(X_b,X_a,F,X_2)))
& hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_3),X_2)) )
| ~ 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_183_xt6]) ).
fof(f_246_2,plain,
! [U_856,U_855] :
( ! [U_854,U_853,U_852,U_851] :
( hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less(U_855),hAPP(U_856,U_855,U_853,U_854)),U_851))
| ? [U_850,U_849] :
( ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less(U_855),hAPP(U_856,U_855,U_853,U_849)),hAPP(U_856,U_855,U_853,U_850)))
& hBOOL(hAPP(U_856,bool,hAPP(U_856,fun(U_856,bool),ord_less(U_856),U_849),U_850)) )
| ~ hBOOL(hAPP(U_856,bool,hAPP(U_856,fun(U_856,bool),ord_less(U_856),U_854),U_852))
| ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_856,U_855,U_853,U_852)),U_851)) )
| ~ ord(U_856)
| ~ order(U_855) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_856,U_855] :
( ! [U_854,U_853,U_852,U_851] :
( hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less(U_855),hAPP(U_856,U_855,U_853,U_854)),U_851))
| ? [U_849] :
( ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less(U_855),hAPP(U_856,U_855,U_853,U_849)),hAPP(U_856,U_855,U_853,sK48(U_856,U_855,U_854,U_853,U_852,U_851))))
& hBOOL(hAPP(U_856,bool,hAPP(U_856,fun(U_856,bool),ord_less(U_856),U_849),sK48(U_856,U_855,U_854,U_853,U_852,U_851))) )
| ~ hBOOL(hAPP(U_856,bool,hAPP(U_856,fun(U_856,bool),ord_less(U_856),U_854),U_852))
| ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_856,U_855,U_853,U_852)),U_851)) )
| ~ ord(U_856)
| ~ order(U_855) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_850,sK48(U_856,U_855,U_854,U_853,U_852,U_851))],[f_246_2]) ).
fof(f_246_4,plain,
! [U_856,U_855] :
( ! [U_854,U_853,U_852,U_851] :
( hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less(U_855),hAPP(U_856,U_855,U_853,U_854)),U_851))
| ( ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less(U_855),hAPP(U_856,U_855,U_853,sK49(U_856,U_855,U_854,U_853,U_852,U_851))),hAPP(U_856,U_855,U_853,sK48(U_856,U_855,U_854,U_853,U_852,U_851))))
& hBOOL(hAPP(U_856,bool,hAPP(U_856,fun(U_856,bool),ord_less(U_856),sK49(U_856,U_855,U_854,U_853,U_852,U_851)),sK48(U_856,U_855,U_854,U_853,U_852,U_851))) )
| ~ hBOOL(hAPP(U_856,bool,hAPP(U_856,fun(U_856,bool),ord_less(U_856),U_854),U_852))
| ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_856,U_855,U_853,U_852)),U_851)) )
| ~ ord(U_856)
| ~ order(U_855) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_849,sK49(U_856,U_855,U_854,U_853,U_852,U_851))],[f_246_3]) ).
cnf(f_246_5,plain,
( hBOOL(hAPP(U_856,bool,hAPP(U_856,fun(U_856,bool),ord_less(U_856),sK49(U_856,U_855,U_854,U_853,U_852,U_851)),sK48(U_856,U_855,U_854,U_853,U_852,U_851)))
| hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less(U_855),hAPP(U_856,U_855,U_853,U_854)),U_851))
| ~ hBOOL(hAPP(U_856,bool,hAPP(U_856,fun(U_856,bool),ord_less(U_856),U_854),U_852))
| ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_856,U_855,U_853,U_852)),U_851))
| ~ ord(U_856)
| ~ order(U_855) ),
inference(clausify,[status(thm)],[f_246_4]) ).
cnf(f_246_6,plain,
( ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less(U_855),hAPP(U_856,U_855,U_853,sK49(U_856,U_855,U_854,U_853,U_852,U_851))),hAPP(U_856,U_855,U_853,sK48(U_856,U_855,U_854,U_853,U_852,U_851))))
| hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less(U_855),hAPP(U_856,U_855,U_853,U_854)),U_851))
| ~ hBOOL(hAPP(U_856,bool,hAPP(U_856,fun(U_856,bool),ord_less(U_856),U_854),U_852))
| ~ hBOOL(hAPP(U_855,bool,hAPP(U_855,fun(U_855,bool),ord_less_eq(U_855),hAPP(U_856,U_855,U_853,U_852)),U_851))
| ~ ord(U_856)
| ~ order(U_855) ),
inference(clausify,[status(thm)],[f_246_4]) ).
fof(f_247_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_2,Y_3] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_3)),hAPP(X_b,X_a,F,X_2)))
& hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_3),X_2)) )
| ~ 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_184_xt4]) ).
fof(f_247_2,plain,
! [U_864,U_863] :
( ! [U_862,U_861,U_860,U_859] :
( hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less(U_863),hAPP(U_864,U_863,U_861,U_862)),U_859))
| ? [U_858,U_857] :
( ~ hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less_eq(U_863),hAPP(U_864,U_863,U_861,U_857)),hAPP(U_864,U_863,U_861,U_858)))
& hBOOL(hAPP(U_864,bool,hAPP(U_864,fun(U_864,bool),ord_less_eq(U_864),U_857),U_858)) )
| ~ hBOOL(hAPP(U_864,bool,hAPP(U_864,fun(U_864,bool),ord_less_eq(U_864),U_862),U_860))
| ~ hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less(U_863),hAPP(U_864,U_863,U_861,U_860)),U_859)) )
| ~ order(U_864)
| ~ order(U_863) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_864,U_863] :
( ! [U_862,U_861,U_860,U_859] :
( hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less(U_863),hAPP(U_864,U_863,U_861,U_862)),U_859))
| ? [U_857] :
( ~ hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less_eq(U_863),hAPP(U_864,U_863,U_861,U_857)),hAPP(U_864,U_863,U_861,sK50(U_864,U_863,U_862,U_861,U_860,U_859))))
& hBOOL(hAPP(U_864,bool,hAPP(U_864,fun(U_864,bool),ord_less_eq(U_864),U_857),sK50(U_864,U_863,U_862,U_861,U_860,U_859))) )
| ~ hBOOL(hAPP(U_864,bool,hAPP(U_864,fun(U_864,bool),ord_less_eq(U_864),U_862),U_860))
| ~ hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less(U_863),hAPP(U_864,U_863,U_861,U_860)),U_859)) )
| ~ order(U_864)
| ~ order(U_863) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_858,sK50(U_864,U_863,U_862,U_861,U_860,U_859))],[f_247_2]) ).
fof(f_247_4,plain,
! [U_864,U_863] :
( ! [U_862,U_861,U_860,U_859] :
( hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less(U_863),hAPP(U_864,U_863,U_861,U_862)),U_859))
| ( ~ hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less_eq(U_863),hAPP(U_864,U_863,U_861,sK51(U_864,U_863,U_862,U_861,U_860,U_859))),hAPP(U_864,U_863,U_861,sK50(U_864,U_863,U_862,U_861,U_860,U_859))))
& hBOOL(hAPP(U_864,bool,hAPP(U_864,fun(U_864,bool),ord_less_eq(U_864),sK51(U_864,U_863,U_862,U_861,U_860,U_859)),sK50(U_864,U_863,U_862,U_861,U_860,U_859))) )
| ~ hBOOL(hAPP(U_864,bool,hAPP(U_864,fun(U_864,bool),ord_less_eq(U_864),U_862),U_860))
| ~ hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less(U_863),hAPP(U_864,U_863,U_861,U_860)),U_859)) )
| ~ order(U_864)
| ~ order(U_863) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_857,sK51(U_864,U_863,U_862,U_861,U_860,U_859))],[f_247_3]) ).
cnf(f_247_5,plain,
( hBOOL(hAPP(U_864,bool,hAPP(U_864,fun(U_864,bool),ord_less_eq(U_864),sK51(U_864,U_863,U_862,U_861,U_860,U_859)),sK50(U_864,U_863,U_862,U_861,U_860,U_859)))
| hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less(U_863),hAPP(U_864,U_863,U_861,U_862)),U_859))
| ~ hBOOL(hAPP(U_864,bool,hAPP(U_864,fun(U_864,bool),ord_less_eq(U_864),U_862),U_860))
| ~ hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less(U_863),hAPP(U_864,U_863,U_861,U_860)),U_859))
| ~ order(U_864)
| ~ order(U_863) ),
inference(clausify,[status(thm)],[f_247_4]) ).
cnf(f_247_6,plain,
( ~ hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less_eq(U_863),hAPP(U_864,U_863,U_861,sK51(U_864,U_863,U_862,U_861,U_860,U_859))),hAPP(U_864,U_863,U_861,sK50(U_864,U_863,U_862,U_861,U_860,U_859))))
| hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less(U_863),hAPP(U_864,U_863,U_861,U_862)),U_859))
| ~ hBOOL(hAPP(U_864,bool,hAPP(U_864,fun(U_864,bool),ord_less_eq(U_864),U_862),U_860))
| ~ hBOOL(hAPP(U_863,bool,hAPP(U_863,fun(U_863,bool),ord_less(U_863),hAPP(U_864,U_863,U_861,U_860)),U_859))
| ~ order(U_864)
| ~ order(U_863) ),
inference(clausify,[status(thm)],[f_247_4]) ).
fof(f_248_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_2,Y_3] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_3)))
& hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_3)) )
| ~ 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_185_order__le__less__subst1]) ).
fof(f_248_2,plain,
! [U_872,U_871] :
( ! [U_870,U_869,U_868,U_867] :
( hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less(U_872),U_869),hAPP(U_871,U_872,U_868,U_870)))
| ? [U_866,U_865] :
( ~ hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less(U_872),hAPP(U_871,U_872,U_868,U_866)),hAPP(U_871,U_872,U_868,U_865)))
& hBOOL(hAPP(U_871,bool,hAPP(U_871,fun(U_871,bool),ord_less(U_871),U_866),U_865)) )
| ~ hBOOL(hAPP(U_871,bool,hAPP(U_871,fun(U_871,bool),ord_less(U_871),U_867),U_870))
| ~ hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less_eq(U_872),U_869),hAPP(U_871,U_872,U_868,U_867))) )
| ~ order(U_872)
| ~ order(U_871) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_872,U_871] :
( ! [U_870,U_869,U_868,U_867] :
( hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less(U_872),U_869),hAPP(U_871,U_872,U_868,U_870)))
| ? [U_865] :
( ~ hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less(U_872),hAPP(U_871,U_872,U_868,sK52(U_872,U_871,U_870,U_869,U_868,U_867))),hAPP(U_871,U_872,U_868,U_865)))
& hBOOL(hAPP(U_871,bool,hAPP(U_871,fun(U_871,bool),ord_less(U_871),sK52(U_872,U_871,U_870,U_869,U_868,U_867)),U_865)) )
| ~ hBOOL(hAPP(U_871,bool,hAPP(U_871,fun(U_871,bool),ord_less(U_871),U_867),U_870))
| ~ hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less_eq(U_872),U_869),hAPP(U_871,U_872,U_868,U_867))) )
| ~ order(U_872)
| ~ order(U_871) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_866,sK52(U_872,U_871,U_870,U_869,U_868,U_867))],[f_248_2]) ).
fof(f_248_4,plain,
! [U_872,U_871] :
( ! [U_870,U_869,U_868,U_867] :
( hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less(U_872),U_869),hAPP(U_871,U_872,U_868,U_870)))
| ( ~ hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less(U_872),hAPP(U_871,U_872,U_868,sK52(U_872,U_871,U_870,U_869,U_868,U_867))),hAPP(U_871,U_872,U_868,sK53(U_872,U_871,U_870,U_869,U_868,U_867))))
& hBOOL(hAPP(U_871,bool,hAPP(U_871,fun(U_871,bool),ord_less(U_871),sK52(U_872,U_871,U_870,U_869,U_868,U_867)),sK53(U_872,U_871,U_870,U_869,U_868,U_867))) )
| ~ hBOOL(hAPP(U_871,bool,hAPP(U_871,fun(U_871,bool),ord_less(U_871),U_867),U_870))
| ~ hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less_eq(U_872),U_869),hAPP(U_871,U_872,U_868,U_867))) )
| ~ order(U_872)
| ~ order(U_871) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_865,sK53(U_872,U_871,U_870,U_869,U_868,U_867))],[f_248_3]) ).
cnf(f_248_5,plain,
( hBOOL(hAPP(U_871,bool,hAPP(U_871,fun(U_871,bool),ord_less(U_871),sK52(U_872,U_871,U_870,U_869,U_868,U_867)),sK53(U_872,U_871,U_870,U_869,U_868,U_867)))
| hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less(U_872),U_869),hAPP(U_871,U_872,U_868,U_870)))
| ~ hBOOL(hAPP(U_871,bool,hAPP(U_871,fun(U_871,bool),ord_less(U_871),U_867),U_870))
| ~ hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less_eq(U_872),U_869),hAPP(U_871,U_872,U_868,U_867)))
| ~ order(U_872)
| ~ order(U_871) ),
inference(clausify,[status(thm)],[f_248_4]) ).
cnf(f_248_6,plain,
( ~ hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less(U_872),hAPP(U_871,U_872,U_868,sK52(U_872,U_871,U_870,U_869,U_868,U_867))),hAPP(U_871,U_872,U_868,sK53(U_872,U_871,U_870,U_869,U_868,U_867))))
| hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less(U_872),U_869),hAPP(U_871,U_872,U_868,U_870)))
| ~ hBOOL(hAPP(U_871,bool,hAPP(U_871,fun(U_871,bool),ord_less(U_871),U_867),U_870))
| ~ hBOOL(hAPP(U_872,bool,hAPP(U_872,fun(U_872,bool),ord_less_eq(U_872),U_869),hAPP(U_871,U_872,U_868,U_867)))
| ~ order(U_872)
| ~ order(U_871) ),
inference(clausify,[status(thm)],[f_248_4]) ).
fof(f_249_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_2,Y_3] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_3)))
& hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_3)) )
| ~ 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_186_order__less__le__subst1]) ).
fof(f_249_2,plain,
! [U_880,U_879] :
( ! [U_878,U_877,U_876,U_875] :
( hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less(U_880),U_877),hAPP(U_879,U_880,U_876,U_878)))
| ? [U_874,U_873] :
( ~ hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less_eq(U_880),hAPP(U_879,U_880,U_876,U_874)),hAPP(U_879,U_880,U_876,U_873)))
& hBOOL(hAPP(U_879,bool,hAPP(U_879,fun(U_879,bool),ord_less_eq(U_879),U_874),U_873)) )
| ~ hBOOL(hAPP(U_879,bool,hAPP(U_879,fun(U_879,bool),ord_less_eq(U_879),U_875),U_878))
| ~ hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less(U_880),U_877),hAPP(U_879,U_880,U_876,U_875))) )
| ~ order(U_880)
| ~ order(U_879) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_880,U_879] :
( ! [U_878,U_877,U_876,U_875] :
( hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less(U_880),U_877),hAPP(U_879,U_880,U_876,U_878)))
| ? [U_873] :
( ~ hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less_eq(U_880),hAPP(U_879,U_880,U_876,sK54(U_880,U_879,U_878,U_877,U_876,U_875))),hAPP(U_879,U_880,U_876,U_873)))
& hBOOL(hAPP(U_879,bool,hAPP(U_879,fun(U_879,bool),ord_less_eq(U_879),sK54(U_880,U_879,U_878,U_877,U_876,U_875)),U_873)) )
| ~ hBOOL(hAPP(U_879,bool,hAPP(U_879,fun(U_879,bool),ord_less_eq(U_879),U_875),U_878))
| ~ hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less(U_880),U_877),hAPP(U_879,U_880,U_876,U_875))) )
| ~ order(U_880)
| ~ order(U_879) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_874,sK54(U_880,U_879,U_878,U_877,U_876,U_875))],[f_249_2]) ).
fof(f_249_4,plain,
! [U_880,U_879] :
( ! [U_878,U_877,U_876,U_875] :
( hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less(U_880),U_877),hAPP(U_879,U_880,U_876,U_878)))
| ( ~ hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less_eq(U_880),hAPP(U_879,U_880,U_876,sK54(U_880,U_879,U_878,U_877,U_876,U_875))),hAPP(U_879,U_880,U_876,sK55(U_880,U_879,U_878,U_877,U_876,U_875))))
& hBOOL(hAPP(U_879,bool,hAPP(U_879,fun(U_879,bool),ord_less_eq(U_879),sK54(U_880,U_879,U_878,U_877,U_876,U_875)),sK55(U_880,U_879,U_878,U_877,U_876,U_875))) )
| ~ hBOOL(hAPP(U_879,bool,hAPP(U_879,fun(U_879,bool),ord_less_eq(U_879),U_875),U_878))
| ~ hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less(U_880),U_877),hAPP(U_879,U_880,U_876,U_875))) )
| ~ order(U_880)
| ~ order(U_879) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_873,sK55(U_880,U_879,U_878,U_877,U_876,U_875))],[f_249_3]) ).
cnf(f_249_5,plain,
( hBOOL(hAPP(U_879,bool,hAPP(U_879,fun(U_879,bool),ord_less_eq(U_879),sK54(U_880,U_879,U_878,U_877,U_876,U_875)),sK55(U_880,U_879,U_878,U_877,U_876,U_875)))
| hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less(U_880),U_877),hAPP(U_879,U_880,U_876,U_878)))
| ~ hBOOL(hAPP(U_879,bool,hAPP(U_879,fun(U_879,bool),ord_less_eq(U_879),U_875),U_878))
| ~ hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less(U_880),U_877),hAPP(U_879,U_880,U_876,U_875)))
| ~ order(U_880)
| ~ order(U_879) ),
inference(clausify,[status(thm)],[f_249_4]) ).
cnf(f_249_6,plain,
( ~ hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less_eq(U_880),hAPP(U_879,U_880,U_876,sK54(U_880,U_879,U_878,U_877,U_876,U_875))),hAPP(U_879,U_880,U_876,sK55(U_880,U_879,U_878,U_877,U_876,U_875))))
| hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less(U_880),U_877),hAPP(U_879,U_880,U_876,U_878)))
| ~ hBOOL(hAPP(U_879,bool,hAPP(U_879,fun(U_879,bool),ord_less_eq(U_879),U_875),U_878))
| ~ hBOOL(hAPP(U_880,bool,hAPP(U_880,fun(U_880,bool),ord_less(U_880),U_877),hAPP(U_879,U_880,U_876,U_875)))
| ~ order(U_880)
| ~ order(U_879) ),
inference(clausify,[status(thm)],[f_249_4]) ).
fof(f_250_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_2,Y_3] :
( ~ 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,F,Y_3)))
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_3)) )
| ~ 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_187_order__le__less__subst2]) ).
fof(f_250_2,plain,
! [U_888,U_887] :
( ! [U_886,U_885,U_884,U_883] :
( hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less(U_887),hAPP(U_888,U_887,U_886,U_884)),U_885))
| ? [U_882,U_881] :
( ~ hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less_eq(U_887),hAPP(U_888,U_887,U_886,U_882)),hAPP(U_888,U_887,U_886,U_881)))
& hBOOL(hAPP(U_888,bool,hAPP(U_888,fun(U_888,bool),ord_less_eq(U_888),U_882),U_881)) )
| ~ hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less(U_887),hAPP(U_888,U_887,U_886,U_883)),U_885))
| ~ hBOOL(hAPP(U_888,bool,hAPP(U_888,fun(U_888,bool),ord_less_eq(U_888),U_884),U_883)) )
| ~ order(U_888)
| ~ order(U_887) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_888,U_887] :
( ! [U_886,U_885,U_884,U_883] :
( hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less(U_887),hAPP(U_888,U_887,U_886,U_884)),U_885))
| ? [U_881] :
( ~ hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less_eq(U_887),hAPP(U_888,U_887,U_886,sK56(U_888,U_887,U_886,U_885,U_884,U_883))),hAPP(U_888,U_887,U_886,U_881)))
& hBOOL(hAPP(U_888,bool,hAPP(U_888,fun(U_888,bool),ord_less_eq(U_888),sK56(U_888,U_887,U_886,U_885,U_884,U_883)),U_881)) )
| ~ hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less(U_887),hAPP(U_888,U_887,U_886,U_883)),U_885))
| ~ hBOOL(hAPP(U_888,bool,hAPP(U_888,fun(U_888,bool),ord_less_eq(U_888),U_884),U_883)) )
| ~ order(U_888)
| ~ order(U_887) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_882,sK56(U_888,U_887,U_886,U_885,U_884,U_883))],[f_250_2]) ).
fof(f_250_4,plain,
! [U_888,U_887] :
( ! [U_886,U_885,U_884,U_883] :
( hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less(U_887),hAPP(U_888,U_887,U_886,U_884)),U_885))
| ( ~ hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less_eq(U_887),hAPP(U_888,U_887,U_886,sK56(U_888,U_887,U_886,U_885,U_884,U_883))),hAPP(U_888,U_887,U_886,sK57(U_888,U_887,U_886,U_885,U_884,U_883))))
& hBOOL(hAPP(U_888,bool,hAPP(U_888,fun(U_888,bool),ord_less_eq(U_888),sK56(U_888,U_887,U_886,U_885,U_884,U_883)),sK57(U_888,U_887,U_886,U_885,U_884,U_883))) )
| ~ hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less(U_887),hAPP(U_888,U_887,U_886,U_883)),U_885))
| ~ hBOOL(hAPP(U_888,bool,hAPP(U_888,fun(U_888,bool),ord_less_eq(U_888),U_884),U_883)) )
| ~ order(U_888)
| ~ order(U_887) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_881,sK57(U_888,U_887,U_886,U_885,U_884,U_883))],[f_250_3]) ).
cnf(f_250_5,plain,
( hBOOL(hAPP(U_888,bool,hAPP(U_888,fun(U_888,bool),ord_less_eq(U_888),sK56(U_888,U_887,U_886,U_885,U_884,U_883)),sK57(U_888,U_887,U_886,U_885,U_884,U_883)))
| hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less(U_887),hAPP(U_888,U_887,U_886,U_884)),U_885))
| ~ hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less(U_887),hAPP(U_888,U_887,U_886,U_883)),U_885))
| ~ hBOOL(hAPP(U_888,bool,hAPP(U_888,fun(U_888,bool),ord_less_eq(U_888),U_884),U_883))
| ~ order(U_888)
| ~ order(U_887) ),
inference(clausify,[status(thm)],[f_250_4]) ).
cnf(f_250_6,plain,
( ~ hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less_eq(U_887),hAPP(U_888,U_887,U_886,sK56(U_888,U_887,U_886,U_885,U_884,U_883))),hAPP(U_888,U_887,U_886,sK57(U_888,U_887,U_886,U_885,U_884,U_883))))
| hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less(U_887),hAPP(U_888,U_887,U_886,U_884)),U_885))
| ~ hBOOL(hAPP(U_887,bool,hAPP(U_887,fun(U_887,bool),ord_less(U_887),hAPP(U_888,U_887,U_886,U_883)),U_885))
| ~ hBOOL(hAPP(U_888,bool,hAPP(U_888,fun(U_888,bool),ord_less_eq(U_888),U_884),U_883))
| ~ order(U_888)
| ~ order(U_887) ),
inference(clausify,[status(thm)],[f_250_4]) ).
fof(f_251_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_188_equalityI]) ).
fof(f_251_2,plain,
! [U_891,U_890,U_889] :
( ti(fun(U_891,bool),U_890) = ti(fun(U_891,bool),U_889)
| ~ hBOOL(hAPP(fun(U_891,bool),bool,hAPP(fun(U_891,bool),fun(fun(U_891,bool),bool),ord_less_eq(fun(U_891,bool)),U_889),U_890))
| ~ hBOOL(hAPP(fun(U_891,bool),bool,hAPP(fun(U_891,bool),fun(fun(U_891,bool),bool),ord_less_eq(fun(U_891,bool)),U_890),U_889)) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
cnf(f_251_3,plain,
( ti(fun(U_891,bool),U_890) = ti(fun(U_891,bool),U_889)
| ~ hBOOL(hAPP(fun(U_891,bool),bool,hAPP(fun(U_891,bool),fun(fun(U_891,bool),bool),ord_less_eq(fun(U_891,bool)),U_889),U_890))
| ~ hBOOL(hAPP(fun(U_891,bool),bool,hAPP(fun(U_891,bool),fun(fun(U_891,bool),bool),ord_less_eq(fun(U_891,bool)),U_890),U_889)) ),
inference(clausify,[status(thm)],[f_251_2]) ).
fof(f_252_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_189_subsetD]) ).
fof(f_252_2,plain,
! [U_895,U_894,U_893,U_892] :
( hBOOL(hAPP(fun(U_895,bool),bool,hAPP(U_895,fun(fun(U_895,bool),bool),member(U_895),U_894),U_892))
| ~ hBOOL(hAPP(fun(U_895,bool),bool,hAPP(U_895,fun(fun(U_895,bool),bool),member(U_895),U_894),U_893))
| ~ hBOOL(hAPP(fun(U_895,bool),bool,hAPP(fun(U_895,bool),fun(fun(U_895,bool),bool),ord_less_eq(fun(U_895,bool)),U_893),U_892)) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
cnf(f_252_3,plain,
( hBOOL(hAPP(fun(U_895,bool),bool,hAPP(U_895,fun(fun(U_895,bool),bool),member(U_895),U_894),U_892))
| ~ hBOOL(hAPP(fun(U_895,bool),bool,hAPP(U_895,fun(fun(U_895,bool),bool),member(U_895),U_894),U_893))
| ~ hBOOL(hAPP(fun(U_895,bool),bool,hAPP(fun(U_895,bool),fun(fun(U_895,bool),bool),ord_less_eq(fun(U_895,bool)),U_893),U_892)) ),
inference(clausify,[status(thm)],[f_252_2]) ).
fof(f_253_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_190_psubset__eq]) ).
fof(f_253_2,plain,
! [U_898,U_897,U_896] :
( ( hBOOL(hAPP(fun(U_898,bool),bool,hAPP(fun(U_898,bool),fun(fun(U_898,bool),bool),ord_less(fun(U_898,bool)),U_897),U_896))
| ti(fun(U_898,bool),U_897) = ti(fun(U_898,bool),U_896)
| ~ hBOOL(hAPP(fun(U_898,bool),bool,hAPP(fun(U_898,bool),fun(fun(U_898,bool),bool),ord_less_eq(fun(U_898,bool)),U_897),U_896)) )
& ( ( ti(fun(U_898,bool),U_897) != ti(fun(U_898,bool),U_896)
& hBOOL(hAPP(fun(U_898,bool),bool,hAPP(fun(U_898,bool),fun(fun(U_898,bool),bool),ord_less_eq(fun(U_898,bool)),U_897),U_896)) )
| ~ hBOOL(hAPP(fun(U_898,bool),bool,hAPP(fun(U_898,bool),fun(fun(U_898,bool),bool),ord_less(fun(U_898,bool)),U_897),U_896)) ) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
( ! [U_904,U_902,U_900] :
( hBOOL(hAPP(fun(U_904,bool),bool,hAPP(fun(U_904,bool),fun(fun(U_904,bool),bool),ord_less(fun(U_904,bool)),U_902),U_900))
| ti(fun(U_904,bool),U_902) = ti(fun(U_904,bool),U_900)
| ~ hBOOL(hAPP(fun(U_904,bool),bool,hAPP(fun(U_904,bool),fun(fun(U_904,bool),bool),ord_less_eq(fun(U_904,bool)),U_902),U_900)) )
& ! [U_903,U_901,U_899] :
( ( ti(fun(U_903,bool),U_901) != ti(fun(U_903,bool),U_899)
& hBOOL(hAPP(fun(U_903,bool),bool,hAPP(fun(U_903,bool),fun(fun(U_903,bool),bool),ord_less_eq(fun(U_903,bool)),U_901),U_899)) )
| ~ hBOOL(hAPP(fun(U_903,bool),bool,hAPP(fun(U_903,bool),fun(fun(U_903,bool),bool),ord_less(fun(U_903,bool)),U_901),U_899)) ) ),
inference(miniscope,[status(thm)],[f_253_2]) ).
cnf(f_253_4,plain,
( hBOOL(hAPP(fun(U_903,bool),bool,hAPP(fun(U_903,bool),fun(fun(U_903,bool),bool),ord_less_eq(fun(U_903,bool)),U_901),U_899))
| ~ hBOOL(hAPP(fun(U_903,bool),bool,hAPP(fun(U_903,bool),fun(fun(U_903,bool),bool),ord_less(fun(U_903,bool)),U_901),U_899)) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_5,plain,
( ti(fun(U_903,bool),U_901) != ti(fun(U_903,bool),U_899)
| ~ hBOOL(hAPP(fun(U_903,bool),bool,hAPP(fun(U_903,bool),fun(fun(U_903,bool),bool),ord_less(fun(U_903,bool)),U_901),U_899)) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_6,plain,
( hBOOL(hAPP(fun(U_904,bool),bool,hAPP(fun(U_904,bool),fun(fun(U_904,bool),bool),ord_less(fun(U_904,bool)),U_902),U_900))
| ti(fun(U_904,bool),U_902) = ti(fun(U_904,bool),U_900)
| ~ hBOOL(hAPP(fun(U_904,bool),bool,hAPP(fun(U_904,bool),fun(fun(U_904,bool),bool),ord_less_eq(fun(U_904,bool)),U_902),U_900)) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_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_191_subset__iff__psubset__eq]) ).
fof(f_254_2,plain,
! [U_907,U_906,U_905] :
( ( hBOOL(hAPP(fun(U_907,bool),bool,hAPP(fun(U_907,bool),fun(fun(U_907,bool),bool),ord_less_eq(fun(U_907,bool)),U_906),U_905))
| ( ti(fun(U_907,bool),U_906) != ti(fun(U_907,bool),U_905)
& ~ hBOOL(hAPP(fun(U_907,bool),bool,hAPP(fun(U_907,bool),fun(fun(U_907,bool),bool),ord_less(fun(U_907,bool)),U_906),U_905)) ) )
& ( ti(fun(U_907,bool),U_906) = ti(fun(U_907,bool),U_905)
| hBOOL(hAPP(fun(U_907,bool),bool,hAPP(fun(U_907,bool),fun(fun(U_907,bool),bool),ord_less(fun(U_907,bool)),U_906),U_905))
| ~ hBOOL(hAPP(fun(U_907,bool),bool,hAPP(fun(U_907,bool),fun(fun(U_907,bool),bool),ord_less_eq(fun(U_907,bool)),U_906),U_905)) ) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
( ! [U_913,U_911,U_909] :
( hBOOL(hAPP(fun(U_913,bool),bool,hAPP(fun(U_913,bool),fun(fun(U_913,bool),bool),ord_less_eq(fun(U_913,bool)),U_911),U_909))
| ( ti(fun(U_913,bool),U_911) != ti(fun(U_913,bool),U_909)
& ~ hBOOL(hAPP(fun(U_913,bool),bool,hAPP(fun(U_913,bool),fun(fun(U_913,bool),bool),ord_less(fun(U_913,bool)),U_911),U_909)) ) )
& ! [U_912,U_910,U_908] :
( ti(fun(U_912,bool),U_910) = ti(fun(U_912,bool),U_908)
| hBOOL(hAPP(fun(U_912,bool),bool,hAPP(fun(U_912,bool),fun(fun(U_912,bool),bool),ord_less(fun(U_912,bool)),U_910),U_908))
| ~ hBOOL(hAPP(fun(U_912,bool),bool,hAPP(fun(U_912,bool),fun(fun(U_912,bool),bool),ord_less_eq(fun(U_912,bool)),U_910),U_908)) ) ),
inference(miniscope,[status(thm)],[f_254_2]) ).
cnf(f_254_4,plain,
( ti(fun(U_912,bool),U_910) = ti(fun(U_912,bool),U_908)
| hBOOL(hAPP(fun(U_912,bool),bool,hAPP(fun(U_912,bool),fun(fun(U_912,bool),bool),ord_less(fun(U_912,bool)),U_910),U_908))
| ~ hBOOL(hAPP(fun(U_912,bool),bool,hAPP(fun(U_912,bool),fun(fun(U_912,bool),bool),ord_less_eq(fun(U_912,bool)),U_910),U_908)) ),
inference(clausify,[status(thm)],[f_254_3]) ).
cnf(f_254_5,plain,
( ~ hBOOL(hAPP(fun(U_913,bool),bool,hAPP(fun(U_913,bool),fun(fun(U_913,bool),bool),ord_less(fun(U_913,bool)),U_911),U_909))
| hBOOL(hAPP(fun(U_913,bool),bool,hAPP(fun(U_913,bool),fun(fun(U_913,bool),bool),ord_less_eq(fun(U_913,bool)),U_911),U_909)) ),
inference(clausify,[status(thm)],[f_254_3]) ).
cnf(f_254_6,plain,
( ti(fun(U_913,bool),U_911) != ti(fun(U_913,bool),U_909)
| hBOOL(hAPP(fun(U_913,bool),bool,hAPP(fun(U_913,bool),fun(fun(U_913,bool),bool),ord_less_eq(fun(U_913,bool)),U_911),U_909)) ),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_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_192_psubset__imp__subset]) ).
fof(f_255_2,plain,
! [U_916,U_915,U_914] :
( hBOOL(hAPP(fun(U_916,bool),bool,hAPP(fun(U_916,bool),fun(fun(U_916,bool),bool),ord_less_eq(fun(U_916,bool)),U_915),U_914))
| ~ hBOOL(hAPP(fun(U_916,bool),bool,hAPP(fun(U_916,bool),fun(fun(U_916,bool),bool),ord_less(fun(U_916,bool)),U_915),U_914)) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
( hBOOL(hAPP(fun(U_916,bool),bool,hAPP(fun(U_916,bool),fun(fun(U_916,bool),bool),ord_less_eq(fun(U_916,bool)),U_915),U_914))
| ~ hBOOL(hAPP(fun(U_916,bool),bool,hAPP(fun(U_916,bool),fun(fun(U_916,bool),bool),ord_less(fun(U_916,bool)),U_915),U_914)) ),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_1,plain,
! [X_a,C_1,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_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),C_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_193_psubset__subset__trans]) ).
fof(f_256_2,plain,
! [U_920,U_919,U_918,U_917] :
( hBOOL(hAPP(fun(U_920,bool),bool,hAPP(fun(U_920,bool),fun(fun(U_920,bool),bool),ord_less(fun(U_920,bool)),U_918),U_919))
| ~ hBOOL(hAPP(fun(U_920,bool),bool,hAPP(fun(U_920,bool),fun(fun(U_920,bool),bool),ord_less_eq(fun(U_920,bool)),U_917),U_919))
| ~ hBOOL(hAPP(fun(U_920,bool),bool,hAPP(fun(U_920,bool),fun(fun(U_920,bool),bool),ord_less(fun(U_920,bool)),U_918),U_917)) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
( hBOOL(hAPP(fun(U_920,bool),bool,hAPP(fun(U_920,bool),fun(fun(U_920,bool),bool),ord_less(fun(U_920,bool)),U_918),U_919))
| ~ hBOOL(hAPP(fun(U_920,bool),bool,hAPP(fun(U_920,bool),fun(fun(U_920,bool),bool),ord_less_eq(fun(U_920,bool)),U_917),U_919))
| ~ hBOOL(hAPP(fun(U_920,bool),bool,hAPP(fun(U_920,bool),fun(fun(U_920,bool),bool),ord_less(fun(U_920,bool)),U_918),U_917)) ),
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_1,plain,
! [X_a,C_1,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_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)),B),C_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_subset__psubset__trans]) ).
fof(f_257_2,plain,
! [U_924,U_923,U_922,U_921] :
( hBOOL(hAPP(fun(U_924,bool),bool,hAPP(fun(U_924,bool),fun(fun(U_924,bool),bool),ord_less(fun(U_924,bool)),U_922),U_923))
| ~ hBOOL(hAPP(fun(U_924,bool),bool,hAPP(fun(U_924,bool),fun(fun(U_924,bool),bool),ord_less(fun(U_924,bool)),U_921),U_923))
| ~ hBOOL(hAPP(fun(U_924,bool),bool,hAPP(fun(U_924,bool),fun(fun(U_924,bool),bool),ord_less_eq(fun(U_924,bool)),U_922),U_921)) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
cnf(f_257_3,plain,
( hBOOL(hAPP(fun(U_924,bool),bool,hAPP(fun(U_924,bool),fun(fun(U_924,bool),bool),ord_less(fun(U_924,bool)),U_922),U_923))
| ~ hBOOL(hAPP(fun(U_924,bool),bool,hAPP(fun(U_924,bool),fun(fun(U_924,bool),bool),ord_less(fun(U_924,bool)),U_921),U_923))
| ~ hBOOL(hAPP(fun(U_924,bool),bool,hAPP(fun(U_924,bool),fun(fun(U_924,bool),bool),ord_less_eq(fun(U_924,bool)),U_922),U_921)) ),
inference(clausify,[status(thm)],[f_257_2]) ).
fof(f_258_1,plain,
! [X_b,X_a,Q_1,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))
| ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_2)) ),
inference(fof_nnf,[status(thm)],[fact_195_rev__predicate2D]) ).
fof(f_258_2,plain,
! [U_930,U_929,U_928,U_927,U_926,U_925] :
( hBOOL(hAPP(U_930,bool,hAPP(U_929,fun(U_930,bool),U_928,U_926),U_925))
| ~ hBOOL(hAPP(fun(U_929,fun(U_930,bool)),bool,hAPP(fun(U_929,fun(U_930,bool)),fun(fun(U_929,fun(U_930,bool)),bool),ord_less_eq(fun(U_929,fun(U_930,bool))),U_927),U_928))
| ~ hBOOL(hAPP(U_930,bool,hAPP(U_929,fun(U_930,bool),U_927,U_926),U_925)) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
cnf(f_258_3,plain,
( hBOOL(hAPP(U_930,bool,hAPP(U_929,fun(U_930,bool),U_928,U_926),U_925))
| ~ hBOOL(hAPP(fun(U_929,fun(U_930,bool)),bool,hAPP(fun(U_929,fun(U_930,bool)),fun(fun(U_929,fun(U_930,bool)),bool),ord_less_eq(fun(U_929,fun(U_930,bool))),U_927),U_928))
| ~ hBOOL(hAPP(U_930,bool,hAPP(U_929,fun(U_930,bool),U_927,U_926),U_925)) ),
inference(clausify,[status(thm)],[f_258_2]) ).
fof(f_259_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_196_equalityE]) ).
fof(f_259_2,plain,
! [U_933,U_932,U_931] :
( ( hBOOL(hAPP(fun(U_933,bool),bool,hAPP(fun(U_933,bool),fun(fun(U_933,bool),bool),ord_less_eq(fun(U_933,bool)),U_931),U_932))
& hBOOL(hAPP(fun(U_933,bool),bool,hAPP(fun(U_933,bool),fun(fun(U_933,bool),bool),ord_less_eq(fun(U_933,bool)),U_932),U_931)) )
| ti(fun(U_933,bool),U_932) != ti(fun(U_933,bool),U_931) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
cnf(f_259_3,plain,
( hBOOL(hAPP(fun(U_933,bool),bool,hAPP(fun(U_933,bool),fun(fun(U_933,bool),bool),ord_less_eq(fun(U_933,bool)),U_932),U_931))
| ti(fun(U_933,bool),U_932) != ti(fun(U_933,bool),U_931) ),
inference(clausify,[status(thm)],[f_259_2]) ).
cnf(f_259_4,plain,
( hBOOL(hAPP(fun(U_933,bool),bool,hAPP(fun(U_933,bool),fun(fun(U_933,bool),bool),ord_less_eq(fun(U_933,bool)),U_931),U_932))
| ti(fun(U_933,bool),U_932) != ti(fun(U_933,bool),U_931) ),
inference(clausify,[status(thm)],[f_259_2]) ).
fof(f_260_1,plain,
! [X_a,X_b,X_1,Y_2,Pa,Q_1] :
( 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))
| ~ 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_197_predicate2D]) ).
fof(f_260_2,plain,
! [U_939,U_938,U_937,U_936,U_935,U_934] :
( hBOOL(hAPP(U_938,bool,hAPP(U_939,fun(U_938,bool),U_934,U_937),U_936))
| ~ hBOOL(hAPP(U_938,bool,hAPP(U_939,fun(U_938,bool),U_935,U_937),U_936))
| ~ hBOOL(hAPP(fun(U_939,fun(U_938,bool)),bool,hAPP(fun(U_939,fun(U_938,bool)),fun(fun(U_939,fun(U_938,bool)),bool),ord_less_eq(fun(U_939,fun(U_938,bool))),U_935),U_934)) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
cnf(f_260_3,plain,
( hBOOL(hAPP(U_938,bool,hAPP(U_939,fun(U_938,bool),U_934,U_937),U_936))
| ~ hBOOL(hAPP(U_938,bool,hAPP(U_939,fun(U_938,bool),U_935,U_937),U_936))
| ~ hBOOL(hAPP(fun(U_939,fun(U_938,bool)),bool,hAPP(fun(U_939,fun(U_938,bool)),fun(fun(U_939,fun(U_938,bool)),bool),ord_less_eq(fun(U_939,fun(U_938,bool))),U_935),U_934)) ),
inference(clausify,[status(thm)],[f_260_2]) ).
fof(f_261_1,plain,
! [X_a,C_1,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_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),C_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_198_subset__trans]) ).
fof(f_261_2,plain,
! [U_943,U_942,U_941,U_940] :
( hBOOL(hAPP(fun(U_943,bool),bool,hAPP(fun(U_943,bool),fun(fun(U_943,bool),bool),ord_less_eq(fun(U_943,bool)),U_941),U_942))
| ~ hBOOL(hAPP(fun(U_943,bool),bool,hAPP(fun(U_943,bool),fun(fun(U_943,bool),bool),ord_less_eq(fun(U_943,bool)),U_940),U_942))
| ~ hBOOL(hAPP(fun(U_943,bool),bool,hAPP(fun(U_943,bool),fun(fun(U_943,bool),bool),ord_less_eq(fun(U_943,bool)),U_941),U_940)) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( hBOOL(hAPP(fun(U_943,bool),bool,hAPP(fun(U_943,bool),fun(fun(U_943,bool),bool),ord_less_eq(fun(U_943,bool)),U_941),U_942))
| ~ hBOOL(hAPP(fun(U_943,bool),bool,hAPP(fun(U_943,bool),fun(fun(U_943,bool),bool),ord_less_eq(fun(U_943,bool)),U_940),U_942))
| ~ hBOOL(hAPP(fun(U_943,bool),bool,hAPP(fun(U_943,bool),fun(fun(U_943,bool),bool),ord_less_eq(fun(U_943,bool)),U_941),U_940)) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_1,plain,
! [X_a,X_1,A_1,B] :
( 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))
| ~ 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_199_set__mp]) ).
fof(f_262_2,plain,
! [U_947,U_946,U_945,U_944] :
( hBOOL(hAPP(fun(U_947,bool),bool,hAPP(U_947,fun(fun(U_947,bool),bool),member(U_947),U_946),U_944))
| ~ hBOOL(hAPP(fun(U_947,bool),bool,hAPP(U_947,fun(fun(U_947,bool),bool),member(U_947),U_946),U_945))
| ~ hBOOL(hAPP(fun(U_947,bool),bool,hAPP(fun(U_947,bool),fun(fun(U_947,bool),bool),ord_less_eq(fun(U_947,bool)),U_945),U_944)) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
cnf(f_262_3,plain,
( hBOOL(hAPP(fun(U_947,bool),bool,hAPP(U_947,fun(fun(U_947,bool),bool),member(U_947),U_946),U_944))
| ~ hBOOL(hAPP(fun(U_947,bool),bool,hAPP(U_947,fun(fun(U_947,bool),bool),member(U_947),U_946),U_945))
| ~ hBOOL(hAPP(fun(U_947,bool),bool,hAPP(fun(U_947,bool),fun(fun(U_947,bool),bool),ord_less_eq(fun(U_947,bool)),U_945),U_944)) ),
inference(clausify,[status(thm)],[f_262_2]) ).
fof(f_263_1,plain,
! [X_a,B,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))
| ~ 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_200_set__rev__mp]) ).
fof(f_263_2,plain,
! [U_951,U_950,U_949,U_948] :
( hBOOL(hAPP(fun(U_951,bool),bool,hAPP(U_951,fun(fun(U_951,bool),bool),member(U_951),U_949),U_950))
| ~ hBOOL(hAPP(fun(U_951,bool),bool,hAPP(fun(U_951,bool),fun(fun(U_951,bool),bool),ord_less_eq(fun(U_951,bool)),U_948),U_950))
| ~ hBOOL(hAPP(fun(U_951,bool),bool,hAPP(U_951,fun(fun(U_951,bool),bool),member(U_951),U_949),U_948)) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
cnf(f_263_3,plain,
( hBOOL(hAPP(fun(U_951,bool),bool,hAPP(U_951,fun(fun(U_951,bool),bool),member(U_951),U_949),U_950))
| ~ hBOOL(hAPP(fun(U_951,bool),bool,hAPP(fun(U_951,bool),fun(fun(U_951,bool),bool),ord_less_eq(fun(U_951,bool)),U_948),U_950))
| ~ hBOOL(hAPP(fun(U_951,bool),bool,hAPP(U_951,fun(fun(U_951,bool),bool),member(U_951),U_949),U_948)) ),
inference(clausify,[status(thm)],[f_263_2]) ).
fof(f_264_1,plain,
! [X_a,X_1,Pa,Q_1] :
( hBOOL(hAPP(X_a,bool,Q_1,X_1))
| ~ hBOOL(hAPP(X_a,bool,Pa,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)) ),
inference(fof_nnf,[status(thm)],[fact_201_predicate1D]) ).
fof(f_264_2,plain,
! [U_955,U_954,U_953,U_952] :
( hBOOL(hAPP(U_955,bool,U_952,U_954))
| ~ hBOOL(hAPP(U_955,bool,U_953,U_954))
| ~ hBOOL(hAPP(fun(U_955,bool),bool,hAPP(fun(U_955,bool),fun(fun(U_955,bool),bool),ord_less_eq(fun(U_955,bool)),U_953),U_952)) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
( hBOOL(hAPP(U_955,bool,U_952,U_954))
| ~ hBOOL(hAPP(U_955,bool,U_953,U_954))
| ~ hBOOL(hAPP(fun(U_955,bool),bool,hAPP(fun(U_955,bool),fun(fun(U_955,bool),bool),ord_less_eq(fun(U_955,bool)),U_953),U_952)) ),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_1,plain,
! [X_a,X_1,A_1,B] :
( 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))
| ~ 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_202_in__mono]) ).
fof(f_265_2,plain,
! [U_959,U_958,U_957,U_956] :
( hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_958),U_956))
| ~ hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_958),U_957))
| ~ hBOOL(hAPP(fun(U_959,bool),bool,hAPP(fun(U_959,bool),fun(fun(U_959,bool),bool),ord_less_eq(fun(U_959,bool)),U_957),U_956)) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
( hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_958),U_956))
| ~ hBOOL(hAPP(fun(U_959,bool),bool,hAPP(U_959,fun(fun(U_959,bool),bool),member(U_959),U_958),U_957))
| ~ hBOOL(hAPP(fun(U_959,bool),bool,hAPP(fun(U_959,bool),fun(fun(U_959,bool),bool),ord_less_eq(fun(U_959,bool)),U_957),U_956)) ),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_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_203_equalityD2]) ).
fof(f_266_2,plain,
! [U_962,U_961,U_960] :
( hBOOL(hAPP(fun(U_962,bool),bool,hAPP(fun(U_962,bool),fun(fun(U_962,bool),bool),ord_less_eq(fun(U_962,bool)),U_960),U_961))
| ti(fun(U_962,bool),U_961) != ti(fun(U_962,bool),U_960) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
( hBOOL(hAPP(fun(U_962,bool),bool,hAPP(fun(U_962,bool),fun(fun(U_962,bool),bool),ord_less_eq(fun(U_962,bool)),U_960),U_961))
| ti(fun(U_962,bool),U_961) != ti(fun(U_962,bool),U_960) ),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_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_204_equalityD1]) ).
fof(f_267_2,plain,
! [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_964),U_963))
| ti(fun(U_965,bool),U_964) != ti(fun(U_965,bool),U_963) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
cnf(f_267_3,plain,
( 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_964),U_963))
| ti(fun(U_965,bool),U_964) != ti(fun(U_965,bool),U_963) ),
inference(clausify,[status(thm)],[f_267_2]) ).
fof(f_268_1,plain,
! [X_a,Q_1,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))
| ~ hBOOL(hAPP(X_a,bool,Pa,X_1)) ),
inference(fof_nnf,[status(thm)],[fact_205_rev__predicate1D]) ).
fof(f_268_2,plain,
! [U_969,U_968,U_967,U_966] :
( hBOOL(hAPP(U_969,bool,U_968,U_966))
| ~ hBOOL(hAPP(fun(U_969,bool),bool,hAPP(fun(U_969,bool),fun(fun(U_969,bool),bool),ord_less_eq(fun(U_969,bool)),U_967),U_968))
| ~ hBOOL(hAPP(U_969,bool,U_967,U_966)) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( hBOOL(hAPP(U_969,bool,U_968,U_966))
| ~ hBOOL(hAPP(fun(U_969,bool),bool,hAPP(fun(U_969,bool),fun(fun(U_969,bool),bool),ord_less_eq(fun(U_969,bool)),U_967),U_968))
| ~ hBOOL(hAPP(U_969,bool,U_967,U_966)) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_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_206_set__eq__subset]) ).
fof(f_269_2,plain,
! [U_972,U_971,U_970] :
( ( ti(fun(U_972,bool),U_971) = ti(fun(U_972,bool),U_970)
| ~ hBOOL(hAPP(fun(U_972,bool),bool,hAPP(fun(U_972,bool),fun(fun(U_972,bool),bool),ord_less_eq(fun(U_972,bool)),U_970),U_971))
| ~ hBOOL(hAPP(fun(U_972,bool),bool,hAPP(fun(U_972,bool),fun(fun(U_972,bool),bool),ord_less_eq(fun(U_972,bool)),U_971),U_970)) )
& ( ( hBOOL(hAPP(fun(U_972,bool),bool,hAPP(fun(U_972,bool),fun(fun(U_972,bool),bool),ord_less_eq(fun(U_972,bool)),U_970),U_971))
& hBOOL(hAPP(fun(U_972,bool),bool,hAPP(fun(U_972,bool),fun(fun(U_972,bool),bool),ord_less_eq(fun(U_972,bool)),U_971),U_970)) )
| ti(fun(U_972,bool),U_971) != ti(fun(U_972,bool),U_970) ) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
( ! [U_978,U_976,U_974] :
( ti(fun(U_978,bool),U_976) = ti(fun(U_978,bool),U_974)
| ~ hBOOL(hAPP(fun(U_978,bool),bool,hAPP(fun(U_978,bool),fun(fun(U_978,bool),bool),ord_less_eq(fun(U_978,bool)),U_974),U_976))
| ~ hBOOL(hAPP(fun(U_978,bool),bool,hAPP(fun(U_978,bool),fun(fun(U_978,bool),bool),ord_less_eq(fun(U_978,bool)),U_976),U_974)) )
& ! [U_977,U_975,U_973] :
( ( 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_973),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_975),U_973)) )
| ti(fun(U_977,bool),U_975) != ti(fun(U_977,bool),U_973) ) ),
inference(miniscope,[status(thm)],[f_269_2]) ).
cnf(f_269_4,plain,
( 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_975),U_973))
| ti(fun(U_977,bool),U_975) != ti(fun(U_977,bool),U_973) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_5,plain,
( 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_973),U_975))
| ti(fun(U_977,bool),U_975) != ti(fun(U_977,bool),U_973) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_6,plain,
( ti(fun(U_978,bool),U_976) = ti(fun(U_978,bool),U_974)
| ~ hBOOL(hAPP(fun(U_978,bool),bool,hAPP(fun(U_978,bool),fun(fun(U_978,bool),bool),ord_less_eq(fun(U_978,bool)),U_974),U_976))
| ~ hBOOL(hAPP(fun(U_978,bool),bool,hAPP(fun(U_978,bool),fun(fun(U_978,bool),bool),ord_less_eq(fun(U_978,bool)),U_976),U_974)) ),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_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_207_subset__refl]) ).
fof(f_270_2,plain,
! [U_980,U_979] : hBOOL(hAPP(fun(U_980,bool),bool,hAPP(fun(U_980,bool),fun(fun(U_980,bool),bool),ord_less_eq(fun(U_980,bool)),U_979),U_979)),
inference(variable_rename,[status(thm)],[f_270_1]) ).
cnf(f_270_3,plain,
hBOOL(hAPP(fun(U_980,bool),bool,hAPP(fun(U_980,bool),fun(fun(U_980,bool),bool),ord_less_eq(fun(U_980,bool)),U_979),U_979)),
inference(clausify,[status(thm)],[f_270_2]) ).
fof(f_271_1,plain,
! [X_a,R_1,S_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,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_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)),S_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)),R_1),S_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)),R_1),S_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,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_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)),S_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_208_pred__subset__eq]) ).
fof(f_271_2,plain,
! [U_983,U_982,U_981] :
( ( 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)),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(fun(U_983,bool),bool)),fun(fun(U_983,bool),fun(U_983,bool)),combc(U_983,fun(U_983,bool),bool),member(U_983)),U_982)),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(fun(U_983,bool),bool)),fun(fun(U_983,bool),fun(U_983,bool)),combc(U_983,fun(U_983,bool),bool),member(U_983)),U_981)))
| ~ 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_982),U_981)) )
& ( 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_982),U_981))
| ~ 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)),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(fun(U_983,bool),bool)),fun(fun(U_983,bool),fun(U_983,bool)),combc(U_983,fun(U_983,bool),bool),member(U_983)),U_982)),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(fun(U_983,bool),bool)),fun(fun(U_983,bool),fun(U_983,bool)),combc(U_983,fun(U_983,bool),bool),member(U_983)),U_981))) ) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
( ! [U_989,U_987,U_985] :
( hBOOL(hAPP(fun(U_989,bool),bool,hAPP(fun(U_989,bool),fun(fun(U_989,bool),bool),ord_less_eq(fun(U_989,bool)),hAPP(fun(U_989,bool),fun(U_989,bool),hAPP(fun(U_989,fun(fun(U_989,bool),bool)),fun(fun(U_989,bool),fun(U_989,bool)),combc(U_989,fun(U_989,bool),bool),member(U_989)),U_987)),hAPP(fun(U_989,bool),fun(U_989,bool),hAPP(fun(U_989,fun(fun(U_989,bool),bool)),fun(fun(U_989,bool),fun(U_989,bool)),combc(U_989,fun(U_989,bool),bool),member(U_989)),U_985)))
| ~ hBOOL(hAPP(fun(U_989,bool),bool,hAPP(fun(U_989,bool),fun(fun(U_989,bool),bool),ord_less_eq(fun(U_989,bool)),U_987),U_985)) )
& ! [U_988,U_986,U_984] :
( hBOOL(hAPP(fun(U_988,bool),bool,hAPP(fun(U_988,bool),fun(fun(U_988,bool),bool),ord_less_eq(fun(U_988,bool)),U_986),U_984))
| ~ hBOOL(hAPP(fun(U_988,bool),bool,hAPP(fun(U_988,bool),fun(fun(U_988,bool),bool),ord_less_eq(fun(U_988,bool)),hAPP(fun(U_988,bool),fun(U_988,bool),hAPP(fun(U_988,fun(fun(U_988,bool),bool)),fun(fun(U_988,bool),fun(U_988,bool)),combc(U_988,fun(U_988,bool),bool),member(U_988)),U_986)),hAPP(fun(U_988,bool),fun(U_988,bool),hAPP(fun(U_988,fun(fun(U_988,bool),bool)),fun(fun(U_988,bool),fun(U_988,bool)),combc(U_988,fun(U_988,bool),bool),member(U_988)),U_984))) ) ),
inference(miniscope,[status(thm)],[f_271_2]) ).
cnf(f_271_4,plain,
( hBOOL(hAPP(fun(U_988,bool),bool,hAPP(fun(U_988,bool),fun(fun(U_988,bool),bool),ord_less_eq(fun(U_988,bool)),U_986),U_984))
| ~ hBOOL(hAPP(fun(U_988,bool),bool,hAPP(fun(U_988,bool),fun(fun(U_988,bool),bool),ord_less_eq(fun(U_988,bool)),hAPP(fun(U_988,bool),fun(U_988,bool),hAPP(fun(U_988,fun(fun(U_988,bool),bool)),fun(fun(U_988,bool),fun(U_988,bool)),combc(U_988,fun(U_988,bool),bool),member(U_988)),U_986)),hAPP(fun(U_988,bool),fun(U_988,bool),hAPP(fun(U_988,fun(fun(U_988,bool),bool)),fun(fun(U_988,bool),fun(U_988,bool)),combc(U_988,fun(U_988,bool),bool),member(U_988)),U_984))) ),
inference(clausify,[status(thm)],[f_271_3]) ).
cnf(f_271_5,plain,
( hBOOL(hAPP(fun(U_989,bool),bool,hAPP(fun(U_989,bool),fun(fun(U_989,bool),bool),ord_less_eq(fun(U_989,bool)),hAPP(fun(U_989,bool),fun(U_989,bool),hAPP(fun(U_989,fun(fun(U_989,bool),bool)),fun(fun(U_989,bool),fun(U_989,bool)),combc(U_989,fun(U_989,bool),bool),member(U_989)),U_987)),hAPP(fun(U_989,bool),fun(U_989,bool),hAPP(fun(U_989,fun(fun(U_989,bool),bool)),fun(fun(U_989,bool),fun(U_989,bool)),combc(U_989,fun(U_989,bool),bool),member(U_989)),U_985)))
| ~ hBOOL(hAPP(fun(U_989,bool),bool,hAPP(fun(U_989,bool),fun(fun(U_989,bool),bool),ord_less_eq(fun(U_989,bool)),U_987),U_985)) ),
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_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_2,Y_3] :
( ~ hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_3))
& hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_2),Y_3)) ) ),
inference(fof_nnf,[status(thm)],[fact_209_predicate2I]) ).
fof(f_272_2,plain,
! [U_995,U_994,U_993,U_992] :
( hBOOL(hAPP(fun(U_994,fun(U_995,bool)),bool,hAPP(fun(U_994,fun(U_995,bool)),fun(fun(U_994,fun(U_995,bool)),bool),ord_less_eq(fun(U_994,fun(U_995,bool))),U_992),U_993))
| ? [U_991,U_990] :
( ~ hBOOL(hAPP(U_995,bool,hAPP(U_994,fun(U_995,bool),U_993,U_991),U_990))
& hBOOL(hAPP(U_995,bool,hAPP(U_994,fun(U_995,bool),U_992,U_991),U_990)) ) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_995,U_994,U_993,U_992] :
( hBOOL(hAPP(fun(U_994,fun(U_995,bool)),bool,hAPP(fun(U_994,fun(U_995,bool)),fun(fun(U_994,fun(U_995,bool)),bool),ord_less_eq(fun(U_994,fun(U_995,bool))),U_992),U_993))
| ? [U_990] :
( ~ hBOOL(hAPP(U_995,bool,hAPP(U_994,fun(U_995,bool),U_993,sK58(U_995,U_994,U_993,U_992)),U_990))
& hBOOL(hAPP(U_995,bool,hAPP(U_994,fun(U_995,bool),U_992,sK58(U_995,U_994,U_993,U_992)),U_990)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_991,sK58(U_995,U_994,U_993,U_992))],[f_272_2]) ).
fof(f_272_4,plain,
! [U_995,U_994,U_993,U_992] :
( hBOOL(hAPP(fun(U_994,fun(U_995,bool)),bool,hAPP(fun(U_994,fun(U_995,bool)),fun(fun(U_994,fun(U_995,bool)),bool),ord_less_eq(fun(U_994,fun(U_995,bool))),U_992),U_993))
| ( ~ hBOOL(hAPP(U_995,bool,hAPP(U_994,fun(U_995,bool),U_993,sK58(U_995,U_994,U_993,U_992)),sK59(U_995,U_994,U_993,U_992)))
& hBOOL(hAPP(U_995,bool,hAPP(U_994,fun(U_995,bool),U_992,sK58(U_995,U_994,U_993,U_992)),sK59(U_995,U_994,U_993,U_992))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_990,sK59(U_995,U_994,U_993,U_992))],[f_272_3]) ).
cnf(f_272_5,plain,
( hBOOL(hAPP(U_995,bool,hAPP(U_994,fun(U_995,bool),U_992,sK58(U_995,U_994,U_993,U_992)),sK59(U_995,U_994,U_993,U_992)))
| hBOOL(hAPP(fun(U_994,fun(U_995,bool)),bool,hAPP(fun(U_994,fun(U_995,bool)),fun(fun(U_994,fun(U_995,bool)),bool),ord_less_eq(fun(U_994,fun(U_995,bool))),U_992),U_993)) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_6,plain,
( ~ hBOOL(hAPP(U_995,bool,hAPP(U_994,fun(U_995,bool),U_993,sK58(U_995,U_994,U_993,U_992)),sK59(U_995,U_994,U_993,U_992)))
| hBOOL(hAPP(fun(U_994,fun(U_995,bool)),bool,hAPP(fun(U_994,fun(U_995,bool)),fun(fun(U_994,fun(U_995,bool)),bool),ord_less_eq(fun(U_994,fun(U_995,bool))),U_992),U_993)) ),
inference(clausify,[status(thm)],[f_272_4]) ).
fof(f_273_1,plain,
! [X_b,X_a,B,C_1,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_1)))
| ? [X_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(X_a,fun(X_b,bool),B,X_2)),hAPP(X_a,fun(X_b,bool),C_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_210_Pi__mono]) ).
fof(f_273_2,plain,
! [U_1001,U_1000,U_999,U_998,U_997] :
( hBOOL(hAPP(fun(fun(U_1000,U_1001),bool),bool,hAPP(fun(fun(U_1000,U_1001),bool),fun(fun(fun(U_1000,U_1001),bool),bool),ord_less_eq(fun(fun(U_1000,U_1001),bool)),hAPP(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool),hAPP(fun(U_1000,bool),fun(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool)),pi(U_1000,U_1001),U_997),U_999)),hAPP(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool),hAPP(fun(U_1000,bool),fun(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool)),pi(U_1000,U_1001),U_997),U_998)))
| ? [U_996] :
( ~ hBOOL(hAPP(fun(U_1001,bool),bool,hAPP(fun(U_1001,bool),fun(fun(U_1001,bool),bool),ord_less_eq(fun(U_1001,bool)),hAPP(U_1000,fun(U_1001,bool),U_999,U_996)),hAPP(U_1000,fun(U_1001,bool),U_998,U_996)))
& hBOOL(hAPP(fun(U_1000,bool),bool,hAPP(U_1000,fun(fun(U_1000,bool),bool),member(U_1000),U_996),U_997)) ) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
! [U_1001,U_1000,U_999,U_998,U_997] :
( hBOOL(hAPP(fun(fun(U_1000,U_1001),bool),bool,hAPP(fun(fun(U_1000,U_1001),bool),fun(fun(fun(U_1000,U_1001),bool),bool),ord_less_eq(fun(fun(U_1000,U_1001),bool)),hAPP(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool),hAPP(fun(U_1000,bool),fun(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool)),pi(U_1000,U_1001),U_997),U_999)),hAPP(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool),hAPP(fun(U_1000,bool),fun(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool)),pi(U_1000,U_1001),U_997),U_998)))
| ( ~ hBOOL(hAPP(fun(U_1001,bool),bool,hAPP(fun(U_1001,bool),fun(fun(U_1001,bool),bool),ord_less_eq(fun(U_1001,bool)),hAPP(U_1000,fun(U_1001,bool),U_999,sK60(U_1001,U_1000,U_999,U_998,U_997))),hAPP(U_1000,fun(U_1001,bool),U_998,sK60(U_1001,U_1000,U_999,U_998,U_997))))
& hBOOL(hAPP(fun(U_1000,bool),bool,hAPP(U_1000,fun(fun(U_1000,bool),bool),member(U_1000),sK60(U_1001,U_1000,U_999,U_998,U_997)),U_997)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_996,sK60(U_1001,U_1000,U_999,U_998,U_997))],[f_273_2]) ).
cnf(f_273_4,plain,
( hBOOL(hAPP(fun(U_1000,bool),bool,hAPP(U_1000,fun(fun(U_1000,bool),bool),member(U_1000),sK60(U_1001,U_1000,U_999,U_998,U_997)),U_997))
| hBOOL(hAPP(fun(fun(U_1000,U_1001),bool),bool,hAPP(fun(fun(U_1000,U_1001),bool),fun(fun(fun(U_1000,U_1001),bool),bool),ord_less_eq(fun(fun(U_1000,U_1001),bool)),hAPP(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool),hAPP(fun(U_1000,bool),fun(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool)),pi(U_1000,U_1001),U_997),U_999)),hAPP(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool),hAPP(fun(U_1000,bool),fun(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool)),pi(U_1000,U_1001),U_997),U_998))) ),
inference(clausify,[status(thm)],[f_273_3]) ).
cnf(f_273_5,plain,
( ~ hBOOL(hAPP(fun(U_1001,bool),bool,hAPP(fun(U_1001,bool),fun(fun(U_1001,bool),bool),ord_less_eq(fun(U_1001,bool)),hAPP(U_1000,fun(U_1001,bool),U_999,sK60(U_1001,U_1000,U_999,U_998,U_997))),hAPP(U_1000,fun(U_1001,bool),U_998,sK60(U_1001,U_1000,U_999,U_998,U_997))))
| hBOOL(hAPP(fun(fun(U_1000,U_1001),bool),bool,hAPP(fun(fun(U_1000,U_1001),bool),fun(fun(fun(U_1000,U_1001),bool),bool),ord_less_eq(fun(fun(U_1000,U_1001),bool)),hAPP(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool),hAPP(fun(U_1000,bool),fun(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool)),pi(U_1000,U_1001),U_997),U_999)),hAPP(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool),hAPP(fun(U_1000,bool),fun(fun(U_1000,fun(U_1001,bool)),fun(fun(U_1000,U_1001),bool)),pi(U_1000,U_1001),U_997),U_998))) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_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_2] :
( ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_211_subsetI]) ).
fof(f_274_2,plain,
! [U_1005,U_1004,U_1003] :
( hBOOL(hAPP(fun(U_1005,bool),bool,hAPP(fun(U_1005,bool),fun(fun(U_1005,bool),bool),ord_less_eq(fun(U_1005,bool)),U_1003),U_1004))
| ? [U_1002] :
( ~ hBOOL(hAPP(fun(U_1005,bool),bool,hAPP(U_1005,fun(fun(U_1005,bool),bool),member(U_1005),U_1002),U_1004))
& hBOOL(hAPP(fun(U_1005,bool),bool,hAPP(U_1005,fun(fun(U_1005,bool),bool),member(U_1005),U_1002),U_1003)) ) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
! [U_1005,U_1004,U_1003] :
( hBOOL(hAPP(fun(U_1005,bool),bool,hAPP(fun(U_1005,bool),fun(fun(U_1005,bool),bool),ord_less_eq(fun(U_1005,bool)),U_1003),U_1004))
| ( ~ hBOOL(hAPP(fun(U_1005,bool),bool,hAPP(U_1005,fun(fun(U_1005,bool),bool),member(U_1005),sK61(U_1005,U_1004,U_1003)),U_1004))
& hBOOL(hAPP(fun(U_1005,bool),bool,hAPP(U_1005,fun(fun(U_1005,bool),bool),member(U_1005),sK61(U_1005,U_1004,U_1003)),U_1003)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_1002,sK61(U_1005,U_1004,U_1003))],[f_274_2]) ).
cnf(f_274_4,plain,
( hBOOL(hAPP(fun(U_1005,bool),bool,hAPP(U_1005,fun(fun(U_1005,bool),bool),member(U_1005),sK61(U_1005,U_1004,U_1003)),U_1003))
| hBOOL(hAPP(fun(U_1005,bool),bool,hAPP(fun(U_1005,bool),fun(fun(U_1005,bool),bool),ord_less_eq(fun(U_1005,bool)),U_1003),U_1004)) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_5,plain,
( ~ hBOOL(hAPP(fun(U_1005,bool),bool,hAPP(U_1005,fun(fun(U_1005,bool),bool),member(U_1005),sK61(U_1005,U_1004,U_1003)),U_1004))
| hBOOL(hAPP(fun(U_1005,bool),bool,hAPP(fun(U_1005,bool),fun(fun(U_1005,bool),bool),ord_less_eq(fun(U_1005,bool)),U_1003),U_1004)) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_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_2,Y_3] :
( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_3)),hAPP(X_a,X_b,F,X_2)))
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_3),X_2)) )
| ~ 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_212_xt5]) ).
fof(f_275_2,plain,
! [U_1013,U_1012] :
( ! [U_1011,U_1010,U_1009,U_1008] :
( hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less(U_1013),U_1011),hAPP(U_1012,U_1013,U_1010,U_1008)))
| ? [U_1007,U_1006] :
( ~ hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less(U_1013),hAPP(U_1012,U_1013,U_1010,U_1006)),hAPP(U_1012,U_1013,U_1010,U_1007)))
& hBOOL(hAPP(U_1012,bool,hAPP(U_1012,fun(U_1012,bool),ord_less(U_1012),U_1006),U_1007)) )
| ~ hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less_eq(U_1013),U_1011),hAPP(U_1012,U_1013,U_1010,U_1009)))
| ~ hBOOL(hAPP(U_1012,bool,hAPP(U_1012,fun(U_1012,bool),ord_less(U_1012),U_1009),U_1008)) )
| ~ order(U_1013)
| ~ order(U_1012) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
! [U_1013,U_1012] :
( ! [U_1011,U_1010,U_1009,U_1008] :
( hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less(U_1013),U_1011),hAPP(U_1012,U_1013,U_1010,U_1008)))
| ? [U_1006] :
( ~ hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less(U_1013),hAPP(U_1012,U_1013,U_1010,U_1006)),hAPP(U_1012,U_1013,U_1010,sK62(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008))))
& hBOOL(hAPP(U_1012,bool,hAPP(U_1012,fun(U_1012,bool),ord_less(U_1012),U_1006),sK62(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008))) )
| ~ hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less_eq(U_1013),U_1011),hAPP(U_1012,U_1013,U_1010,U_1009)))
| ~ hBOOL(hAPP(U_1012,bool,hAPP(U_1012,fun(U_1012,bool),ord_less(U_1012),U_1009),U_1008)) )
| ~ order(U_1013)
| ~ order(U_1012) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_1007,sK62(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008))],[f_275_2]) ).
fof(f_275_4,plain,
! [U_1013,U_1012] :
( ! [U_1011,U_1010,U_1009,U_1008] :
( hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less(U_1013),U_1011),hAPP(U_1012,U_1013,U_1010,U_1008)))
| ( ~ hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less(U_1013),hAPP(U_1012,U_1013,U_1010,sK63(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008))),hAPP(U_1012,U_1013,U_1010,sK62(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008))))
& hBOOL(hAPP(U_1012,bool,hAPP(U_1012,fun(U_1012,bool),ord_less(U_1012),sK63(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008)),sK62(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008))) )
| ~ hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less_eq(U_1013),U_1011),hAPP(U_1012,U_1013,U_1010,U_1009)))
| ~ hBOOL(hAPP(U_1012,bool,hAPP(U_1012,fun(U_1012,bool),ord_less(U_1012),U_1009),U_1008)) )
| ~ order(U_1013)
| ~ order(U_1012) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_1006,sK63(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008))],[f_275_3]) ).
cnf(f_275_5,plain,
( hBOOL(hAPP(U_1012,bool,hAPP(U_1012,fun(U_1012,bool),ord_less(U_1012),sK63(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008)),sK62(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008)))
| hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less(U_1013),U_1011),hAPP(U_1012,U_1013,U_1010,U_1008)))
| ~ hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less_eq(U_1013),U_1011),hAPP(U_1012,U_1013,U_1010,U_1009)))
| ~ hBOOL(hAPP(U_1012,bool,hAPP(U_1012,fun(U_1012,bool),ord_less(U_1012),U_1009),U_1008))
| ~ order(U_1013)
| ~ order(U_1012) ),
inference(clausify,[status(thm)],[f_275_4]) ).
cnf(f_275_6,plain,
( ~ hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less(U_1013),hAPP(U_1012,U_1013,U_1010,sK63(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008))),hAPP(U_1012,U_1013,U_1010,sK62(U_1013,U_1012,U_1011,U_1010,U_1009,U_1008))))
| hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less(U_1013),U_1011),hAPP(U_1012,U_1013,U_1010,U_1008)))
| ~ hBOOL(hAPP(U_1013,bool,hAPP(U_1013,fun(U_1013,bool),ord_less_eq(U_1013),U_1011),hAPP(U_1012,U_1013,U_1010,U_1009)))
| ~ hBOOL(hAPP(U_1012,bool,hAPP(U_1012,fun(U_1012,bool),ord_less(U_1012),U_1009),U_1008))
| ~ order(U_1013)
| ~ order(U_1012) ),
inference(clausify,[status(thm)],[f_275_4]) ).
fof(f_276_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_2,Y_3] :
( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_3)),hAPP(X_a,X_b,F,X_2)))
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_3),X_2)) )
| ~ 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_213_xt7]) ).
fof(f_276_2,plain,
! [U_1021,U_1020] :
( ! [U_1019,U_1018,U_1017,U_1016] :
( hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less(U_1021),U_1019),hAPP(U_1020,U_1021,U_1018,U_1016)))
| ? [U_1015,U_1014] :
( ~ hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less_eq(U_1021),hAPP(U_1020,U_1021,U_1018,U_1014)),hAPP(U_1020,U_1021,U_1018,U_1015)))
& hBOOL(hAPP(U_1020,bool,hAPP(U_1020,fun(U_1020,bool),ord_less_eq(U_1020),U_1014),U_1015)) )
| ~ hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less(U_1021),U_1019),hAPP(U_1020,U_1021,U_1018,U_1017)))
| ~ hBOOL(hAPP(U_1020,bool,hAPP(U_1020,fun(U_1020,bool),ord_less_eq(U_1020),U_1017),U_1016)) )
| ~ order(U_1021)
| ~ order(U_1020) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
! [U_1021,U_1020] :
( ! [U_1019,U_1018,U_1017,U_1016] :
( hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less(U_1021),U_1019),hAPP(U_1020,U_1021,U_1018,U_1016)))
| ? [U_1014] :
( ~ hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less_eq(U_1021),hAPP(U_1020,U_1021,U_1018,U_1014)),hAPP(U_1020,U_1021,U_1018,sK64(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016))))
& hBOOL(hAPP(U_1020,bool,hAPP(U_1020,fun(U_1020,bool),ord_less_eq(U_1020),U_1014),sK64(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016))) )
| ~ hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less(U_1021),U_1019),hAPP(U_1020,U_1021,U_1018,U_1017)))
| ~ hBOOL(hAPP(U_1020,bool,hAPP(U_1020,fun(U_1020,bool),ord_less_eq(U_1020),U_1017),U_1016)) )
| ~ order(U_1021)
| ~ order(U_1020) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_1015,sK64(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016))],[f_276_2]) ).
fof(f_276_4,plain,
! [U_1021,U_1020] :
( ! [U_1019,U_1018,U_1017,U_1016] :
( hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less(U_1021),U_1019),hAPP(U_1020,U_1021,U_1018,U_1016)))
| ( ~ hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less_eq(U_1021),hAPP(U_1020,U_1021,U_1018,sK65(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016))),hAPP(U_1020,U_1021,U_1018,sK64(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016))))
& hBOOL(hAPP(U_1020,bool,hAPP(U_1020,fun(U_1020,bool),ord_less_eq(U_1020),sK65(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016)),sK64(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016))) )
| ~ hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less(U_1021),U_1019),hAPP(U_1020,U_1021,U_1018,U_1017)))
| ~ hBOOL(hAPP(U_1020,bool,hAPP(U_1020,fun(U_1020,bool),ord_less_eq(U_1020),U_1017),U_1016)) )
| ~ order(U_1021)
| ~ order(U_1020) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_1014,sK65(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016))],[f_276_3]) ).
cnf(f_276_5,plain,
( hBOOL(hAPP(U_1020,bool,hAPP(U_1020,fun(U_1020,bool),ord_less_eq(U_1020),sK65(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016)),sK64(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016)))
| hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less(U_1021),U_1019),hAPP(U_1020,U_1021,U_1018,U_1016)))
| ~ hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less(U_1021),U_1019),hAPP(U_1020,U_1021,U_1018,U_1017)))
| ~ hBOOL(hAPP(U_1020,bool,hAPP(U_1020,fun(U_1020,bool),ord_less_eq(U_1020),U_1017),U_1016))
| ~ order(U_1021)
| ~ order(U_1020) ),
inference(clausify,[status(thm)],[f_276_4]) ).
cnf(f_276_6,plain,
( ~ hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less_eq(U_1021),hAPP(U_1020,U_1021,U_1018,sK65(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016))),hAPP(U_1020,U_1021,U_1018,sK64(U_1021,U_1020,U_1019,U_1018,U_1017,U_1016))))
| hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less(U_1021),U_1019),hAPP(U_1020,U_1021,U_1018,U_1016)))
| ~ hBOOL(hAPP(U_1021,bool,hAPP(U_1021,fun(U_1021,bool),ord_less(U_1021),U_1019),hAPP(U_1020,U_1021,U_1018,U_1017)))
| ~ hBOOL(hAPP(U_1020,bool,hAPP(U_1020,fun(U_1020,bool),ord_less_eq(U_1020),U_1017),U_1016))
| ~ order(U_1021)
| ~ order(U_1020) ),
inference(clausify,[status(thm)],[f_276_4]) ).
fof(f_277_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_214_psubsetD]) ).
fof(f_277_2,plain,
! [U_1025,U_1024,U_1023,U_1022] :
( hBOOL(hAPP(fun(U_1025,bool),bool,hAPP(U_1025,fun(fun(U_1025,bool),bool),member(U_1025),U_1024),U_1022))
| ~ hBOOL(hAPP(fun(U_1025,bool),bool,hAPP(U_1025,fun(fun(U_1025,bool),bool),member(U_1025),U_1024),U_1023))
| ~ hBOOL(hAPP(fun(U_1025,bool),bool,hAPP(fun(U_1025,bool),fun(fun(U_1025,bool),bool),ord_less(fun(U_1025,bool)),U_1023),U_1022)) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
( hBOOL(hAPP(fun(U_1025,bool),bool,hAPP(U_1025,fun(fun(U_1025,bool),bool),member(U_1025),U_1024),U_1022))
| ~ hBOOL(hAPP(fun(U_1025,bool),bool,hAPP(U_1025,fun(fun(U_1025,bool),bool),member(U_1025),U_1024),U_1023))
| ~ hBOOL(hAPP(fun(U_1025,bool),bool,hAPP(fun(U_1025,bool),fun(fun(U_1025,bool),bool),ord_less(fun(U_1025,bool)),U_1023),U_1022)) ),
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_1,plain,
! [X_a,C_1,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_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)),B),C_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_215_psubset__trans]) ).
fof(f_278_2,plain,
! [U_1029,U_1028,U_1027,U_1026] :
( hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(fun(U_1029,bool),fun(fun(U_1029,bool),bool),ord_less(fun(U_1029,bool)),U_1027),U_1028))
| ~ hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(fun(U_1029,bool),fun(fun(U_1029,bool),bool),ord_less(fun(U_1029,bool)),U_1026),U_1028))
| ~ hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(fun(U_1029,bool),fun(fun(U_1029,bool),bool),ord_less(fun(U_1029,bool)),U_1027),U_1026)) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
( hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(fun(U_1029,bool),fun(fun(U_1029,bool),bool),ord_less(fun(U_1029,bool)),U_1027),U_1028))
| ~ hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(fun(U_1029,bool),fun(fun(U_1029,bool),bool),ord_less(fun(U_1029,bool)),U_1026),U_1028))
| ~ hBOOL(hAPP(fun(U_1029,bool),bool,hAPP(fun(U_1029,bool),fun(fun(U_1029,bool),bool),ord_less(fun(U_1029,bool)),U_1027),U_1026)) ),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_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_2,Y_3] :
( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_3)))
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_3)) )
| ~ 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_216_order__less__le__subst2]) ).
fof(f_279_2,plain,
! [U_1037,U_1036] :
( ! [U_1035,U_1034,U_1033,U_1032] :
( hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less(U_1036),hAPP(U_1037,U_1036,U_1035,U_1033)),U_1034))
| ? [U_1031,U_1030] :
( ~ hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less(U_1036),hAPP(U_1037,U_1036,U_1035,U_1031)),hAPP(U_1037,U_1036,U_1035,U_1030)))
& hBOOL(hAPP(U_1037,bool,hAPP(U_1037,fun(U_1037,bool),ord_less(U_1037),U_1031),U_1030)) )
| ~ hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less_eq(U_1036),hAPP(U_1037,U_1036,U_1035,U_1032)),U_1034))
| ~ hBOOL(hAPP(U_1037,bool,hAPP(U_1037,fun(U_1037,bool),ord_less(U_1037),U_1033),U_1032)) )
| ~ order(U_1037)
| ~ order(U_1036) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_1037,U_1036] :
( ! [U_1035,U_1034,U_1033,U_1032] :
( hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less(U_1036),hAPP(U_1037,U_1036,U_1035,U_1033)),U_1034))
| ? [U_1030] :
( ~ hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less(U_1036),hAPP(U_1037,U_1036,U_1035,sK66(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032))),hAPP(U_1037,U_1036,U_1035,U_1030)))
& hBOOL(hAPP(U_1037,bool,hAPP(U_1037,fun(U_1037,bool),ord_less(U_1037),sK66(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032)),U_1030)) )
| ~ hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less_eq(U_1036),hAPP(U_1037,U_1036,U_1035,U_1032)),U_1034))
| ~ hBOOL(hAPP(U_1037,bool,hAPP(U_1037,fun(U_1037,bool),ord_less(U_1037),U_1033),U_1032)) )
| ~ order(U_1037)
| ~ order(U_1036) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_1031,sK66(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032))],[f_279_2]) ).
fof(f_279_4,plain,
! [U_1037,U_1036] :
( ! [U_1035,U_1034,U_1033,U_1032] :
( hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less(U_1036),hAPP(U_1037,U_1036,U_1035,U_1033)),U_1034))
| ( ~ hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less(U_1036),hAPP(U_1037,U_1036,U_1035,sK66(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032))),hAPP(U_1037,U_1036,U_1035,sK67(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032))))
& hBOOL(hAPP(U_1037,bool,hAPP(U_1037,fun(U_1037,bool),ord_less(U_1037),sK66(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032)),sK67(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032))) )
| ~ hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less_eq(U_1036),hAPP(U_1037,U_1036,U_1035,U_1032)),U_1034))
| ~ hBOOL(hAPP(U_1037,bool,hAPP(U_1037,fun(U_1037,bool),ord_less(U_1037),U_1033),U_1032)) )
| ~ order(U_1037)
| ~ order(U_1036) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_1030,sK67(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032))],[f_279_3]) ).
cnf(f_279_5,plain,
( hBOOL(hAPP(U_1037,bool,hAPP(U_1037,fun(U_1037,bool),ord_less(U_1037),sK66(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032)),sK67(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032)))
| hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less(U_1036),hAPP(U_1037,U_1036,U_1035,U_1033)),U_1034))
| ~ hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less_eq(U_1036),hAPP(U_1037,U_1036,U_1035,U_1032)),U_1034))
| ~ hBOOL(hAPP(U_1037,bool,hAPP(U_1037,fun(U_1037,bool),ord_less(U_1037),U_1033),U_1032))
| ~ order(U_1037)
| ~ order(U_1036) ),
inference(clausify,[status(thm)],[f_279_4]) ).
cnf(f_279_6,plain,
( ~ hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less(U_1036),hAPP(U_1037,U_1036,U_1035,sK66(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032))),hAPP(U_1037,U_1036,U_1035,sK67(U_1037,U_1036,U_1035,U_1034,U_1033,U_1032))))
| hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less(U_1036),hAPP(U_1037,U_1036,U_1035,U_1033)),U_1034))
| ~ hBOOL(hAPP(U_1036,bool,hAPP(U_1036,fun(U_1036,bool),ord_less_eq(U_1036),hAPP(U_1037,U_1036,U_1035,U_1032)),U_1034))
| ~ hBOOL(hAPP(U_1037,bool,hAPP(U_1037,fun(U_1037,bool),ord_less(U_1037),U_1033),U_1032))
| ~ order(U_1037)
| ~ order(U_1036) ),
inference(clausify,[status(thm)],[f_279_4]) ).
fof(f_280_1,plain,
! [X_1,Y_2,L_3,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_3),Aa),Ba)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
& ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Aa) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Y_2)),L_3))
& ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Ba)
& ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa) ) )
& ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Aa) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Ba)),L_3))
& ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Aa) )
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Y_2) )
& ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),L_3))
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Y_2)),L_3))
| ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Ba)
| ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Aa) ) )
| ti(arrow_490897120le_alt,Y_2) = ti(arrow_490897120le_alt,Aa) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Ba)),L_3))
| ti(arrow_490897120le_alt,Y_2) != ti(arrow_490897120le_alt,Aa) )
& ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_2) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_3),Aa),Ba))) ) )
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_217_in__below]) ).
fof(f_280_2,plain,
! [U_1042,U_1041,U_1040,U_1039,U_1038] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),U_1040))
& ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1039) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1038),U_1041)),U_1040))
& ti(arrow_490897120le_alt,U_1041) != ti(arrow_490897120le_alt,U_1038)
& ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1039) ) )
& ti(arrow_490897120le_alt,U_1041) != ti(arrow_490897120le_alt,U_1039) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1038)),U_1040))
& ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039) )
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041) )
& ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1039) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1038),U_1041)),U_1040))
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1038)
| ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1039) ) )
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039) )
& ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1038)),U_1040))
| ti(arrow_490897120le_alt,U_1041) != ti(arrow_490897120le_alt,U_1039) )
& ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1041) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038))) ) )
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
( ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1041)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_4,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1038)),U_1040))
| ti(arrow_490897120le_alt,U_1041) != ti(arrow_490897120le_alt,U_1039)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_5,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1038),U_1041)),U_1040))
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1038)
| ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_7,plain,
( ti(arrow_490897120le_alt,U_1041) != ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_8,plain,
( ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_10,plain,
( ti(arrow_490897120le_alt,U_1041) != ti(arrow_490897120le_alt,U_1038)
| ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1038),U_1041)),U_1040))
| ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_12,plain,
( ti(arrow_490897120le_alt,U_1041) != ti(arrow_490897120le_alt,U_1038)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),U_1040))
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1038),U_1041)),U_1040))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),U_1040))
| ti(arrow_490897120le_alt,U_1041) = ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_14,plain,
( ti(arrow_490897120le_alt,U_1041) != ti(arrow_490897120le_alt,U_1039)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1038)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_15,plain,
( ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1039)
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1039)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1038)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_16,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1039)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1038)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_17,plain,
( ti(arrow_490897120le_alt,U_1041) != ti(arrow_490897120le_alt,U_1038)
| ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1039)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1038)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_18,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1038),U_1041)),U_1040))
| ti(arrow_490897120le_alt,U_1042) != ti(arrow_490897120le_alt,U_1039)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1038)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_19,plain,
( ti(arrow_490897120le_alt,U_1041) != ti(arrow_490897120le_alt,U_1038)
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),U_1040))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1038)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_20,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1038),U_1041)),U_1040))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),U_1040))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1038)),U_1040))
| ti(arrow_490897120le_alt,U_1042) = ti(arrow_490897120le_alt,U_1041)
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),U_1042),U_1041)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1040),U_1039),U_1038)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1040),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1039) = ti(arrow_490897120le_alt,U_1038) ),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_1,plain,
! [M_3,K_1,N_1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_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),M_3),K_1)),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_218_add__leE]) ).
fof(f_281_2,plain,
! [U_1045,U_1044,U_1043] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1044),U_1043))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1045),U_1043)) )
| ~ 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_1045),U_1044)),U_1043)) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1045),U_1043))
| ~ 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_1045),U_1044)),U_1043)) ),
inference(clausify,[status(thm)],[f_281_2]) ).
cnf(f_281_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1044),U_1043))
| ~ 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_1045),U_1044)),U_1043)) ),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_1,plain,
! [M_3,K_1,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_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),M_3),K_1)),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_219_add__leD1]) ).
fof(f_282_2,plain,
! [U_1048,U_1047,U_1046] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1048),U_1046))
| ~ 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_1048),U_1047)),U_1046)) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
cnf(f_282_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1048),U_1046))
| ~ 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_1048),U_1047)),U_1046)) ),
inference(clausify,[status(thm)],[f_282_2]) ).
fof(f_283_1,plain,
! [M_3,K_1,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_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),M_3),K_1)),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_220_add__leD2]) ).
fof(f_283_2,plain,
! [U_1051,U_1050,U_1049] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1050),U_1049))
| ~ 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_1051),U_1050)),U_1049)) ),
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_1050),U_1049))
| ~ 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_1051),U_1050)),U_1049)) ),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_1,plain,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)),
inference(fof_nnf,[status(thm)],[fact_221_less__not__refl]) ).
fof(f_284_2,plain,
! [U_1052] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1052),U_1052)),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1052),U_1052)),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_1,plain,
! [M_2,Na] :
( ( M_2 != Na
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| M_2 = Na ) ),
inference(fof_nnf,[status(thm)],[fact_222_nat__neq__iff]) ).
fof(f_285_2,plain,
! [U_1054,U_1053] :
( ( U_1054 != U_1053
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1053),U_1054))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1054),U_1053)) ) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1053),U_1054))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1054),U_1053))
| U_1054 = U_1053 ) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
( ! [U_1058,U_1056] :
( U_1058 != U_1056
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1056),U_1058))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1058),U_1056)) ) )
& ! [U_1057,U_1055] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1055),U_1057))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1057),U_1055))
| U_1057 = U_1055 ) ),
inference(miniscope,[status(thm)],[f_285_2]) ).
cnf(f_285_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1055),U_1057))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1057),U_1055))
| U_1057 = U_1055 ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_5,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1058),U_1056))
| U_1058 != U_1056 ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_6,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1056),U_1058))
| U_1058 != U_1056 ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_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_223_linorder__neqE__nat]) ).
fof(f_286_2,plain,
! [U_1060,U_1059] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1059),U_1060))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1060),U_1059))
| U_1060 = U_1059 ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
cnf(f_286_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1059),U_1060))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1060),U_1059))
| U_1060 = U_1059 ),
inference(clausify,[status(thm)],[f_286_2]) ).
fof(f_287_1,plain,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1)),
inference(fof_nnf,[status(thm)],[fact_224_less__irrefl__nat]) ).
fof(f_287_2,plain,
! [U_1061] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1061),U_1061)),
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1061),U_1061)),
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_1,plain,
! [N_1,M_3] :
( M_3 != N_1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_3)) ),
inference(fof_nnf,[status(thm)],[fact_225_less__not__refl2]) ).
fof(f_288_2,plain,
! [U_1063,U_1062] :
( U_1062 != U_1063
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1063),U_1062)) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
cnf(f_288_3,plain,
( U_1062 != U_1063
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1063),U_1062)) ),
inference(clausify,[status(thm)],[f_288_2]) ).
fof(f_289_1,plain,
! [S,T_3] :
( S != T_3
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) ),
inference(fof_nnf,[status(thm)],[fact_226_less__not__refl3]) ).
fof(f_289_2,plain,
! [U_1065,U_1064] :
( U_1065 != U_1064
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1065),U_1064)) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
( U_1065 != U_1064
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1065),U_1064)) ),
inference(clausify,[status(thm)],[f_289_2]) ).
fof(f_290_1,plain,
! [Pa,M_2,Na] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2)) )
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2))
& M_2 = Na )
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_2))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) ),
inference(fof_nnf,[status(thm)],[fact_227_nat__less__cases]) ).
fof(f_290_2,plain,
! [U_1068,U_1067,U_1066] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1066),U_1067)) )
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
& U_1067 = U_1066 )
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1067),U_1066)) ) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
cnf(f_290_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1066),U_1067))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| U_1067 = U_1066
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1067),U_1066)) ),
inference(clausify,[status(thm)],[f_290_2]) ).
cnf(f_290_4,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| U_1067 = U_1066
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1067),U_1066)) ),
inference(clausify,[status(thm)],[f_290_2]) ).
cnf(f_290_5,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1066),U_1067))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1067),U_1066)) ),
inference(clausify,[status(thm)],[f_290_2]) ).
cnf(f_290_6,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1067),U_1066)) ),
inference(clausify,[status(thm)],[f_290_2]) ).
cnf(f_290_7,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1066),U_1067))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| U_1067 = U_1066
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067)) ),
inference(clausify,[status(thm)],[f_290_2]) ).
cnf(f_290_8,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| U_1067 = U_1066
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067)) ),
inference(clausify,[status(thm)],[f_290_2]) ).
cnf(f_290_9,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1066),U_1067))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067)) ),
inference(clausify,[status(thm)],[f_290_2]) ).
cnf(f_290_10,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1068,U_1066),U_1067)) ),
inference(clausify,[status(thm)],[f_290_2]) ).
fof(f_291_1,plain,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_3),
inference(fof_nnf,[status(thm)],[fact_228_nat__add__commute]) ).
fof(f_291_2,plain,
! [U_1070,U_1069] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1070),U_1069) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1069),U_1070),
inference(variable_rename,[status(thm)],[f_291_1]) ).
cnf(f_291_3,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1070),U_1069) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1069),U_1070),
inference(clausify,[status(thm)],[f_291_2]) ).
fof(f_292_1,plain,
! [X,Y,Z_1] : 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_1)) = 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_1)),
inference(fof_nnf,[status(thm)],[fact_229_nat__add__left__commute]) ).
fof(f_292_2,plain,
! [U_1073,U_1072,U_1071] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1073),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1072),U_1071)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1072),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1073),U_1071)),
inference(variable_rename,[status(thm)],[f_292_1]) ).
cnf(f_292_3,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1073),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1072),U_1071)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1072),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1073),U_1071)),
inference(clausify,[status(thm)],[f_292_2]) ).
fof(f_293_1,plain,
! [M_3,N_1,K_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1)),K_1) = 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_1),K_1)),
inference(fof_nnf,[status(thm)],[fact_230_nat__add__assoc]) ).
fof(f_293_2,plain,
! [U_1076,U_1075,U_1074] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1076),U_1075)),U_1074) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1076),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1075),U_1074)),
inference(variable_rename,[status(thm)],[f_293_1]) ).
cnf(f_293_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_1076),U_1075)),U_1074) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1076),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1075),U_1074)),
inference(clausify,[status(thm)],[f_293_2]) ).
fof(f_294_1,plain,
! [K,M_2,Na] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na)
| M_2 != Na )
& ( M_2 = Na
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M_2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na) ) ),
inference(fof_nnf,[status(thm)],[fact_231_nat__add__left__cancel]) ).
fof(f_294_2,plain,
! [U_1079,U_1078,U_1077] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1079),U_1078) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1079),U_1077)
| U_1078 != U_1077 )
& ( U_1078 = U_1077
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1079),U_1078) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1079),U_1077) ) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
( ! [U_1085,U_1083,U_1081] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1085),U_1083) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1085),U_1081)
| U_1083 != U_1081 )
& ! [U_1084,U_1082,U_1080] :
( U_1082 = U_1080
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1084),U_1082) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1084),U_1080) ) ),
inference(miniscope,[status(thm)],[f_294_2]) ).
cnf(f_294_4,plain,
( U_1082 = U_1080
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1084),U_1082) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1084),U_1080) ),
inference(clausify,[status(thm)],[f_294_3]) ).
cnf(f_294_5,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1085),U_1083) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1085),U_1081)
| U_1083 != U_1081 ),
inference(clausify,[status(thm)],[f_294_3]) ).
fof(f_295_1,plain,
! [M_2,K,Na] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K)
| M_2 != Na )
& ( M_2 = Na
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K) ) ),
inference(fof_nnf,[status(thm)],[fact_232_nat__add__right__cancel]) ).
fof(f_295_2,plain,
! [U_1088,U_1087,U_1086] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1088),U_1087) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1086),U_1087)
| U_1088 != U_1086 )
& ( U_1088 = U_1086
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1088),U_1087) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1086),U_1087) ) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
( ! [U_1094,U_1092,U_1090] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1094),U_1092) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1090),U_1092)
| U_1094 != U_1090 )
& ! [U_1093,U_1091,U_1089] :
( U_1093 = 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_1089),U_1091) ) ),
inference(miniscope,[status(thm)],[f_295_2]) ).
cnf(f_295_4,plain,
( U_1093 = 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_1089),U_1091) ),
inference(clausify,[status(thm)],[f_295_3]) ).
cnf(f_295_5,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1094),U_1092) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1090),U_1092)
| U_1094 != U_1090 ),
inference(clausify,[status(thm)],[f_295_3]) ).
fof(f_296_1,plain,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1)),
inference(fof_nnf,[status(thm)],[fact_233_le__refl]) ).
fof(f_296_2,plain,
! [U_1095] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1095),U_1095)),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1095),U_1095)),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_234_nat__le__linear]) ).
fof(f_297_2,plain,
! [U_1097,U_1096] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1096),U_1097))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1097),U_1096)) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
cnf(f_297_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1096),U_1097))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1097),U_1096)) ),
inference(clausify,[status(thm)],[f_297_2]) ).
fof(f_298_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
| M_3 != N_1 ),
inference(fof_nnf,[status(thm)],[fact_235_eq__imp__le]) ).
fof(f_298_2,plain,
! [U_1099,U_1098] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1099),U_1098))
| U_1099 != U_1098 ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1099),U_1098))
| U_1099 != U_1098 ),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_1,plain,
! [K_1,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_236_le__trans]) ).
fof(f_299_2,plain,
! [U_1102,U_1101,U_1100] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1101),U_1102))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1100),U_1102))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1101),U_1100)) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1101),U_1102))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1100),U_1102))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1101),U_1100)) ),
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_1,plain,
! [M_3,N_1] :
( M_3 = N_1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_237_le__antisym]) ).
fof(f_300_2,plain,
! [U_1104,U_1103] :
( U_1104 = U_1103
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1103),U_1104))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1104),U_1103)) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
cnf(f_300_3,plain,
( U_1104 = U_1103
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1103),U_1104))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1104),U_1103)) ),
inference(clausify,[status(thm)],[f_300_2]) ).
fof(f_301_1,plain,
! [L_3,X_1,Y_2] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_3),X_1),Y_2)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_3),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Y_2) ),
inference(fof_nnf,[status(thm)],[fact_238_below__Lin]) ).
fof(f_301_2,plain,
! [U_1107,U_1106,U_1105] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1107),U_1106),U_1105)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1107),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1106) = ti(arrow_490897120le_alt,U_1105) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
cnf(f_301_3,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,U_1107),U_1106),U_1105)),arrow_2064824852le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1107),arrow_2064824852le_Lin))
| ti(arrow_490897120le_alt,U_1106) = ti(arrow_490897120le_alt,U_1105) ),
inference(clausify,[status(thm)],[f_301_2]) ).
fof(f_302_1,plain,
! [K,N_3] : 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_3)),
inference(fof_nnf,[status(thm)],[fact_239_inj__on__add__nat]) ).
fof(f_302_2,plain,
! [U_1109,U_1108] : 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_1109)),U_1108)),
inference(variable_rename,[status(thm)],[f_302_1]) ).
cnf(f_302_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_1109)),U_1108)),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_1,plain,
! [I,J_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),J_2)),I)),
inference(fof_nnf,[status(thm)],[fact_240_not__add__less1]) ).
fof(f_303_2,plain,
! [U_1111,U_1110] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1111),U_1110)),U_1111)),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_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_1111),U_1110)),U_1111)),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_1,plain,
! [J_2,I] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),I)),
inference(fof_nnf,[status(thm)],[fact_241_not__add__less2]) ).
fof(f_304_2,plain,
! [U_1113,U_1112] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1113),U_1112)),U_1112)),
inference(variable_rename,[status(thm)],[f_304_1]) ).
cnf(f_304_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_1113),U_1112)),U_1112)),
inference(clausify,[status(thm)],[f_304_2]) ).
fof(f_305_1,plain,
! [K,M_2,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_2)),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_2),Na)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),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_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na))) ) ),
inference(fof_nnf,[status(thm)],[fact_242_nat__add__left__cancel__less]) ).
fof(f_305_2,plain,
! [U_1116,U_1115,U_1114] :
( ( 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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1116),U_1114)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1115),U_1114)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1115),U_1114))
| ~ 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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1116),U_1114))) ) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
( ! [U_1122,U_1120,U_1118] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1122),U_1120)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1122),U_1118)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1120),U_1118)) )
& ! [U_1121,U_1119,U_1117] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1119),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_1121),U_1119)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),U_1117))) ) ),
inference(miniscope,[status(thm)],[f_305_2]) ).
cnf(f_305_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1119),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_1121),U_1119)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1121),U_1117))) ),
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_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_1122),U_1120)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1122),U_1118)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1120),U_1118)) ),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_1,plain,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M_3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_243_trans__less__add1]) ).
fof(f_306_2,plain,
! [U_1125,U_1124,U_1123] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1124),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1123),U_1125)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1124),U_1123)) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1124),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1123),U_1125)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1124),U_1123)) ),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_1,plain,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),J_2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_244_trans__less__add2]) ).
fof(f_307_2,plain,
! [U_1128,U_1127,U_1126] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1127),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1128),U_1126)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1127),U_1126)) ),
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_1127),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1128),U_1126)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1127),U_1126)) ),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_1,plain,
! [K_1,I,J_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),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_245_add__less__mono1]) ).
fof(f_308_2,plain,
! [U_1131,U_1130,U_1129] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1130),U_1131)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1129),U_1131)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1130),U_1129)) ),
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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1130),U_1131)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1129),U_1131)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1130),U_1129)) ),
inference(clausify,[status(thm)],[f_308_2]) ).
fof(f_309_1,plain,
! [K_1,L_2,I,J_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),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_246_add__less__mono]) ).
fof(f_309_2,plain,
! [U_1135,U_1134,U_1133,U_1132] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1133),U_1135)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),U_1134)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1135),U_1134))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1133),U_1132)) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
cnf(f_309_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_1133),U_1135)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),U_1134)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1135),U_1134))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1133),U_1132)) ),
inference(clausify,[status(thm)],[f_309_2]) ).
fof(f_310_1,plain,
! [M_3,N_1,K_1,L_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),L_2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_2)) ),
inference(fof_nnf,[status(thm)],[fact_247_less__add__eq__less]) ).
fof(f_310_2,plain,
! [U_1139,U_1138,U_1137,U_1136] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1139),U_1138))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1139),U_1136) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1137),U_1138)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1137),U_1136)) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
cnf(f_310_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1139),U_1138))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1139),U_1136) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1137),U_1138)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1137),U_1136)) ),
inference(clausify,[status(thm)],[f_310_2]) ).
fof(f_311_1,plain,
! [I,J_2,K_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_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),J_2)),K_1)) ),
inference(fof_nnf,[status(thm)],[fact_248_add__lessD1]) ).
fof(f_311_2,plain,
! [U_1142,U_1141,U_1140] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1142),U_1140))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1142),U_1141)),U_1140)) ),
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_1142),U_1140))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1142),U_1141)),U_1140)) ),
inference(clausify,[status(thm)],[f_311_2]) ).
fof(f_312_1,plain,
! [M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| M_2 = Na
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) )
& ( ( M_2 != Na
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) ),
inference(fof_nnf,[status(thm)],[fact_249_nat__less__le]) ).
fof(f_312_2,plain,
! [U_1144,U_1143] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1144),U_1143))
| U_1144 = U_1143
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1144),U_1143)) )
& ( ( U_1144 != U_1143
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1144),U_1143)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1144),U_1143)) ) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
( ! [U_1148,U_1146] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1148),U_1146))
| U_1148 = U_1146
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1148),U_1146)) )
& ! [U_1147,U_1145] :
( ( U_1147 != U_1145
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1147),U_1145)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1147),U_1145)) ) ),
inference(miniscope,[status(thm)],[f_312_2]) ).
cnf(f_312_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1147),U_1145))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1147),U_1145)) ),
inference(clausify,[status(thm)],[f_312_3]) ).
cnf(f_312_5,plain,
( U_1147 != U_1145
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1147),U_1145)) ),
inference(clausify,[status(thm)],[f_312_3]) ).
cnf(f_312_6,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1148),U_1146))
| U_1148 = U_1146
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1148),U_1146)) ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_1,plain,
! [M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
| ( M_2 != Na
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) )
& ( M_2 = Na
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) ) ),
inference(fof_nnf,[status(thm)],[fact_250_le__eq__less__or__eq]) ).
fof(f_313_2,plain,
! [U_1150,U_1149] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1150),U_1149))
| ( U_1150 != U_1149
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1150),U_1149)) ) )
& ( U_1150 = U_1149
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1150),U_1149))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1150),U_1149)) ) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
( ! [U_1154,U_1152] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1154),U_1152))
| ( U_1154 != U_1152
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1154),U_1152)) ) )
& ! [U_1153,U_1151] :
( U_1153 = U_1151
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1153),U_1151))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1153),U_1151)) ) ),
inference(miniscope,[status(thm)],[f_313_2]) ).
cnf(f_313_4,plain,
( U_1153 = U_1151
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),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_313_3]) ).
cnf(f_313_5,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1154),U_1152))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1154),U_1152)) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_6,plain,
( U_1154 != U_1152
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1154),U_1152)) ),
inference(clausify,[status(thm)],[f_313_3]) ).
fof(f_314_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_251_less__imp__le__nat]) ).
fof(f_314_2,plain,
! [U_1156,U_1155] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1156),U_1155))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1156),U_1155)) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
cnf(f_314_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1156),U_1155))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1156),U_1155)) ),
inference(clausify,[status(thm)],[f_314_2]) ).
fof(f_315_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
| M_3 = N_1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_252_le__neq__implies__less]) ).
fof(f_315_2,plain,
! [U_1158,U_1157] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1158),U_1157))
| U_1158 = U_1157
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1158),U_1157)) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
cnf(f_315_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1158),U_1157))
| U_1158 = U_1157
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1158),U_1157)) ),
inference(clausify,[status(thm)],[f_315_2]) ).
fof(f_316_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
| ( M_3 != N_1
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_253_less__or__eq__imp__le]) ).
fof(f_316_2,plain,
! [U_1160,U_1159] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1160),U_1159))
| ( U_1160 != U_1159
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1160),U_1159)) ) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
cnf(f_316_3,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1160),U_1159))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1160),U_1159)) ),
inference(clausify,[status(thm)],[f_316_2]) ).
cnf(f_316_4,plain,
( U_1160 != U_1159
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1160),U_1159)) ),
inference(clausify,[status(thm)],[f_316_2]) ).
fof(f_317_1,plain,
! [N_1,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1))),
inference(fof_nnf,[status(thm)],[fact_254_le__add2]) ).
fof(f_317_2,plain,
! [U_1162,U_1161] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1162),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1161),U_1162))),
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_1162),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1161),U_1162))),
inference(clausify,[status(thm)],[f_317_2]) ).
fof(f_318_1,plain,
! [N_1,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_3))),
inference(fof_nnf,[status(thm)],[fact_255_le__add1]) ).
fof(f_318_2,plain,
! [U_1164,U_1163] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1164),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1164),U_1163))),
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_1164),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1164),U_1163))),
inference(clausify,[status(thm)],[f_318_2]) ).
fof(f_319_1,plain,
! [M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
| ! [K_2] : Na != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_2) )
& ( ? [K_2] : Na = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) ) ),
inference(fof_nnf,[status(thm)],[fact_256_le__iff__add]) ).
fof(f_319_2,plain,
! [U_1168,U_1167] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1168),U_1167))
| ! [U_1166] : U_1167 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1168),U_1166) )
& ( ? [U_1165] : U_1167 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1168),U_1165)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1168),U_1167)) ) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
( ! [U_1172,U_1170] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1172),U_1170))
| ! [U_1166] : U_1170 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1172),U_1166) )
& ! [U_1171,U_1169] :
( ? [U_1165] : U_1169 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1171),U_1165)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1171),U_1169)) ) ),
inference(miniscope,[status(thm)],[f_319_2]) ).
fof(f_319_4,plain,
( ! [U_1172,U_1170] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1172),U_1170))
| ! [U_1166] : U_1170 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1172),U_1166) )
& ! [U_1171,U_1169] :
( U_1169 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1171),sK68(U_1171,U_1169))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1171),U_1169)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_1165,sK68(U_1171,U_1169))],[f_319_3]) ).
cnf(f_319_5,plain,
( U_1169 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1171),sK68(U_1171,U_1169))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1171),U_1169)) ),
inference(clausify,[status(thm)],[f_319_4]) ).
cnf(f_319_6,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1172),U_1170))
| U_1170 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1172),U_1166) ),
inference(clausify,[status(thm)],[f_319_4]) ).
fof(f_320_1,plain,
! [K,M_2,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_2)),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_2),Na)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),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_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na))) ) ),
inference(fof_nnf,[status(thm)],[fact_257_nat__add__left__cancel__le]) ).
fof(f_320_2,plain,
! [U_1175,U_1174,U_1173] :
( ( 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_1175),U_1174)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1175),U_1173)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1174),U_1173)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1174),U_1173))
| ~ 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_1175),U_1174)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1175),U_1173))) ) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
( ! [U_1181,U_1179,U_1177] :
( 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_1181),U_1179)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1181),U_1177)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1179),U_1177)) )
& ! [U_1180,U_1178,U_1176] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1178),U_1176))
| ~ 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_1178)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1180),U_1176))) ) ),
inference(miniscope,[status(thm)],[f_320_2]) ).
cnf(f_320_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1178),U_1176))
| ~ 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_1178)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1180),U_1176))) ),
inference(clausify,[status(thm)],[f_320_3]) ).
cnf(f_320_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_1181),U_1179)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1181),U_1177)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1179),U_1177)) ),
inference(clausify,[status(thm)],[f_320_3]) ).
fof(f_321_1,plain,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M_3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_258_trans__le__add1]) ).
fof(f_321_2,plain,
! [U_1184,U_1183,U_1182] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1183),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1182),U_1184)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1183),U_1182)) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
cnf(f_321_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1183),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1182),U_1184)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1183),U_1182)) ),
inference(clausify,[status(thm)],[f_321_2]) ).
fof(f_322_1,plain,
! [M_3,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),J_2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_259_trans__le__add2]) ).
fof(f_322_2,plain,
! [U_1187,U_1186,U_1185] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1186),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1187),U_1185)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1186),U_1185)) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
cnf(f_322_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1186),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1187),U_1185)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1186),U_1185)) ),
inference(clausify,[status(thm)],[f_322_2]) ).
fof(f_323_1,plain,
! [K_1,I,J_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),I),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_260_add__le__mono1]) ).
fof(f_323_2,plain,
! [U_1190,U_1189,U_1188] :
( 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_1189),U_1190)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1188),U_1190)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1189),U_1188)) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
cnf(f_323_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_1189),U_1190)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1188),U_1190)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1189),U_1188)) ),
inference(clausify,[status(thm)],[f_323_2]) ).
fof(f_324_1,plain,
! [K_1,L_2,I,J_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),I),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),L_2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_261_add__le__mono]) ).
fof(f_324_2,plain,
! [U_1194,U_1193,U_1192,U_1191] :
( 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_1192),U_1194)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1191),U_1193)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1194),U_1193))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1192),U_1191)) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
cnf(f_324_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_1192),U_1194)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1191),U_1193)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1194),U_1193))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1192),U_1191)) ),
inference(clausify,[status(thm)],[f_324_2]) ).
fof(f_325_1,plain,
! [M_2,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_2)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K))))
| ? [M,N] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M)),hAPP(nat,nat,F,N)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ) ),
inference(fof_nnf,[status(thm)],[fact_262_mono__nat__linear__lb]) ).
fof(f_325_2,plain,
! [U_1199,U_1198,U_1197] :
( 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_1197,U_1199)),U_1198)),hAPP(nat,nat,U_1197,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1199),U_1198))))
| ? [U_1196,U_1195] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1197,U_1196)),hAPP(nat,nat,U_1197,U_1195)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1196),U_1195)) ) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
! [U_1199,U_1198,U_1197] :
( 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_1197,U_1199)),U_1198)),hAPP(nat,nat,U_1197,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1199),U_1198))))
| ? [U_1195] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1197,sK69(U_1199,U_1198,U_1197))),hAPP(nat,nat,U_1197,U_1195)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK69(U_1199,U_1198,U_1197)),U_1195)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_1196,sK69(U_1199,U_1198,U_1197))],[f_325_2]) ).
fof(f_325_4,plain,
! [U_1199,U_1198,U_1197] :
( 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_1197,U_1199)),U_1198)),hAPP(nat,nat,U_1197,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1199),U_1198))))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1197,sK69(U_1199,U_1198,U_1197))),hAPP(nat,nat,U_1197,sK70(U_1199,U_1198,U_1197))))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK69(U_1199,U_1198,U_1197)),sK70(U_1199,U_1198,U_1197))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_1195,sK70(U_1199,U_1198,U_1197))],[f_325_3]) ).
cnf(f_325_5,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK69(U_1199,U_1198,U_1197)),sK70(U_1199,U_1198,U_1197)))
| 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_1197,U_1199)),U_1198)),hAPP(nat,nat,U_1197,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1199),U_1198)))) ),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_6,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1197,sK69(U_1199,U_1198,U_1197))),hAPP(nat,nat,U_1197,sK70(U_1199,U_1198,U_1197))))
| 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_1197,U_1199)),U_1198)),hAPP(nat,nat,U_1197,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1199),U_1198)))) ),
inference(clausify,[status(thm)],[f_325_4]) ).
fof(f_326_1,plain,
! [I_1,J_1,F] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1))
| ? [I_2,J] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) ) ),
inference(fof_nnf,[status(thm)],[fact_263_less__mono__imp__le__mono]) ).
fof(f_326_2,plain,
! [U_1204,U_1203,U_1202] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1202,U_1204)),hAPP(nat,nat,U_1202,U_1203)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1204),U_1203))
| ? [U_1201,U_1200] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1202,U_1201)),hAPP(nat,nat,U_1202,U_1200)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1201),U_1200)) ) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_1204,U_1203,U_1202] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1202,U_1204)),hAPP(nat,nat,U_1202,U_1203)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1204),U_1203))
| ? [U_1200] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1202,sK71(U_1204,U_1203,U_1202))),hAPP(nat,nat,U_1202,U_1200)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK71(U_1204,U_1203,U_1202)),U_1200)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_1201,sK71(U_1204,U_1203,U_1202))],[f_326_2]) ).
fof(f_326_4,plain,
! [U_1204,U_1203,U_1202] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1202,U_1204)),hAPP(nat,nat,U_1202,U_1203)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1204),U_1203))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1202,sK71(U_1204,U_1203,U_1202))),hAPP(nat,nat,U_1202,sK72(U_1204,U_1203,U_1202))))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK71(U_1204,U_1203,U_1202)),sK72(U_1204,U_1203,U_1202))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_1200,sK72(U_1204,U_1203,U_1202))],[f_326_3]) ).
cnf(f_326_5,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK71(U_1204,U_1203,U_1202)),sK72(U_1204,U_1203,U_1202)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1202,U_1204)),hAPP(nat,nat,U_1202,U_1203)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1204),U_1203)) ),
inference(clausify,[status(thm)],[f_326_4]) ).
cnf(f_326_6,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1202,sK71(U_1204,U_1203,U_1202))),hAPP(nat,nat,U_1202,sK72(U_1204,U_1203,U_1202))))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1202,U_1204)),hAPP(nat,nat,U_1202,U_1203)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1204),U_1203)) ),
inference(clausify,[status(thm)],[f_326_4]) ).
fof(f_327_1,plain,
! [Z_1,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_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) ),
inference(fof_nnf,[status(thm)],[fact_264_termination__basic__simps_I3_J]) ).
fof(f_327_2,plain,
! [U_1207,U_1206,U_1205] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1206),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1205),U_1207)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1206),U_1205)) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1206),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1205),U_1207)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1206),U_1205)) ),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_1,plain,
! [Y,X,Z_1] :
( 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_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z_1)) ),
inference(fof_nnf,[status(thm)],[fact_265_termination__basic__simps_I4_J]) ).
fof(f_328_2,plain,
! [U_1210,U_1209,U_1208] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1209),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1210),U_1208)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1209),U_1208)) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
cnf(f_328_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1209),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1210),U_1208)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1209),U_1208)) ),
inference(clausify,[status(thm)],[f_328_2]) ).
fof(f_329_1,plain,
! [Y,X,Z_1] :
( 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_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1)) ),
inference(fof_nnf,[status(thm)],[fact_266_termination__basic__simps_I2_J]) ).
fof(f_329_2,plain,
! [U_1213,U_1212,U_1211] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1212),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1213),U_1211)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1212),U_1211)) ),
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),U_1212),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1213),U_1211)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1212),U_1211)) ),
inference(clausify,[status(thm)],[f_329_2]) ).
fof(f_330_1,plain,
! [Z_1,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_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) ),
inference(fof_nnf,[status(thm)],[fact_267_termination__basic__simps_I1_J]) ).
fof(f_330_2,plain,
! [U_1216,U_1215,U_1214] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1215),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1214),U_1216)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1215),U_1214)) ),
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_1215),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1214),U_1216)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1215),U_1214)) ),
inference(clausify,[status(thm)],[f_330_2]) ).
fof(f_331_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_268_termination__basic__simps_I5_J]) ).
fof(f_331_2,plain,
! [U_1218,U_1217] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1218),U_1217))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1218),U_1217)) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
cnf(f_331_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1218),U_1217))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1218),U_1217)) ),
inference(clausify,[status(thm)],[f_331_2]) ).
fof(f_332_1,plain,
! [X_b,X_a,R_1,X_1,Y_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_1),X_1),Y_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),Y_2)),R_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_1),Y_2)),R_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_1),X_1),Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_269_in__rel__def]) ).
fof(f_332_2,plain,
! [U_1223,U_1222,U_1221,U_1220,U_1219] :
( ( hBOOL(hAPP(U_1223,bool,hAPP(U_1222,fun(U_1223,bool),hAPP(fun(product_prod(U_1222,U_1223),bool),fun(U_1222,fun(U_1223,bool)),in_rel(U_1222,U_1223),U_1221),U_1220),U_1219))
| ~ hBOOL(hAPP(fun(product_prod(U_1222,U_1223),bool),bool,hAPP(product_prod(U_1222,U_1223),fun(fun(product_prod(U_1222,U_1223),bool),bool),member(product_prod(U_1222,U_1223)),hAPP(U_1223,product_prod(U_1222,U_1223),hAPP(U_1222,fun(U_1223,product_prod(U_1222,U_1223)),product_Pair(U_1222,U_1223),U_1220),U_1219)),U_1221)) )
& ( hBOOL(hAPP(fun(product_prod(U_1222,U_1223),bool),bool,hAPP(product_prod(U_1222,U_1223),fun(fun(product_prod(U_1222,U_1223),bool),bool),member(product_prod(U_1222,U_1223)),hAPP(U_1223,product_prod(U_1222,U_1223),hAPP(U_1222,fun(U_1223,product_prod(U_1222,U_1223)),product_Pair(U_1222,U_1223),U_1220),U_1219)),U_1221))
| ~ hBOOL(hAPP(U_1223,bool,hAPP(U_1222,fun(U_1223,bool),hAPP(fun(product_prod(U_1222,U_1223),bool),fun(U_1222,fun(U_1223,bool)),in_rel(U_1222,U_1223),U_1221),U_1220),U_1219)) ) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
( ! [U_1233,U_1231,U_1229,U_1227,U_1225] :
( hBOOL(hAPP(U_1233,bool,hAPP(U_1231,fun(U_1233,bool),hAPP(fun(product_prod(U_1231,U_1233),bool),fun(U_1231,fun(U_1233,bool)),in_rel(U_1231,U_1233),U_1229),U_1227),U_1225))
| ~ hBOOL(hAPP(fun(product_prod(U_1231,U_1233),bool),bool,hAPP(product_prod(U_1231,U_1233),fun(fun(product_prod(U_1231,U_1233),bool),bool),member(product_prod(U_1231,U_1233)),hAPP(U_1233,product_prod(U_1231,U_1233),hAPP(U_1231,fun(U_1233,product_prod(U_1231,U_1233)),product_Pair(U_1231,U_1233),U_1227),U_1225)),U_1229)) )
& ! [U_1232,U_1230,U_1228,U_1226,U_1224] :
( hBOOL(hAPP(fun(product_prod(U_1230,U_1232),bool),bool,hAPP(product_prod(U_1230,U_1232),fun(fun(product_prod(U_1230,U_1232),bool),bool),member(product_prod(U_1230,U_1232)),hAPP(U_1232,product_prod(U_1230,U_1232),hAPP(U_1230,fun(U_1232,product_prod(U_1230,U_1232)),product_Pair(U_1230,U_1232),U_1226),U_1224)),U_1228))
| ~ hBOOL(hAPP(U_1232,bool,hAPP(U_1230,fun(U_1232,bool),hAPP(fun(product_prod(U_1230,U_1232),bool),fun(U_1230,fun(U_1232,bool)),in_rel(U_1230,U_1232),U_1228),U_1226),U_1224)) ) ),
inference(miniscope,[status(thm)],[f_332_2]) ).
cnf(f_332_4,plain,
( hBOOL(hAPP(fun(product_prod(U_1230,U_1232),bool),bool,hAPP(product_prod(U_1230,U_1232),fun(fun(product_prod(U_1230,U_1232),bool),bool),member(product_prod(U_1230,U_1232)),hAPP(U_1232,product_prod(U_1230,U_1232),hAPP(U_1230,fun(U_1232,product_prod(U_1230,U_1232)),product_Pair(U_1230,U_1232),U_1226),U_1224)),U_1228))
| ~ hBOOL(hAPP(U_1232,bool,hAPP(U_1230,fun(U_1232,bool),hAPP(fun(product_prod(U_1230,U_1232),bool),fun(U_1230,fun(U_1232,bool)),in_rel(U_1230,U_1232),U_1228),U_1226),U_1224)) ),
inference(clausify,[status(thm)],[f_332_3]) ).
cnf(f_332_5,plain,
( hBOOL(hAPP(U_1233,bool,hAPP(U_1231,fun(U_1233,bool),hAPP(fun(product_prod(U_1231,U_1233),bool),fun(U_1231,fun(U_1233,bool)),in_rel(U_1231,U_1233),U_1229),U_1227),U_1225))
| ~ hBOOL(hAPP(fun(product_prod(U_1231,U_1233),bool),bool,hAPP(product_prod(U_1231,U_1233),fun(fun(product_prod(U_1231,U_1233),bool),bool),member(product_prod(U_1231,U_1233)),hAPP(U_1233,product_prod(U_1231,U_1233),hAPP(U_1231,fun(U_1233,product_prod(U_1231,U_1233)),product_Pair(U_1231,U_1233),U_1227),U_1225)),U_1229)) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_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_2] :
( ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_270_funcsetI]) ).
fof(f_333_2,plain,
! [U_1239,U_1238,U_1237,U_1236,U_1235] :
( hBOOL(hAPP(fun(fun(U_1238,U_1239),bool),bool,hAPP(fun(U_1238,U_1239),fun(fun(fun(U_1238,U_1239),bool),bool),member(fun(U_1238,U_1239)),U_1237),hAPP(fun(U_1238,fun(U_1239,bool)),fun(fun(U_1238,U_1239),bool),hAPP(fun(U_1238,bool),fun(fun(U_1238,fun(U_1239,bool)),fun(fun(U_1238,U_1239),bool)),pi(U_1238,U_1239),U_1235),hAPP(fun(U_1239,bool),fun(U_1238,fun(U_1239,bool)),combk(fun(U_1239,bool),U_1238),U_1236))))
| ? [U_1234] :
( ~ hBOOL(hAPP(fun(U_1239,bool),bool,hAPP(U_1239,fun(fun(U_1239,bool),bool),member(U_1239),hAPP(U_1238,U_1239,U_1237,U_1234)),U_1236))
& hBOOL(hAPP(fun(U_1238,bool),bool,hAPP(U_1238,fun(fun(U_1238,bool),bool),member(U_1238),U_1234),U_1235)) ) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
! [U_1239,U_1238,U_1237,U_1236,U_1235] :
( hBOOL(hAPP(fun(fun(U_1238,U_1239),bool),bool,hAPP(fun(U_1238,U_1239),fun(fun(fun(U_1238,U_1239),bool),bool),member(fun(U_1238,U_1239)),U_1237),hAPP(fun(U_1238,fun(U_1239,bool)),fun(fun(U_1238,U_1239),bool),hAPP(fun(U_1238,bool),fun(fun(U_1238,fun(U_1239,bool)),fun(fun(U_1238,U_1239),bool)),pi(U_1238,U_1239),U_1235),hAPP(fun(U_1239,bool),fun(U_1238,fun(U_1239,bool)),combk(fun(U_1239,bool),U_1238),U_1236))))
| ( ~ hBOOL(hAPP(fun(U_1239,bool),bool,hAPP(U_1239,fun(fun(U_1239,bool),bool),member(U_1239),hAPP(U_1238,U_1239,U_1237,sK73(U_1239,U_1238,U_1237,U_1236,U_1235))),U_1236))
& hBOOL(hAPP(fun(U_1238,bool),bool,hAPP(U_1238,fun(fun(U_1238,bool),bool),member(U_1238),sK73(U_1239,U_1238,U_1237,U_1236,U_1235)),U_1235)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_1234,sK73(U_1239,U_1238,U_1237,U_1236,U_1235))],[f_333_2]) ).
cnf(f_333_4,plain,
( hBOOL(hAPP(fun(U_1238,bool),bool,hAPP(U_1238,fun(fun(U_1238,bool),bool),member(U_1238),sK73(U_1239,U_1238,U_1237,U_1236,U_1235)),U_1235))
| hBOOL(hAPP(fun(fun(U_1238,U_1239),bool),bool,hAPP(fun(U_1238,U_1239),fun(fun(fun(U_1238,U_1239),bool),bool),member(fun(U_1238,U_1239)),U_1237),hAPP(fun(U_1238,fun(U_1239,bool)),fun(fun(U_1238,U_1239),bool),hAPP(fun(U_1238,bool),fun(fun(U_1238,fun(U_1239,bool)),fun(fun(U_1238,U_1239),bool)),pi(U_1238,U_1239),U_1235),hAPP(fun(U_1239,bool),fun(U_1238,fun(U_1239,bool)),combk(fun(U_1239,bool),U_1238),U_1236)))) ),
inference(clausify,[status(thm)],[f_333_3]) ).
cnf(f_333_5,plain,
( ~ hBOOL(hAPP(fun(U_1239,bool),bool,hAPP(U_1239,fun(fun(U_1239,bool),bool),member(U_1239),hAPP(U_1238,U_1239,U_1237,sK73(U_1239,U_1238,U_1237,U_1236,U_1235))),U_1236))
| hBOOL(hAPP(fun(fun(U_1238,U_1239),bool),bool,hAPP(fun(U_1238,U_1239),fun(fun(fun(U_1238,U_1239),bool),bool),member(fun(U_1238,U_1239)),U_1237),hAPP(fun(U_1238,fun(U_1239,bool)),fun(fun(U_1238,U_1239),bool),hAPP(fun(U_1238,bool),fun(fun(U_1238,fun(U_1239,bool)),fun(fun(U_1238,U_1239),bool)),pi(U_1238,U_1239),U_1235),hAPP(fun(U_1239,bool),fun(U_1238,fun(U_1239,bool)),combk(fun(U_1239,bool),U_1238),U_1236)))) ),
inference(clausify,[status(thm)],[f_333_3]) ).
fof(f_334_1,plain,
? [L_1] : hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)),
inference(fof_nnf,[status(thm)],[fact_271_linear__alt]) ).
fof(f_334_2,plain,
? [U_1240] : hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),U_1240),arrow_2064824852le_Lin)),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sK74),arrow_2064824852le_Lin)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_1240,sK74)],[f_334_2]) ).
cnf(f_334_4,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sK74),arrow_2064824852le_Lin)),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_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] :
( hAPP(X_a,X_b,F,W) != hAPP(X_a,X_b,G,W)
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W),A_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_272_Pi__cong]) ).
fof(f_335_2,plain,
! [U_1247,U_1246,U_1245,U_1244,U_1243,U_1242] :
( ( ( hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1244),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| ~ hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1243),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245))) )
& ( hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1243),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| ~ hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1244),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245))) ) )
| ? [U_1241] :
( hAPP(U_1246,U_1247,U_1244,U_1241) != hAPP(U_1246,U_1247,U_1243,U_1241)
& hBOOL(hAPP(fun(U_1246,bool),bool,hAPP(U_1246,fun(fun(U_1246,bool),bool),member(U_1246),U_1241),U_1242)) ) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
! [U_1247,U_1246,U_1245,U_1244,U_1243,U_1242] :
( ( ( hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1244),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| ~ hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1243),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245))) )
& ( hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1243),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| ~ hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1244),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245))) ) )
| ( hAPP(U_1246,U_1247,U_1244,sK75(U_1247,U_1246,U_1245,U_1244,U_1243,U_1242)) != hAPP(U_1246,U_1247,U_1243,sK75(U_1247,U_1246,U_1245,U_1244,U_1243,U_1242))
& hBOOL(hAPP(fun(U_1246,bool),bool,hAPP(U_1246,fun(fun(U_1246,bool),bool),member(U_1246),sK75(U_1247,U_1246,U_1245,U_1244,U_1243,U_1242)),U_1242)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_1241,sK75(U_1247,U_1246,U_1245,U_1244,U_1243,U_1242))],[f_335_2]) ).
cnf(f_335_4,plain,
( hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1243),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| ~ hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1244),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| hBOOL(hAPP(fun(U_1246,bool),bool,hAPP(U_1246,fun(fun(U_1246,bool),bool),member(U_1246),sK75(U_1247,U_1246,U_1245,U_1244,U_1243,U_1242)),U_1242)) ),
inference(clausify,[status(thm)],[f_335_3]) ).
cnf(f_335_5,plain,
( hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1244),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| ~ hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1243),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| hBOOL(hAPP(fun(U_1246,bool),bool,hAPP(U_1246,fun(fun(U_1246,bool),bool),member(U_1246),sK75(U_1247,U_1246,U_1245,U_1244,U_1243,U_1242)),U_1242)) ),
inference(clausify,[status(thm)],[f_335_3]) ).
cnf(f_335_6,plain,
( hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1243),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| ~ hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1244),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| hAPP(U_1246,U_1247,U_1244,sK75(U_1247,U_1246,U_1245,U_1244,U_1243,U_1242)) != hAPP(U_1246,U_1247,U_1243,sK75(U_1247,U_1246,U_1245,U_1244,U_1243,U_1242)) ),
inference(clausify,[status(thm)],[f_335_3]) ).
cnf(f_335_7,plain,
( hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1244),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| ~ hBOOL(hAPP(fun(fun(U_1246,U_1247),bool),bool,hAPP(fun(U_1246,U_1247),fun(fun(fun(U_1246,U_1247),bool),bool),member(fun(U_1246,U_1247)),U_1243),hAPP(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool),hAPP(fun(U_1246,bool),fun(fun(U_1246,fun(U_1247,bool)),fun(fun(U_1246,U_1247),bool)),pi(U_1246,U_1247),U_1242),U_1245)))
| hAPP(U_1246,U_1247,U_1244,sK75(U_1247,U_1246,U_1245,U_1244,U_1243,U_1242)) != hAPP(U_1246,U_1247,U_1243,sK75(U_1247,U_1246,U_1245,U_1244,U_1243,U_1242)) ),
inference(clausify,[status(thm)],[f_335_3]) ).
fof(f_336_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_2] :
( ~ 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_273_Pi__I_H]) ).
fof(f_336_2,plain,
! [U_1253,U_1252,U_1251,U_1250,U_1249] :
( hBOOL(hAPP(fun(fun(U_1252,U_1253),bool),bool,hAPP(fun(U_1252,U_1253),fun(fun(fun(U_1252,U_1253),bool),bool),member(fun(U_1252,U_1253)),U_1251),hAPP(fun(U_1252,fun(U_1253,bool)),fun(fun(U_1252,U_1253),bool),hAPP(fun(U_1252,bool),fun(fun(U_1252,fun(U_1253,bool)),fun(fun(U_1252,U_1253),bool)),pi(U_1252,U_1253),U_1249),U_1250)))
| ? [U_1248] :
( ~ hBOOL(hAPP(fun(U_1253,bool),bool,hAPP(U_1253,fun(fun(U_1253,bool),bool),member(U_1253),hAPP(U_1252,U_1253,U_1251,U_1248)),hAPP(U_1252,fun(U_1253,bool),U_1250,U_1248)))
& hBOOL(hAPP(fun(U_1252,bool),bool,hAPP(U_1252,fun(fun(U_1252,bool),bool),member(U_1252),U_1248),U_1249)) ) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
! [U_1253,U_1252,U_1251,U_1250,U_1249] :
( hBOOL(hAPP(fun(fun(U_1252,U_1253),bool),bool,hAPP(fun(U_1252,U_1253),fun(fun(fun(U_1252,U_1253),bool),bool),member(fun(U_1252,U_1253)),U_1251),hAPP(fun(U_1252,fun(U_1253,bool)),fun(fun(U_1252,U_1253),bool),hAPP(fun(U_1252,bool),fun(fun(U_1252,fun(U_1253,bool)),fun(fun(U_1252,U_1253),bool)),pi(U_1252,U_1253),U_1249),U_1250)))
| ( ~ hBOOL(hAPP(fun(U_1253,bool),bool,hAPP(U_1253,fun(fun(U_1253,bool),bool),member(U_1253),hAPP(U_1252,U_1253,U_1251,sK76(U_1253,U_1252,U_1251,U_1250,U_1249))),hAPP(U_1252,fun(U_1253,bool),U_1250,sK76(U_1253,U_1252,U_1251,U_1250,U_1249))))
& hBOOL(hAPP(fun(U_1252,bool),bool,hAPP(U_1252,fun(fun(U_1252,bool),bool),member(U_1252),sK76(U_1253,U_1252,U_1251,U_1250,U_1249)),U_1249)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_1248,sK76(U_1253,U_1252,U_1251,U_1250,U_1249))],[f_336_2]) ).
cnf(f_336_4,plain,
( hBOOL(hAPP(fun(U_1252,bool),bool,hAPP(U_1252,fun(fun(U_1252,bool),bool),member(U_1252),sK76(U_1253,U_1252,U_1251,U_1250,U_1249)),U_1249))
| hBOOL(hAPP(fun(fun(U_1252,U_1253),bool),bool,hAPP(fun(U_1252,U_1253),fun(fun(fun(U_1252,U_1253),bool),bool),member(fun(U_1252,U_1253)),U_1251),hAPP(fun(U_1252,fun(U_1253,bool)),fun(fun(U_1252,U_1253),bool),hAPP(fun(U_1252,bool),fun(fun(U_1252,fun(U_1253,bool)),fun(fun(U_1252,U_1253),bool)),pi(U_1252,U_1253),U_1249),U_1250))) ),
inference(clausify,[status(thm)],[f_336_3]) ).
cnf(f_336_5,plain,
( ~ hBOOL(hAPP(fun(U_1253,bool),bool,hAPP(U_1253,fun(fun(U_1253,bool),bool),member(U_1253),hAPP(U_1252,U_1253,U_1251,sK76(U_1253,U_1252,U_1251,U_1250,U_1249))),hAPP(U_1252,fun(U_1253,bool),U_1250,sK76(U_1253,U_1252,U_1251,U_1250,U_1249))))
| hBOOL(hAPP(fun(fun(U_1252,U_1253),bool),bool,hAPP(fun(U_1252,U_1253),fun(fun(fun(U_1252,U_1253),bool),bool),member(fun(U_1252,U_1253)),U_1251),hAPP(fun(U_1252,fun(U_1253,bool)),fun(fun(U_1252,U_1253),bool),hAPP(fun(U_1252,bool),fun(fun(U_1252,fun(U_1253,bool)),fun(fun(U_1252,U_1253),bool)),pi(U_1252,U_1253),U_1249),U_1250))) ),
inference(clausify,[status(thm)],[f_336_3]) ).
fof(f_337_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_337_2,plain,
! [U_1258,U_1257,U_1256,U_1255,U_1254] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1258,bool),nat,finite_card(U_1258),U_1255)),hAPP(fun(U_1257,bool),nat,finite_card(U_1257),U_1254)))
| ~ hBOOL(hAPP(fun(U_1257,bool),bool,finite_finite_1(U_1257),U_1254))
| ~ hBOOL(hAPP(fun(U_1258,bool),bool,hAPP(fun(U_1258,U_1257),fun(fun(U_1258,bool),bool),inj_on(U_1258,U_1257),U_1256),U_1255))
| ~ hBOOL(hAPP(fun(fun(U_1258,U_1257),bool),bool,hAPP(fun(U_1258,U_1257),fun(fun(fun(U_1258,U_1257),bool),bool),member(fun(U_1258,U_1257)),U_1256),hAPP(fun(U_1258,fun(U_1257,bool)),fun(fun(U_1258,U_1257),bool),hAPP(fun(U_1258,bool),fun(fun(U_1258,fun(U_1257,bool)),fun(fun(U_1258,U_1257),bool)),pi(U_1258,U_1257),U_1255),hAPP(fun(U_1257,bool),fun(U_1258,fun(U_1257,bool)),combk(fun(U_1257,bool),U_1258),U_1254)))) ),
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),hAPP(fun(U_1258,bool),nat,finite_card(U_1258),U_1255)),hAPP(fun(U_1257,bool),nat,finite_card(U_1257),U_1254)))
| ~ hBOOL(hAPP(fun(U_1257,bool),bool,finite_finite_1(U_1257),U_1254))
| ~ hBOOL(hAPP(fun(U_1258,bool),bool,hAPP(fun(U_1258,U_1257),fun(fun(U_1258,bool),bool),inj_on(U_1258,U_1257),U_1256),U_1255))
| ~ hBOOL(hAPP(fun(fun(U_1258,U_1257),bool),bool,hAPP(fun(U_1258,U_1257),fun(fun(fun(U_1258,U_1257),bool),bool),member(fun(U_1258,U_1257)),U_1256),hAPP(fun(U_1258,fun(U_1257,bool)),fun(fun(U_1258,U_1257),bool),hAPP(fun(U_1258,bool),fun(fun(U_1258,fun(U_1257,bool)),fun(fun(U_1258,U_1257),bool)),pi(U_1258,U_1257),U_1255),hAPP(fun(U_1257,bool),fun(U_1258,fun(U_1257,bool)),combk(fun(U_1257,bool),U_1258),U_1254)))) ),
inference(clausify,[status(thm)],[f_337_2]) ).
fof(f_338_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_2,Y_3] :
( ti(X_a,X_2) != ti(X_a,Y_3)
& hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_3)
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_3),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_275_inj__onI]) ).
fof(f_338_2,plain,
! [U_1264,U_1263,U_1262,U_1261] :
( hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(fun(U_1263,U_1264),fun(fun(U_1263,bool),bool),inj_on(U_1263,U_1264),U_1262),U_1261))
| ? [U_1260,U_1259] :
( ti(U_1263,U_1260) != ti(U_1263,U_1259)
& hAPP(U_1263,U_1264,U_1262,U_1260) = hAPP(U_1263,U_1264,U_1262,U_1259)
& hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(U_1263,fun(fun(U_1263,bool),bool),member(U_1263),U_1259),U_1261))
& hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(U_1263,fun(fun(U_1263,bool),bool),member(U_1263),U_1260),U_1261)) ) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_1264,U_1263,U_1262,U_1261] :
( hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(fun(U_1263,U_1264),fun(fun(U_1263,bool),bool),inj_on(U_1263,U_1264),U_1262),U_1261))
| ? [U_1260] :
( ? [U_1259] :
( ti(U_1263,U_1260) != ti(U_1263,U_1259)
& hAPP(U_1263,U_1264,U_1262,U_1260) = hAPP(U_1263,U_1264,U_1262,U_1259)
& hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(U_1263,fun(fun(U_1263,bool),bool),member(U_1263),U_1259),U_1261)) )
& hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(U_1263,fun(fun(U_1263,bool),bool),member(U_1263),U_1260),U_1261)) ) ),
inference(miniscope,[status(thm)],[f_338_2]) ).
fof(f_338_4,plain,
! [U_1264,U_1263,U_1262,U_1261] :
( hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(fun(U_1263,U_1264),fun(fun(U_1263,bool),bool),inj_on(U_1263,U_1264),U_1262),U_1261))
| ( ? [U_1259] :
( ti(U_1263,sK77(U_1264,U_1263,U_1262,U_1261)) != ti(U_1263,U_1259)
& hAPP(U_1263,U_1264,U_1262,sK77(U_1264,U_1263,U_1262,U_1261)) = hAPP(U_1263,U_1264,U_1262,U_1259)
& hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(U_1263,fun(fun(U_1263,bool),bool),member(U_1263),U_1259),U_1261)) )
& hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(U_1263,fun(fun(U_1263,bool),bool),member(U_1263),sK77(U_1264,U_1263,U_1262,U_1261)),U_1261)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_1260,sK77(U_1264,U_1263,U_1262,U_1261))],[f_338_3]) ).
fof(f_338_5,plain,
! [U_1264,U_1263,U_1262,U_1261] :
( hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(fun(U_1263,U_1264),fun(fun(U_1263,bool),bool),inj_on(U_1263,U_1264),U_1262),U_1261))
| ( ti(U_1263,sK77(U_1264,U_1263,U_1262,U_1261)) != ti(U_1263,sK78(U_1264,U_1263,U_1262,U_1261))
& hAPP(U_1263,U_1264,U_1262,sK77(U_1264,U_1263,U_1262,U_1261)) = hAPP(U_1263,U_1264,U_1262,sK78(U_1264,U_1263,U_1262,U_1261))
& hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(U_1263,fun(fun(U_1263,bool),bool),member(U_1263),sK78(U_1264,U_1263,U_1262,U_1261)),U_1261))
& hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(U_1263,fun(fun(U_1263,bool),bool),member(U_1263),sK77(U_1264,U_1263,U_1262,U_1261)),U_1261)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_1259,sK78(U_1264,U_1263,U_1262,U_1261))],[f_338_4]) ).
cnf(f_338_6,plain,
( hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(U_1263,fun(fun(U_1263,bool),bool),member(U_1263),sK77(U_1264,U_1263,U_1262,U_1261)),U_1261))
| hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(fun(U_1263,U_1264),fun(fun(U_1263,bool),bool),inj_on(U_1263,U_1264),U_1262),U_1261)) ),
inference(clausify,[status(thm)],[f_338_5]) ).
cnf(f_338_7,plain,
( hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(U_1263,fun(fun(U_1263,bool),bool),member(U_1263),sK78(U_1264,U_1263,U_1262,U_1261)),U_1261))
| hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(fun(U_1263,U_1264),fun(fun(U_1263,bool),bool),inj_on(U_1263,U_1264),U_1262),U_1261)) ),
inference(clausify,[status(thm)],[f_338_5]) ).
cnf(f_338_8,plain,
( hAPP(U_1263,U_1264,U_1262,sK77(U_1264,U_1263,U_1262,U_1261)) = hAPP(U_1263,U_1264,U_1262,sK78(U_1264,U_1263,U_1262,U_1261))
| hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(fun(U_1263,U_1264),fun(fun(U_1263,bool),bool),inj_on(U_1263,U_1264),U_1262),U_1261)) ),
inference(clausify,[status(thm)],[f_338_5]) ).
cnf(f_338_9,plain,
( ti(U_1263,sK77(U_1264,U_1263,U_1262,U_1261)) != ti(U_1263,sK78(U_1264,U_1263,U_1262,U_1261))
| hBOOL(hAPP(fun(U_1263,bool),bool,hAPP(fun(U_1263,U_1264),fun(fun(U_1263,bool),bool),inj_on(U_1263,U_1264),U_1262),U_1261)) ),
inference(clausify,[status(thm)],[f_338_5]) ).
fof(f_339_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_3] :
( hAPP(X_a,X_b,F,A_3) != hAPP(X_a,X_b,G,A_3)
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_276_inj__on__cong]) ).
fof(f_339_2,plain,
! [U_1270,U_1269,U_1268,U_1267,U_1266] :
( ( ( hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1268),U_1266))
| ~ hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1267),U_1266)) )
& ( hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1267),U_1266))
| ~ hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1268),U_1266)) ) )
| ? [U_1265] :
( hAPP(U_1269,U_1270,U_1268,U_1265) != hAPP(U_1269,U_1270,U_1267,U_1265)
& hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(U_1269,fun(fun(U_1269,bool),bool),member(U_1269),U_1265),U_1266)) ) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
! [U_1270,U_1269,U_1268,U_1267,U_1266] :
( ( ( hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1268),U_1266))
| ~ hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1267),U_1266)) )
& ( hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1267),U_1266))
| ~ hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1268),U_1266)) ) )
| ( hAPP(U_1269,U_1270,U_1268,sK79(U_1270,U_1269,U_1268,U_1267,U_1266)) != hAPP(U_1269,U_1270,U_1267,sK79(U_1270,U_1269,U_1268,U_1267,U_1266))
& hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(U_1269,fun(fun(U_1269,bool),bool),member(U_1269),sK79(U_1270,U_1269,U_1268,U_1267,U_1266)),U_1266)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_1265,sK79(U_1270,U_1269,U_1268,U_1267,U_1266))],[f_339_2]) ).
cnf(f_339_4,plain,
( hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1267),U_1266))
| ~ hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1268),U_1266))
| hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(U_1269,fun(fun(U_1269,bool),bool),member(U_1269),sK79(U_1270,U_1269,U_1268,U_1267,U_1266)),U_1266)) ),
inference(clausify,[status(thm)],[f_339_3]) ).
cnf(f_339_5,plain,
( hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1268),U_1266))
| ~ hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1267),U_1266))
| hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(U_1269,fun(fun(U_1269,bool),bool),member(U_1269),sK79(U_1270,U_1269,U_1268,U_1267,U_1266)),U_1266)) ),
inference(clausify,[status(thm)],[f_339_3]) ).
cnf(f_339_6,plain,
( hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1267),U_1266))
| ~ hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1268),U_1266))
| hAPP(U_1269,U_1270,U_1268,sK79(U_1270,U_1269,U_1268,U_1267,U_1266)) != hAPP(U_1269,U_1270,U_1267,sK79(U_1270,U_1269,U_1268,U_1267,U_1266)) ),
inference(clausify,[status(thm)],[f_339_3]) ).
cnf(f_339_7,plain,
( hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1268),U_1266))
| ~ hBOOL(hAPP(fun(U_1269,bool),bool,hAPP(fun(U_1269,U_1270),fun(fun(U_1269,bool),bool),inj_on(U_1269,U_1270),U_1267),U_1266))
| hAPP(U_1269,U_1270,U_1268,sK79(U_1270,U_1269,U_1268,U_1267,U_1266)) != hAPP(U_1269,U_1270,U_1267,sK79(U_1270,U_1269,U_1268,U_1267,U_1266)) ),
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_1,plain,
hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
inference(fof_nnf,[status(thm)],[fact_277_finite__indi]) ).
cnf(f_340_2,plain,
hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
inference(clausify,[status(thm)],[f_340_1]) ).
fof(f_341_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_278_card__bij]) ).
fof(f_341_2,plain,
! [U_1276,U_1275,U_1274,U_1273,U_1272,U_1271] :
( hAPP(fun(U_1276,bool),nat,finite_card(U_1276),U_1272) = hAPP(fun(U_1275,bool),nat,finite_card(U_1275),U_1271)
| ~ hBOOL(hAPP(fun(U_1275,bool),bool,finite_finite_1(U_1275),U_1271))
| ~ hBOOL(hAPP(fun(U_1276,bool),bool,finite_finite_1(U_1276),U_1272))
| ~ hBOOL(hAPP(fun(U_1275,bool),bool,hAPP(fun(U_1275,U_1276),fun(fun(U_1275,bool),bool),inj_on(U_1275,U_1276),U_1274),U_1271))
| ~ hBOOL(hAPP(fun(fun(U_1275,U_1276),bool),bool,hAPP(fun(U_1275,U_1276),fun(fun(fun(U_1275,U_1276),bool),bool),member(fun(U_1275,U_1276)),U_1274),hAPP(fun(U_1275,fun(U_1276,bool)),fun(fun(U_1275,U_1276),bool),hAPP(fun(U_1275,bool),fun(fun(U_1275,fun(U_1276,bool)),fun(fun(U_1275,U_1276),bool)),pi(U_1275,U_1276),U_1271),hAPP(fun(U_1276,bool),fun(U_1275,fun(U_1276,bool)),combk(fun(U_1276,bool),U_1275),U_1272))))
| ~ hBOOL(hAPP(fun(U_1276,bool),bool,hAPP(fun(U_1276,U_1275),fun(fun(U_1276,bool),bool),inj_on(U_1276,U_1275),U_1273),U_1272))
| ~ hBOOL(hAPP(fun(fun(U_1276,U_1275),bool),bool,hAPP(fun(U_1276,U_1275),fun(fun(fun(U_1276,U_1275),bool),bool),member(fun(U_1276,U_1275)),U_1273),hAPP(fun(U_1276,fun(U_1275,bool)),fun(fun(U_1276,U_1275),bool),hAPP(fun(U_1276,bool),fun(fun(U_1276,fun(U_1275,bool)),fun(fun(U_1276,U_1275),bool)),pi(U_1276,U_1275),U_1272),hAPP(fun(U_1275,bool),fun(U_1276,fun(U_1275,bool)),combk(fun(U_1275,bool),U_1276),U_1271)))) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
cnf(f_341_3,plain,
( hAPP(fun(U_1276,bool),nat,finite_card(U_1276),U_1272) = hAPP(fun(U_1275,bool),nat,finite_card(U_1275),U_1271)
| ~ hBOOL(hAPP(fun(U_1275,bool),bool,finite_finite_1(U_1275),U_1271))
| ~ hBOOL(hAPP(fun(U_1276,bool),bool,finite_finite_1(U_1276),U_1272))
| ~ hBOOL(hAPP(fun(U_1275,bool),bool,hAPP(fun(U_1275,U_1276),fun(fun(U_1275,bool),bool),inj_on(U_1275,U_1276),U_1274),U_1271))
| ~ hBOOL(hAPP(fun(fun(U_1275,U_1276),bool),bool,hAPP(fun(U_1275,U_1276),fun(fun(fun(U_1275,U_1276),bool),bool),member(fun(U_1275,U_1276)),U_1274),hAPP(fun(U_1275,fun(U_1276,bool)),fun(fun(U_1275,U_1276),bool),hAPP(fun(U_1275,bool),fun(fun(U_1275,fun(U_1276,bool)),fun(fun(U_1275,U_1276),bool)),pi(U_1275,U_1276),U_1271),hAPP(fun(U_1276,bool),fun(U_1275,fun(U_1276,bool)),combk(fun(U_1276,bool),U_1275),U_1272))))
| ~ hBOOL(hAPP(fun(U_1276,bool),bool,hAPP(fun(U_1276,U_1275),fun(fun(U_1276,bool),bool),inj_on(U_1276,U_1275),U_1273),U_1272))
| ~ hBOOL(hAPP(fun(fun(U_1276,U_1275),bool),bool,hAPP(fun(U_1276,U_1275),fun(fun(fun(U_1276,U_1275),bool),bool),member(fun(U_1276,U_1275)),U_1273),hAPP(fun(U_1276,fun(U_1275,bool)),fun(fun(U_1276,U_1275),bool),hAPP(fun(U_1276,bool),fun(fun(U_1276,fun(U_1275,bool)),fun(fun(U_1276,U_1275),bool)),pi(U_1276,U_1275),U_1272),hAPP(fun(U_1275,bool),fun(U_1276,fun(U_1275,bool)),combk(fun(U_1275,bool),U_1276),U_1271)))) ),
inference(clausify,[status(thm)],[f_341_2]) ).
fof(f_342_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_279_finite__Collect__subsets]) ).
fof(f_342_2,plain,
! [U_1278,U_1277] :
( hBOOL(hAPP(fun(fun(U_1278,bool),bool),bool,finite_finite_1(fun(U_1278,bool)),hAPP(fun(fun(U_1278,bool),bool),fun(fun(U_1278,bool),bool),collect(fun(U_1278,bool)),hAPP(fun(U_1278,bool),fun(fun(U_1278,bool),bool),hAPP(fun(fun(U_1278,bool),fun(fun(U_1278,bool),bool)),fun(fun(U_1278,bool),fun(fun(U_1278,bool),bool)),combc(fun(U_1278,bool),fun(U_1278,bool),bool),ord_less_eq(fun(U_1278,bool))),U_1277))))
| ~ hBOOL(hAPP(fun(U_1278,bool),bool,finite_finite_1(U_1278),U_1277)) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
cnf(f_342_3,plain,
( hBOOL(hAPP(fun(fun(U_1278,bool),bool),bool,finite_finite_1(fun(U_1278,bool)),hAPP(fun(fun(U_1278,bool),bool),fun(fun(U_1278,bool),bool),collect(fun(U_1278,bool)),hAPP(fun(U_1278,bool),fun(fun(U_1278,bool),bool),hAPP(fun(fun(U_1278,bool),fun(fun(U_1278,bool),bool)),fun(fun(U_1278,bool),fun(fun(U_1278,bool),bool)),combc(fun(U_1278,bool),fun(U_1278,bool),bool),ord_less_eq(fun(U_1278,bool))),U_1277))))
| ~ hBOOL(hAPP(fun(U_1278,bool),bool,finite_finite_1(U_1278),U_1277)) ),
inference(clausify,[status(thm)],[f_342_2]) ).
fof(f_343_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_280_card__psubset]) ).
fof(f_343_2,plain,
! [U_1281,U_1280,U_1279] :
( hBOOL(hAPP(fun(U_1281,bool),bool,hAPP(fun(U_1281,bool),fun(fun(U_1281,bool),bool),ord_less(fun(U_1281,bool)),U_1280),U_1279))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1281,bool),nat,finite_card(U_1281),U_1280)),hAPP(fun(U_1281,bool),nat,finite_card(U_1281),U_1279)))
| ~ hBOOL(hAPP(fun(U_1281,bool),bool,hAPP(fun(U_1281,bool),fun(fun(U_1281,bool),bool),ord_less_eq(fun(U_1281,bool)),U_1280),U_1279))
| ~ hBOOL(hAPP(fun(U_1281,bool),bool,finite_finite_1(U_1281),U_1279)) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
cnf(f_343_3,plain,
( hBOOL(hAPP(fun(U_1281,bool),bool,hAPP(fun(U_1281,bool),fun(fun(U_1281,bool),bool),ord_less(fun(U_1281,bool)),U_1280),U_1279))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1281,bool),nat,finite_card(U_1281),U_1280)),hAPP(fun(U_1281,bool),nat,finite_card(U_1281),U_1279)))
| ~ hBOOL(hAPP(fun(U_1281,bool),bool,hAPP(fun(U_1281,bool),fun(fun(U_1281,bool),bool),ord_less_eq(fun(U_1281,bool)),U_1280),U_1279))
| ~ hBOOL(hAPP(fun(U_1281,bool),bool,finite_finite_1(U_1281),U_1279)) ),
inference(clausify,[status(thm)],[f_343_2]) ).
fof(f_344_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_281_psubset__card__mono]) ).
fof(f_344_2,plain,
! [U_1284,U_1283,U_1282] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1284,bool),nat,finite_card(U_1284),U_1283)),hAPP(fun(U_1284,bool),nat,finite_card(U_1284),U_1282)))
| ~ hBOOL(hAPP(fun(U_1284,bool),bool,hAPP(fun(U_1284,bool),fun(fun(U_1284,bool),bool),ord_less(fun(U_1284,bool)),U_1283),U_1282))
| ~ hBOOL(hAPP(fun(U_1284,bool),bool,finite_finite_1(U_1284),U_1282)) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
cnf(f_344_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1284,bool),nat,finite_card(U_1284),U_1283)),hAPP(fun(U_1284,bool),nat,finite_card(U_1284),U_1282)))
| ~ hBOOL(hAPP(fun(U_1284,bool),bool,hAPP(fun(U_1284,bool),fun(fun(U_1284,bool),bool),ord_less(fun(U_1284,bool)),U_1283),U_1282))
| ~ hBOOL(hAPP(fun(U_1284,bool),bool,finite_finite_1(U_1284),U_1282)) ),
inference(clausify,[status(thm)],[f_344_2]) ).
fof(f_345_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_345_2,plain,
! [U_1287,U_1286,U_1285] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1287,bool),nat,finite_card(U_1287),U_1286)),hAPP(fun(U_1287,bool),nat,finite_card(U_1287),U_1285)))
| ~ hBOOL(hAPP(fun(U_1287,bool),bool,hAPP(fun(U_1287,bool),fun(fun(U_1287,bool),bool),ord_less_eq(fun(U_1287,bool)),U_1286),U_1285))
| ~ hBOOL(hAPP(fun(U_1287,bool),bool,finite_finite_1(U_1287),U_1285)) ),
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),hAPP(fun(U_1287,bool),nat,finite_card(U_1287),U_1286)),hAPP(fun(U_1287,bool),nat,finite_card(U_1287),U_1285)))
| ~ hBOOL(hAPP(fun(U_1287,bool),bool,hAPP(fun(U_1287,bool),fun(fun(U_1287,bool),bool),ord_less_eq(fun(U_1287,bool)),U_1286),U_1285))
| ~ hBOOL(hAPP(fun(U_1287,bool),bool,finite_finite_1(U_1287),U_1285)) ),
inference(clausify,[status(thm)],[f_345_2]) ).
fof(f_346_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_283_finite__Collect__conjI]) ).
fof(f_346_2,plain,
! [U_1290,U_1289,U_1288] :
( hBOOL(hAPP(fun(U_1290,bool),bool,finite_finite_1(U_1290),hAPP(fun(U_1290,bool),fun(U_1290,bool),collect(U_1290),hAPP(fun(U_1290,bool),fun(U_1290,bool),hAPP(fun(U_1290,fun(bool,bool)),fun(fun(U_1290,bool),fun(U_1290,bool)),combs(U_1290,bool,bool),hAPP(fun(U_1290,bool),fun(U_1290,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1290,bool),fun(U_1290,fun(bool,bool))),combb(bool,fun(bool,bool),U_1290),fconj),U_1288)),U_1289))))
| ( ~ hBOOL(hAPP(fun(U_1290,bool),bool,finite_finite_1(U_1290),hAPP(fun(U_1290,bool),fun(U_1290,bool),collect(U_1290),U_1289)))
& ~ hBOOL(hAPP(fun(U_1290,bool),bool,finite_finite_1(U_1290),hAPP(fun(U_1290,bool),fun(U_1290,bool),collect(U_1290),U_1288))) ) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
cnf(f_346_3,plain,
( ~ hBOOL(hAPP(fun(U_1290,bool),bool,finite_finite_1(U_1290),hAPP(fun(U_1290,bool),fun(U_1290,bool),collect(U_1290),U_1288)))
| hBOOL(hAPP(fun(U_1290,bool),bool,finite_finite_1(U_1290),hAPP(fun(U_1290,bool),fun(U_1290,bool),collect(U_1290),hAPP(fun(U_1290,bool),fun(U_1290,bool),hAPP(fun(U_1290,fun(bool,bool)),fun(fun(U_1290,bool),fun(U_1290,bool)),combs(U_1290,bool,bool),hAPP(fun(U_1290,bool),fun(U_1290,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1290,bool),fun(U_1290,fun(bool,bool))),combb(bool,fun(bool,bool),U_1290),fconj),U_1288)),U_1289)))) ),
inference(clausify,[status(thm)],[f_346_2]) ).
cnf(f_346_4,plain,
( ~ hBOOL(hAPP(fun(U_1290,bool),bool,finite_finite_1(U_1290),hAPP(fun(U_1290,bool),fun(U_1290,bool),collect(U_1290),U_1289)))
| hBOOL(hAPP(fun(U_1290,bool),bool,finite_finite_1(U_1290),hAPP(fun(U_1290,bool),fun(U_1290,bool),collect(U_1290),hAPP(fun(U_1290,bool),fun(U_1290,bool),hAPP(fun(U_1290,fun(bool,bool)),fun(fun(U_1290,bool),fun(U_1290,bool)),combs(U_1290,bool,bool),hAPP(fun(U_1290,bool),fun(U_1290,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1290,bool),fun(U_1290,fun(bool,bool))),combb(bool,fun(bool,bool),U_1290),fconj),U_1288)),U_1289)))) ),
inference(clausify,[status(thm)],[f_346_2]) ).
fof(f_347_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_284_finite__Collect__less__nat]) ).
fof(f_347_2,plain,
! [U_1291] : 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_1291)))),
inference(variable_rename,[status(thm)],[f_347_1]) ).
cnf(f_347_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_1291)))),
inference(clausify,[status(thm)],[f_347_2]) ).
fof(f_348_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_285_finite__Collect__le__nat]) ).
fof(f_348_2,plain,
! [U_1292] : 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_1292)))),
inference(variable_rename,[status(thm)],[f_348_1]) ).
cnf(f_348_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_1292)))),
inference(clausify,[status(thm)],[f_348_2]) ).
fof(f_349_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_286_finite]) ).
fof(f_349_2,plain,
! [U_1294] :
( ! [U_1293] : hBOOL(hAPP(fun(U_1294,bool),bool,finite_finite_1(U_1294),U_1293))
| ~ finite_finite(U_1294) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
cnf(f_349_3,plain,
( hBOOL(hAPP(fun(U_1294,bool),bool,finite_finite_1(U_1294),U_1293))
| ~ finite_finite(U_1294) ),
inference(clausify,[status(thm)],[f_349_2]) ).
fof(f_350_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_350_2,plain,
! [U_1296] :
( ! [U_1295] : hBOOL(hAPP(fun(U_1296,bool),bool,finite_finite_1(U_1296),U_1295))
| ~ finite_finite(U_1296) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
cnf(f_350_3,plain,
( hBOOL(hAPP(fun(U_1296,bool),bool,finite_finite_1(U_1296),U_1295))
| ~ finite_finite(U_1296) ),
inference(clausify,[status(thm)],[f_350_2]) ).
fof(f_351_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_288_card__UNIV__unit]) ).
cnf(f_351_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_351_1]) ).
fof(f_352_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_289_finite__Collect__disjI]) ).
fof(f_352_2,plain,
! [U_1299,U_1298,U_1297] :
( ( hBOOL(hAPP(fun(U_1299,bool),bool,finite_finite_1(U_1299),hAPP(fun(U_1299,bool),fun(U_1299,bool),collect(U_1299),hAPP(fun(U_1299,bool),fun(U_1299,bool),hAPP(fun(U_1299,fun(bool,bool)),fun(fun(U_1299,bool),fun(U_1299,bool)),combs(U_1299,bool,bool),hAPP(fun(U_1299,bool),fun(U_1299,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1299,bool),fun(U_1299,fun(bool,bool))),combb(bool,fun(bool,bool),U_1299),fdisj),U_1298)),U_1297))))
| ~ hBOOL(hAPP(fun(U_1299,bool),bool,finite_finite_1(U_1299),hAPP(fun(U_1299,bool),fun(U_1299,bool),collect(U_1299),U_1297)))
| ~ hBOOL(hAPP(fun(U_1299,bool),bool,finite_finite_1(U_1299),hAPP(fun(U_1299,bool),fun(U_1299,bool),collect(U_1299),U_1298))) )
& ( ( hBOOL(hAPP(fun(U_1299,bool),bool,finite_finite_1(U_1299),hAPP(fun(U_1299,bool),fun(U_1299,bool),collect(U_1299),U_1297)))
& hBOOL(hAPP(fun(U_1299,bool),bool,finite_finite_1(U_1299),hAPP(fun(U_1299,bool),fun(U_1299,bool),collect(U_1299),U_1298))) )
| ~ hBOOL(hAPP(fun(U_1299,bool),bool,finite_finite_1(U_1299),hAPP(fun(U_1299,bool),fun(U_1299,bool),collect(U_1299),hAPP(fun(U_1299,bool),fun(U_1299,bool),hAPP(fun(U_1299,fun(bool,bool)),fun(fun(U_1299,bool),fun(U_1299,bool)),combs(U_1299,bool,bool),hAPP(fun(U_1299,bool),fun(U_1299,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1299,bool),fun(U_1299,fun(bool,bool))),combb(bool,fun(bool,bool),U_1299),fdisj),U_1298)),U_1297)))) ) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
( ! [U_1305,U_1303,U_1301] :
( hBOOL(hAPP(fun(U_1305,bool),bool,finite_finite_1(U_1305),hAPP(fun(U_1305,bool),fun(U_1305,bool),collect(U_1305),hAPP(fun(U_1305,bool),fun(U_1305,bool),hAPP(fun(U_1305,fun(bool,bool)),fun(fun(U_1305,bool),fun(U_1305,bool)),combs(U_1305,bool,bool),hAPP(fun(U_1305,bool),fun(U_1305,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1305,bool),fun(U_1305,fun(bool,bool))),combb(bool,fun(bool,bool),U_1305),fdisj),U_1303)),U_1301))))
| ~ hBOOL(hAPP(fun(U_1305,bool),bool,finite_finite_1(U_1305),hAPP(fun(U_1305,bool),fun(U_1305,bool),collect(U_1305),U_1301)))
| ~ hBOOL(hAPP(fun(U_1305,bool),bool,finite_finite_1(U_1305),hAPP(fun(U_1305,bool),fun(U_1305,bool),collect(U_1305),U_1303))) )
& ! [U_1304,U_1302,U_1300] :
( ( hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite_1(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),collect(U_1304),U_1300)))
& hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite_1(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),collect(U_1304),U_1302))) )
| ~ hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite_1(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),collect(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),hAPP(fun(U_1304,fun(bool,bool)),fun(fun(U_1304,bool),fun(U_1304,bool)),combs(U_1304,bool,bool),hAPP(fun(U_1304,bool),fun(U_1304,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1304,bool),fun(U_1304,fun(bool,bool))),combb(bool,fun(bool,bool),U_1304),fdisj),U_1302)),U_1300)))) ) ),
inference(miniscope,[status(thm)],[f_352_2]) ).
cnf(f_352_4,plain,
( hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite_1(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),collect(U_1304),U_1302)))
| ~ hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite_1(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),collect(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),hAPP(fun(U_1304,fun(bool,bool)),fun(fun(U_1304,bool),fun(U_1304,bool)),combs(U_1304,bool,bool),hAPP(fun(U_1304,bool),fun(U_1304,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1304,bool),fun(U_1304,fun(bool,bool))),combb(bool,fun(bool,bool),U_1304),fdisj),U_1302)),U_1300)))) ),
inference(clausify,[status(thm)],[f_352_3]) ).
cnf(f_352_5,plain,
( hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite_1(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),collect(U_1304),U_1300)))
| ~ hBOOL(hAPP(fun(U_1304,bool),bool,finite_finite_1(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),collect(U_1304),hAPP(fun(U_1304,bool),fun(U_1304,bool),hAPP(fun(U_1304,fun(bool,bool)),fun(fun(U_1304,bool),fun(U_1304,bool)),combs(U_1304,bool,bool),hAPP(fun(U_1304,bool),fun(U_1304,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1304,bool),fun(U_1304,fun(bool,bool))),combb(bool,fun(bool,bool),U_1304),fdisj),U_1302)),U_1300)))) ),
inference(clausify,[status(thm)],[f_352_3]) ).
cnf(f_352_6,plain,
( hBOOL(hAPP(fun(U_1305,bool),bool,finite_finite_1(U_1305),hAPP(fun(U_1305,bool),fun(U_1305,bool),collect(U_1305),hAPP(fun(U_1305,bool),fun(U_1305,bool),hAPP(fun(U_1305,fun(bool,bool)),fun(fun(U_1305,bool),fun(U_1305,bool)),combs(U_1305,bool,bool),hAPP(fun(U_1305,bool),fun(U_1305,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1305,bool),fun(U_1305,fun(bool,bool))),combb(bool,fun(bool,bool),U_1305),fdisj),U_1303)),U_1301))))
| ~ hBOOL(hAPP(fun(U_1305,bool),bool,finite_finite_1(U_1305),hAPP(fun(U_1305,bool),fun(U_1305,bool),collect(U_1305),U_1301)))
| ~ hBOOL(hAPP(fun(U_1305,bool),bool,finite_finite_1(U_1305),hAPP(fun(U_1305,bool),fun(U_1305,bool),collect(U_1305),U_1303))) ),
inference(clausify,[status(thm)],[f_352_3]) ).
fof(f_353_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_290_card__Collect__less__nat]) ).
fof(f_353_2,plain,
! [U_1306] : 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_1306))) = U_1306,
inference(variable_rename,[status(thm)],[f_353_1]) ).
cnf(f_353_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_1306))) = U_1306,
inference(clausify,[status(thm)],[f_353_2]) ).
fof(f_354_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_291_finite__subset]) ).
fof(f_354_2,plain,
! [U_1309,U_1308,U_1307] :
( hBOOL(hAPP(fun(U_1309,bool),bool,finite_finite_1(U_1309),U_1308))
| ~ hBOOL(hAPP(fun(U_1309,bool),bool,finite_finite_1(U_1309),U_1307))
| ~ hBOOL(hAPP(fun(U_1309,bool),bool,hAPP(fun(U_1309,bool),fun(fun(U_1309,bool),bool),ord_less_eq(fun(U_1309,bool)),U_1308),U_1307)) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
cnf(f_354_3,plain,
( hBOOL(hAPP(fun(U_1309,bool),bool,finite_finite_1(U_1309),U_1308))
| ~ hBOOL(hAPP(fun(U_1309,bool),bool,finite_finite_1(U_1309),U_1307))
| ~ hBOOL(hAPP(fun(U_1309,bool),bool,hAPP(fun(U_1309,bool),fun(fun(U_1309,bool),bool),ord_less_eq(fun(U_1309,bool)),U_1308),U_1307)) ),
inference(clausify,[status(thm)],[f_354_2]) ).
fof(f_355_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_355_2,plain,
! [U_1312,U_1311,U_1310] :
( hBOOL(hAPP(fun(U_1312,bool),bool,finite_finite_1(U_1312),U_1311))
| ~ hBOOL(hAPP(fun(U_1312,bool),bool,hAPP(fun(U_1312,bool),fun(fun(U_1312,bool),bool),ord_less_eq(fun(U_1312,bool)),U_1311),U_1310))
| ~ hBOOL(hAPP(fun(U_1312,bool),bool,finite_finite_1(U_1312),U_1310)) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
cnf(f_355_3,plain,
( hBOOL(hAPP(fun(U_1312,bool),bool,finite_finite_1(U_1312),U_1311))
| ~ hBOOL(hAPP(fun(U_1312,bool),bool,hAPP(fun(U_1312,bool),fun(fun(U_1312,bool),bool),ord_less_eq(fun(U_1312,bool)),U_1311),U_1310))
| ~ hBOOL(hAPP(fun(U_1312,bool),bool,finite_finite_1(U_1312),U_1310)) ),
inference(clausify,[status(thm)],[f_355_2]) ).
fof(f_356_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_293_finite__UNIV]) ).
fof(f_356_2,plain,
! [U_1313] :
( hBOOL(hAPP(fun(U_1313,bool),bool,finite_finite_1(U_1313),top_top(fun(U_1313,bool))))
| ~ finite_finite(U_1313) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
cnf(f_356_3,plain,
( hBOOL(hAPP(fun(U_1313,bool),bool,finite_finite_1(U_1313),top_top(fun(U_1313,bool))))
| ~ finite_finite(U_1313) ),
inference(clausify,[status(thm)],[f_356_2]) ).
fof(f_357_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_294_finite__Prod__UNIV]) ).
fof(f_357_2,plain,
! [U_1315,U_1314] :
( hBOOL(hAPP(fun(product_prod(U_1314,U_1315),bool),bool,finite_finite_1(product_prod(U_1314,U_1315)),top_top(fun(product_prod(U_1314,U_1315),bool))))
| ~ hBOOL(hAPP(fun(U_1315,bool),bool,finite_finite_1(U_1315),top_top(fun(U_1315,bool))))
| ~ hBOOL(hAPP(fun(U_1314,bool),bool,finite_finite_1(U_1314),top_top(fun(U_1314,bool)))) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
cnf(f_357_3,plain,
( hBOOL(hAPP(fun(product_prod(U_1314,U_1315),bool),bool,finite_finite_1(product_prod(U_1314,U_1315)),top_top(fun(product_prod(U_1314,U_1315),bool))))
| ~ hBOOL(hAPP(fun(U_1315,bool),bool,finite_finite_1(U_1315),top_top(fun(U_1315,bool))))
| ~ hBOOL(hAPP(fun(U_1314,bool),bool,finite_finite_1(U_1314),top_top(fun(U_1314,bool)))) ),
inference(clausify,[status(thm)],[f_357_2]) ).
fof(f_358_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_358_2,plain,
! [U_1317,U_1316] :
( ( hBOOL(hAPP(fun(sum_sum(U_1317,U_1316),bool),bool,finite_finite_1(sum_sum(U_1317,U_1316)),top_top(fun(sum_sum(U_1317,U_1316),bool))))
| ~ hBOOL(hAPP(fun(U_1316,bool),bool,finite_finite_1(U_1316),top_top(fun(U_1316,bool))))
| ~ hBOOL(hAPP(fun(U_1317,bool),bool,finite_finite_1(U_1317),top_top(fun(U_1317,bool)))) )
& ( ( hBOOL(hAPP(fun(U_1316,bool),bool,finite_finite_1(U_1316),top_top(fun(U_1316,bool))))
& hBOOL(hAPP(fun(U_1317,bool),bool,finite_finite_1(U_1317),top_top(fun(U_1317,bool)))) )
| ~ hBOOL(hAPP(fun(sum_sum(U_1317,U_1316),bool),bool,finite_finite_1(sum_sum(U_1317,U_1316)),top_top(fun(sum_sum(U_1317,U_1316),bool)))) ) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
( ! [U_1321,U_1319] :
( hBOOL(hAPP(fun(sum_sum(U_1321,U_1319),bool),bool,finite_finite_1(sum_sum(U_1321,U_1319)),top_top(fun(sum_sum(U_1321,U_1319),bool))))
| ~ hBOOL(hAPP(fun(U_1319,bool),bool,finite_finite_1(U_1319),top_top(fun(U_1319,bool))))
| ~ hBOOL(hAPP(fun(U_1321,bool),bool,finite_finite_1(U_1321),top_top(fun(U_1321,bool)))) )
& ! [U_1320,U_1318] :
( ( hBOOL(hAPP(fun(U_1318,bool),bool,finite_finite_1(U_1318),top_top(fun(U_1318,bool))))
& hBOOL(hAPP(fun(U_1320,bool),bool,finite_finite_1(U_1320),top_top(fun(U_1320,bool)))) )
| ~ hBOOL(hAPP(fun(sum_sum(U_1320,U_1318),bool),bool,finite_finite_1(sum_sum(U_1320,U_1318)),top_top(fun(sum_sum(U_1320,U_1318),bool)))) ) ),
inference(miniscope,[status(thm)],[f_358_2]) ).
cnf(f_358_4,plain,
( hBOOL(hAPP(fun(U_1320,bool),bool,finite_finite_1(U_1320),top_top(fun(U_1320,bool))))
| ~ hBOOL(hAPP(fun(sum_sum(U_1320,U_1318),bool),bool,finite_finite_1(sum_sum(U_1320,U_1318)),top_top(fun(sum_sum(U_1320,U_1318),bool)))) ),
inference(clausify,[status(thm)],[f_358_3]) ).
cnf(f_358_5,plain,
( hBOOL(hAPP(fun(U_1318,bool),bool,finite_finite_1(U_1318),top_top(fun(U_1318,bool))))
| ~ hBOOL(hAPP(fun(sum_sum(U_1320,U_1318),bool),bool,finite_finite_1(sum_sum(U_1320,U_1318)),top_top(fun(sum_sum(U_1320,U_1318),bool)))) ),
inference(clausify,[status(thm)],[f_358_3]) ).
cnf(f_358_6,plain,
( hBOOL(hAPP(fun(sum_sum(U_1321,U_1319),bool),bool,finite_finite_1(sum_sum(U_1321,U_1319)),top_top(fun(sum_sum(U_1321,U_1319),bool))))
| ~ hBOOL(hAPP(fun(U_1319,bool),bool,finite_finite_1(U_1319),top_top(fun(U_1319,bool))))
| ~ hBOOL(hAPP(fun(U_1321,bool),bool,finite_finite_1(U_1321),top_top(fun(U_1321,bool)))) ),
inference(clausify,[status(thm)],[f_358_3]) ).
fof(f_359_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_296_finite__option__UNIV]) ).
fof(f_359_2,plain,
! [U_1322] :
( ( hBOOL(hAPP(fun(option(U_1322),bool),bool,finite_finite_1(option(U_1322)),top_top(fun(option(U_1322),bool))))
| ~ hBOOL(hAPP(fun(U_1322,bool),bool,finite_finite_1(U_1322),top_top(fun(U_1322,bool)))) )
& ( hBOOL(hAPP(fun(U_1322,bool),bool,finite_finite_1(U_1322),top_top(fun(U_1322,bool))))
| ~ hBOOL(hAPP(fun(option(U_1322),bool),bool,finite_finite_1(option(U_1322)),top_top(fun(option(U_1322),bool)))) ) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
( ! [U_1324] :
( hBOOL(hAPP(fun(option(U_1324),bool),bool,finite_finite_1(option(U_1324)),top_top(fun(option(U_1324),bool))))
| ~ hBOOL(hAPP(fun(U_1324,bool),bool,finite_finite_1(U_1324),top_top(fun(U_1324,bool)))) )
& ! [U_1323] :
( hBOOL(hAPP(fun(U_1323,bool),bool,finite_finite_1(U_1323),top_top(fun(U_1323,bool))))
| ~ hBOOL(hAPP(fun(option(U_1323),bool),bool,finite_finite_1(option(U_1323)),top_top(fun(option(U_1323),bool)))) ) ),
inference(miniscope,[status(thm)],[f_359_2]) ).
cnf(f_359_4,plain,
( hBOOL(hAPP(fun(U_1323,bool),bool,finite_finite_1(U_1323),top_top(fun(U_1323,bool))))
| ~ hBOOL(hAPP(fun(option(U_1323),bool),bool,finite_finite_1(option(U_1323)),top_top(fun(option(U_1323),bool)))) ),
inference(clausify,[status(thm)],[f_359_3]) ).
cnf(f_359_5,plain,
( hBOOL(hAPP(fun(option(U_1324),bool),bool,finite_finite_1(option(U_1324)),top_top(fun(option(U_1324),bool))))
| ~ hBOOL(hAPP(fun(U_1324,bool),bool,finite_finite_1(U_1324),top_top(fun(U_1324,bool)))) ),
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_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_297_finite__Collect__not]) ).
fof(f_360_2,plain,
! [U_1326,U_1325] :
( ( ( hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),collect(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(fun(bool,bool),fun(fun(U_1326,bool),fun(U_1326,bool)),combb(bool,bool,U_1326),fNot),U_1325))))
| ~ hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),top_top(fun(U_1326,bool)))) )
& ( hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),top_top(fun(U_1326,bool))))
| ~ hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),collect(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(fun(bool,bool),fun(fun(U_1326,bool),fun(U_1326,bool)),combb(bool,bool,U_1326),fNot),U_1325)))) ) )
| ~ hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),collect(U_1326),U_1325))) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
cnf(f_360_3,plain,
( hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),top_top(fun(U_1326,bool))))
| ~ hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),collect(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(fun(bool,bool),fun(fun(U_1326,bool),fun(U_1326,bool)),combb(bool,bool,U_1326),fNot),U_1325))))
| ~ hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),collect(U_1326),U_1325))) ),
inference(clausify,[status(thm)],[f_360_2]) ).
cnf(f_360_4,plain,
( hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),collect(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),hAPP(fun(bool,bool),fun(fun(U_1326,bool),fun(U_1326,bool)),combb(bool,bool,U_1326),fNot),U_1325))))
| ~ hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),top_top(fun(U_1326,bool))))
| ~ hBOOL(hAPP(fun(U_1326,bool),bool,finite_finite_1(U_1326),hAPP(fun(U_1326,bool),fun(U_1326,bool),collect(U_1326),U_1325))) ),
inference(clausify,[status(thm)],[f_360_2]) ).
fof(f_361_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_298_card__eq__UNIV__imp__eq__UNIV]) ).
fof(f_361_2,plain,
! [U_1328,U_1327] :
( ti(fun(U_1328,bool),U_1327) = top_top(fun(U_1328,bool))
| hAPP(fun(U_1328,bool),nat,finite_card(U_1328),U_1327) != hAPP(fun(U_1328,bool),nat,finite_card(U_1328),top_top(fun(U_1328,bool)))
| ~ hBOOL(hAPP(fun(U_1328,bool),bool,finite_finite_1(U_1328),top_top(fun(U_1328,bool)))) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
! [U_1328] :
( ! [U_1327] :
( ti(fun(U_1328,bool),U_1327) = top_top(fun(U_1328,bool))
| hAPP(fun(U_1328,bool),nat,finite_card(U_1328),U_1327) != hAPP(fun(U_1328,bool),nat,finite_card(U_1328),top_top(fun(U_1328,bool))) )
| ~ hBOOL(hAPP(fun(U_1328,bool),bool,finite_finite_1(U_1328),top_top(fun(U_1328,bool)))) ),
inference(miniscope,[status(thm)],[f_361_2]) ).
cnf(f_361_4,plain,
( ti(fun(U_1328,bool),U_1327) = top_top(fun(U_1328,bool))
| hAPP(fun(U_1328,bool),nat,finite_card(U_1328),U_1327) != hAPP(fun(U_1328,bool),nat,finite_card(U_1328),top_top(fun(U_1328,bool)))
| ~ hBOOL(hAPP(fun(U_1328,bool),bool,finite_finite_1(U_1328),top_top(fun(U_1328,bool)))) ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_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_299_finite__fun__UNIVD2]) ).
fof(f_362_2,plain,
! [U_1330,U_1329] :
( hBOOL(hAPP(fun(U_1329,bool),bool,finite_finite_1(U_1329),top_top(fun(U_1329,bool))))
| ~ hBOOL(hAPP(fun(fun(U_1330,U_1329),bool),bool,finite_finite_1(fun(U_1330,U_1329)),top_top(fun(fun(U_1330,U_1329),bool)))) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
cnf(f_362_3,plain,
( hBOOL(hAPP(fun(U_1329,bool),bool,finite_finite_1(U_1329),top_top(fun(U_1329,bool))))
| ~ hBOOL(hAPP(fun(fun(U_1330,U_1329),bool),bool,finite_finite_1(fun(U_1330,U_1329)),top_top(fun(fun(U_1330,U_1329),bool)))) ),
inference(clausify,[status(thm)],[f_362_2]) ).
fof(f_363_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_300_card__seteq]) ).
fof(f_363_2,plain,
! [U_1333,U_1332,U_1331] :
( ti(fun(U_1333,bool),U_1332) = ti(fun(U_1333,bool),U_1331)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1333,bool),nat,finite_card(U_1333),U_1331)),hAPP(fun(U_1333,bool),nat,finite_card(U_1333),U_1332)))
| ~ hBOOL(hAPP(fun(U_1333,bool),bool,hAPP(fun(U_1333,bool),fun(fun(U_1333,bool),bool),ord_less_eq(fun(U_1333,bool)),U_1332),U_1331))
| ~ hBOOL(hAPP(fun(U_1333,bool),bool,finite_finite_1(U_1333),U_1331)) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
cnf(f_363_3,plain,
( ti(fun(U_1333,bool),U_1332) = ti(fun(U_1333,bool),U_1331)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1333,bool),nat,finite_card(U_1333),U_1331)),hAPP(fun(U_1333,bool),nat,finite_card(U_1333),U_1332)))
| ~ hBOOL(hAPP(fun(U_1333,bool),bool,hAPP(fun(U_1333,bool),fun(fun(U_1333,bool),bool),ord_less_eq(fun(U_1333,bool)),U_1332),U_1331))
| ~ hBOOL(hAPP(fun(U_1333,bool),bool,finite_finite_1(U_1333),U_1331)) ),
inference(clausify,[status(thm)],[f_363_2]) ).
fof(f_364_1,plain,
! [X_a,A_1] :
( ? [A_3] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_301_ex__new__if__finite]) ).
fof(f_364_2,plain,
! [U_1336,U_1335] :
( ? [U_1334] : ~ hBOOL(hAPP(fun(U_1336,bool),bool,hAPP(U_1336,fun(fun(U_1336,bool),bool),member(U_1336),U_1334),U_1335))
| ~ hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),U_1335))
| hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),top_top(fun(U_1336,bool)))) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
! [U_1336] :
( ! [U_1335] :
( ? [U_1334] : ~ hBOOL(hAPP(fun(U_1336,bool),bool,hAPP(U_1336,fun(fun(U_1336,bool),bool),member(U_1336),U_1334),U_1335))
| ~ hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),U_1335)) )
| hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),top_top(fun(U_1336,bool)))) ),
inference(miniscope,[status(thm)],[f_364_2]) ).
fof(f_364_4,plain,
! [U_1336] :
( ! [U_1335] :
( ~ hBOOL(hAPP(fun(U_1336,bool),bool,hAPP(U_1336,fun(fun(U_1336,bool),bool),member(U_1336),sK80(U_1336,U_1335)),U_1335))
| ~ hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),U_1335)) )
| hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),top_top(fun(U_1336,bool)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_1334,sK80(U_1336,U_1335))],[f_364_3]) ).
cnf(f_364_5,plain,
( ~ hBOOL(hAPP(fun(U_1336,bool),bool,hAPP(U_1336,fun(fun(U_1336,bool),bool),member(U_1336),sK80(U_1336,U_1335)),U_1335))
| ~ hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),U_1335))
| hBOOL(hAPP(fun(U_1336,bool),bool,finite_finite_1(U_1336),top_top(fun(U_1336,bool)))) ),
inference(clausify,[status(thm)],[f_364_4]) ).
fof(f_365_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_302_card__Plus]) ).
fof(f_365_2,plain,
! [U_1340,U_1339,U_1338,U_1337] :
( hAPP(fun(sum_sum(U_1339,U_1340),bool),nat,finite_card(sum_sum(U_1339,U_1340)),hAPP(fun(U_1340,bool),fun(sum_sum(U_1339,U_1340),bool),hAPP(fun(U_1339,bool),fun(fun(U_1340,bool),fun(sum_sum(U_1339,U_1340),bool)),sum_Plus(U_1339,U_1340),U_1337),U_1338)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1339,bool),nat,finite_card(U_1339),U_1337)),hAPP(fun(U_1340,bool),nat,finite_card(U_1340),U_1338))
| ~ hBOOL(hAPP(fun(U_1340,bool),bool,finite_finite_1(U_1340),U_1338))
| ~ hBOOL(hAPP(fun(U_1339,bool),bool,finite_finite_1(U_1339),U_1337)) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
cnf(f_365_3,plain,
( hAPP(fun(sum_sum(U_1339,U_1340),bool),nat,finite_card(sum_sum(U_1339,U_1340)),hAPP(fun(U_1340,bool),fun(sum_sum(U_1339,U_1340),bool),hAPP(fun(U_1339,bool),fun(fun(U_1340,bool),fun(sum_sum(U_1339,U_1340),bool)),sum_Plus(U_1339,U_1340),U_1337),U_1338)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1339,bool),nat,finite_card(U_1339),U_1337)),hAPP(fun(U_1340,bool),nat,finite_card(U_1340),U_1338))
| ~ hBOOL(hAPP(fun(U_1340,bool),bool,finite_finite_1(U_1340),U_1338))
| ~ hBOOL(hAPP(fun(U_1339,bool),bool,finite_finite_1(U_1339),U_1337)) ),
inference(clausify,[status(thm)],[f_365_2]) ).
fof(f_366_1,plain,
! [X_b,X_a,B,A_1,F,Z,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),G),Fa)) ),
inference(fof_nnf,[status(thm)],[fact_303_folding__image__simple__idem_Osubset__idem]) ).
fof(f_366_2,plain,
! [U_1348,U_1347,U_1346,U_1345,U_1344,U_1343,U_1342,U_1341] :
( hAPP(U_1347,U_1347,hAPP(U_1347,fun(U_1347,U_1347),U_1344,hAPP(fun(U_1348,bool),U_1347,U_1341,U_1346)),hAPP(fun(U_1348,bool),U_1347,U_1341,U_1345)) = hAPP(fun(U_1348,bool),U_1347,U_1341,U_1345)
| ~ hBOOL(hAPP(fun(U_1348,bool),bool,hAPP(fun(U_1348,bool),fun(fun(U_1348,bool),bool),ord_less_eq(fun(U_1348,bool)),U_1346),U_1345))
| ~ hBOOL(hAPP(fun(U_1348,bool),bool,finite_finite_1(U_1348),U_1345))
| ~ hBOOL(hAPP(fun(fun(U_1348,bool),U_1347),bool,hAPP(fun(U_1348,U_1347),fun(fun(fun(U_1348,bool),U_1347),bool),hAPP(U_1347,fun(fun(U_1348,U_1347),fun(fun(fun(U_1348,bool),U_1347),bool)),hAPP(fun(U_1347,fun(U_1347,U_1347)),fun(U_1347,fun(fun(U_1348,U_1347),fun(fun(fun(U_1348,bool),U_1347),bool))),finite908156982e_idem(U_1347,U_1348),U_1344),U_1343),U_1342),U_1341)) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
cnf(f_366_3,plain,
( hAPP(U_1347,U_1347,hAPP(U_1347,fun(U_1347,U_1347),U_1344,hAPP(fun(U_1348,bool),U_1347,U_1341,U_1346)),hAPP(fun(U_1348,bool),U_1347,U_1341,U_1345)) = hAPP(fun(U_1348,bool),U_1347,U_1341,U_1345)
| ~ hBOOL(hAPP(fun(U_1348,bool),bool,hAPP(fun(U_1348,bool),fun(fun(U_1348,bool),bool),ord_less_eq(fun(U_1348,bool)),U_1346),U_1345))
| ~ hBOOL(hAPP(fun(U_1348,bool),bool,finite_finite_1(U_1348),U_1345))
| ~ hBOOL(hAPP(fun(fun(U_1348,bool),U_1347),bool,hAPP(fun(U_1348,U_1347),fun(fun(fun(U_1348,bool),U_1347),bool),hAPP(U_1347,fun(fun(U_1348,U_1347),fun(fun(fun(U_1348,bool),U_1347),bool)),hAPP(fun(U_1347,fun(U_1347,U_1347)),fun(U_1347,fun(fun(U_1348,U_1347),fun(fun(fun(U_1348,bool),U_1347),bool))),finite908156982e_idem(U_1347,U_1348),U_1344),U_1343),U_1342),U_1341)) ),
inference(clausify,[status(thm)],[f_366_2]) ).
fof(f_367_1,plain,
~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
inference(fof_nnf,[status(thm)],[fact_304_infinite__UNIV__nat]) ).
cnf(f_367_2,plain,
~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
inference(clausify,[status(thm)],[f_367_1]) ).
fof(f_368_1,plain,
! [X_b,X_a,X_1,F,Z,G,Fa] :
( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_1),X_1) = ti(X_a,X_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),G),Fa)) ),
inference(fof_nnf,[status(thm)],[fact_305_folding__image__simple__idem_Oidem]) ).
fof(f_368_2,plain,
! [U_1355,U_1354,U_1353,U_1352,U_1351,U_1350,U_1349] :
( hAPP(U_1354,U_1354,hAPP(U_1354,fun(U_1354,U_1354),U_1352,U_1353),U_1353) = ti(U_1354,U_1353)
| ~ hBOOL(hAPP(fun(fun(U_1355,bool),U_1354),bool,hAPP(fun(U_1355,U_1354),fun(fun(fun(U_1355,bool),U_1354),bool),hAPP(U_1354,fun(fun(U_1355,U_1354),fun(fun(fun(U_1355,bool),U_1354),bool)),hAPP(fun(U_1354,fun(U_1354,U_1354)),fun(U_1354,fun(fun(U_1355,U_1354),fun(fun(fun(U_1355,bool),U_1354),bool))),finite908156982e_idem(U_1354,U_1355),U_1352),U_1351),U_1350),U_1349)) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
fof(f_368_3,plain,
! [U_1355,U_1354,U_1353,U_1352] :
( ! [U_1351,U_1350,U_1349] : ~ hBOOL(hAPP(fun(fun(U_1355,bool),U_1354),bool,hAPP(fun(U_1355,U_1354),fun(fun(fun(U_1355,bool),U_1354),bool),hAPP(U_1354,fun(fun(U_1355,U_1354),fun(fun(fun(U_1355,bool),U_1354),bool)),hAPP(fun(U_1354,fun(U_1354,U_1354)),fun(U_1354,fun(fun(U_1355,U_1354),fun(fun(fun(U_1355,bool),U_1354),bool))),finite908156982e_idem(U_1354,U_1355),U_1352),U_1351),U_1350),U_1349))
| hAPP(U_1354,U_1354,hAPP(U_1354,fun(U_1354,U_1354),U_1352,U_1353),U_1353) = ti(U_1354,U_1353) ),
inference(miniscope,[status(thm)],[f_368_2]) ).
cnf(f_368_4,plain,
( ~ hBOOL(hAPP(fun(fun(U_1355,bool),U_1354),bool,hAPP(fun(U_1355,U_1354),fun(fun(fun(U_1355,bool),U_1354),bool),hAPP(U_1354,fun(fun(U_1355,U_1354),fun(fun(fun(U_1355,bool),U_1354),bool)),hAPP(fun(U_1354,fun(U_1354,U_1354)),fun(U_1354,fun(fun(U_1355,U_1354),fun(fun(fun(U_1355,bool),U_1354),bool))),finite908156982e_idem(U_1354,U_1355),U_1352),U_1351),U_1350),U_1349))
| hAPP(U_1354,U_1354,hAPP(U_1354,fun(U_1354,U_1354),U_1352,U_1353),U_1353) = ti(U_1354,U_1353) ),
inference(clausify,[status(thm)],[f_368_3]) ).
fof(f_369_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_306_finite__Plus__iff]) ).
fof(f_369_2,plain,
! [U_1359,U_1358,U_1357,U_1356] :
( ( hBOOL(hAPP(fun(sum_sum(U_1359,U_1358),bool),bool,finite_finite_1(sum_sum(U_1359,U_1358)),hAPP(fun(U_1358,bool),fun(sum_sum(U_1359,U_1358),bool),hAPP(fun(U_1359,bool),fun(fun(U_1358,bool),fun(sum_sum(U_1359,U_1358),bool)),sum_Plus(U_1359,U_1358),U_1357),U_1356)))
| ~ hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),U_1356))
| ~ hBOOL(hAPP(fun(U_1359,bool),bool,finite_finite_1(U_1359),U_1357)) )
& ( ( hBOOL(hAPP(fun(U_1358,bool),bool,finite_finite_1(U_1358),U_1356))
& hBOOL(hAPP(fun(U_1359,bool),bool,finite_finite_1(U_1359),U_1357)) )
| ~ hBOOL(hAPP(fun(sum_sum(U_1359,U_1358),bool),bool,finite_finite_1(sum_sum(U_1359,U_1358)),hAPP(fun(U_1358,bool),fun(sum_sum(U_1359,U_1358),bool),hAPP(fun(U_1359,bool),fun(fun(U_1358,bool),fun(sum_sum(U_1359,U_1358),bool)),sum_Plus(U_1359,U_1358),U_1357),U_1356))) ) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
fof(f_369_3,plain,
( ! [U_1367,U_1365,U_1363,U_1361] :
( hBOOL(hAPP(fun(sum_sum(U_1367,U_1365),bool),bool,finite_finite_1(sum_sum(U_1367,U_1365)),hAPP(fun(U_1365,bool),fun(sum_sum(U_1367,U_1365),bool),hAPP(fun(U_1367,bool),fun(fun(U_1365,bool),fun(sum_sum(U_1367,U_1365),bool)),sum_Plus(U_1367,U_1365),U_1363),U_1361)))
| ~ hBOOL(hAPP(fun(U_1365,bool),bool,finite_finite_1(U_1365),U_1361))
| ~ hBOOL(hAPP(fun(U_1367,bool),bool,finite_finite_1(U_1367),U_1363)) )
& ! [U_1366,U_1364,U_1362,U_1360] :
( ( hBOOL(hAPP(fun(U_1364,bool),bool,finite_finite_1(U_1364),U_1360))
& hBOOL(hAPP(fun(U_1366,bool),bool,finite_finite_1(U_1366),U_1362)) )
| ~ hBOOL(hAPP(fun(sum_sum(U_1366,U_1364),bool),bool,finite_finite_1(sum_sum(U_1366,U_1364)),hAPP(fun(U_1364,bool),fun(sum_sum(U_1366,U_1364),bool),hAPP(fun(U_1366,bool),fun(fun(U_1364,bool),fun(sum_sum(U_1366,U_1364),bool)),sum_Plus(U_1366,U_1364),U_1362),U_1360))) ) ),
inference(miniscope,[status(thm)],[f_369_2]) ).
cnf(f_369_4,plain,
( hBOOL(hAPP(fun(U_1366,bool),bool,finite_finite_1(U_1366),U_1362))
| ~ hBOOL(hAPP(fun(sum_sum(U_1366,U_1364),bool),bool,finite_finite_1(sum_sum(U_1366,U_1364)),hAPP(fun(U_1364,bool),fun(sum_sum(U_1366,U_1364),bool),hAPP(fun(U_1366,bool),fun(fun(U_1364,bool),fun(sum_sum(U_1366,U_1364),bool)),sum_Plus(U_1366,U_1364),U_1362),U_1360))) ),
inference(clausify,[status(thm)],[f_369_3]) ).
cnf(f_369_5,plain,
( hBOOL(hAPP(fun(U_1364,bool),bool,finite_finite_1(U_1364),U_1360))
| ~ hBOOL(hAPP(fun(sum_sum(U_1366,U_1364),bool),bool,finite_finite_1(sum_sum(U_1366,U_1364)),hAPP(fun(U_1364,bool),fun(sum_sum(U_1366,U_1364),bool),hAPP(fun(U_1366,bool),fun(fun(U_1364,bool),fun(sum_sum(U_1366,U_1364),bool)),sum_Plus(U_1366,U_1364),U_1362),U_1360))) ),
inference(clausify,[status(thm)],[f_369_3]) ).
cnf(f_369_6,plain,
( hBOOL(hAPP(fun(sum_sum(U_1367,U_1365),bool),bool,finite_finite_1(sum_sum(U_1367,U_1365)),hAPP(fun(U_1365,bool),fun(sum_sum(U_1367,U_1365),bool),hAPP(fun(U_1367,bool),fun(fun(U_1365,bool),fun(sum_sum(U_1367,U_1365),bool)),sum_Plus(U_1367,U_1365),U_1363),U_1361)))
| ~ hBOOL(hAPP(fun(U_1365,bool),bool,finite_finite_1(U_1365),U_1361))
| ~ hBOOL(hAPP(fun(U_1367,bool),bool,finite_finite_1(U_1367),U_1363)) ),
inference(clausify,[status(thm)],[f_369_3]) ).
fof(f_370_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_307_finite__Plus]) ).
fof(f_370_2,plain,
! [U_1371,U_1370,U_1369,U_1368] :
( hBOOL(hAPP(fun(sum_sum(U_1370,U_1371),bool),bool,finite_finite_1(sum_sum(U_1370,U_1371)),hAPP(fun(U_1371,bool),fun(sum_sum(U_1370,U_1371),bool),hAPP(fun(U_1370,bool),fun(fun(U_1371,bool),fun(sum_sum(U_1370,U_1371),bool)),sum_Plus(U_1370,U_1371),U_1368),U_1369)))
| ~ hBOOL(hAPP(fun(U_1371,bool),bool,finite_finite_1(U_1371),U_1369))
| ~ hBOOL(hAPP(fun(U_1370,bool),bool,finite_finite_1(U_1370),U_1368)) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
cnf(f_370_3,plain,
( hBOOL(hAPP(fun(sum_sum(U_1370,U_1371),bool),bool,finite_finite_1(sum_sum(U_1370,U_1371)),hAPP(fun(U_1371,bool),fun(sum_sum(U_1370,U_1371),bool),hAPP(fun(U_1370,bool),fun(fun(U_1371,bool),fun(sum_sum(U_1370,U_1371),bool)),sum_Plus(U_1370,U_1371),U_1368),U_1369)))
| ~ hBOOL(hAPP(fun(U_1371,bool),bool,finite_finite_1(U_1371),U_1369))
| ~ hBOOL(hAPP(fun(U_1370,bool),bool,finite_finite_1(U_1370),U_1368)) ),
inference(clausify,[status(thm)],[f_370_2]) ).
fof(f_371_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_308_finite__PlusD_I1_J]) ).
fof(f_371_2,plain,
! [U_1375,U_1374,U_1373,U_1372] :
( hBOOL(hAPP(fun(U_1375,bool),bool,finite_finite_1(U_1375),U_1373))
| ~ hBOOL(hAPP(fun(sum_sum(U_1375,U_1374),bool),bool,finite_finite_1(sum_sum(U_1375,U_1374)),hAPP(fun(U_1374,bool),fun(sum_sum(U_1375,U_1374),bool),hAPP(fun(U_1375,bool),fun(fun(U_1374,bool),fun(sum_sum(U_1375,U_1374),bool)),sum_Plus(U_1375,U_1374),U_1373),U_1372))) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
fof(f_371_3,plain,
! [U_1375,U_1374,U_1373] :
( ! [U_1372] : ~ hBOOL(hAPP(fun(sum_sum(U_1375,U_1374),bool),bool,finite_finite_1(sum_sum(U_1375,U_1374)),hAPP(fun(U_1374,bool),fun(sum_sum(U_1375,U_1374),bool),hAPP(fun(U_1375,bool),fun(fun(U_1374,bool),fun(sum_sum(U_1375,U_1374),bool)),sum_Plus(U_1375,U_1374),U_1373),U_1372)))
| hBOOL(hAPP(fun(U_1375,bool),bool,finite_finite_1(U_1375),U_1373)) ),
inference(miniscope,[status(thm)],[f_371_2]) ).
cnf(f_371_4,plain,
( ~ hBOOL(hAPP(fun(sum_sum(U_1375,U_1374),bool),bool,finite_finite_1(sum_sum(U_1375,U_1374)),hAPP(fun(U_1374,bool),fun(sum_sum(U_1375,U_1374),bool),hAPP(fun(U_1375,bool),fun(fun(U_1374,bool),fun(sum_sum(U_1375,U_1374),bool)),sum_Plus(U_1375,U_1374),U_1373),U_1372)))
| hBOOL(hAPP(fun(U_1375,bool),bool,finite_finite_1(U_1375),U_1373)) ),
inference(clausify,[status(thm)],[f_371_3]) ).
fof(f_372_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_309_finite__PlusD_I2_J]) ).
fof(f_372_2,plain,
! [U_1379,U_1378,U_1377,U_1376] :
( hBOOL(hAPP(fun(U_1378,bool),bool,finite_finite_1(U_1378),U_1376))
| ~ hBOOL(hAPP(fun(sum_sum(U_1379,U_1378),bool),bool,finite_finite_1(sum_sum(U_1379,U_1378)),hAPP(fun(U_1378,bool),fun(sum_sum(U_1379,U_1378),bool),hAPP(fun(U_1379,bool),fun(fun(U_1378,bool),fun(sum_sum(U_1379,U_1378),bool)),sum_Plus(U_1379,U_1378),U_1377),U_1376))) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
cnf(f_372_3,plain,
( hBOOL(hAPP(fun(U_1378,bool),bool,finite_finite_1(U_1378),U_1376))
| ~ hBOOL(hAPP(fun(sum_sum(U_1379,U_1378),bool),bool,finite_finite_1(sum_sum(U_1379,U_1378)),hAPP(fun(U_1378,bool),fun(sum_sum(U_1379,U_1378),bool),hAPP(fun(U_1379,bool),fun(fun(U_1378,bool),fun(sum_sum(U_1379,U_1378),bool)),sum_Plus(U_1379,U_1378),U_1377),U_1376))) ),
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_373_1,plain,
! [X_b,X_a,X_1,A_1,F,Z,G,Fa] :
( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_1)),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_1),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),G),Fa)) ),
inference(fof_nnf,[status(thm)],[fact_310_folding__image__simple__idem_Oin__idem]) ).
fof(f_373_2,plain,
! [U_1387,U_1386,U_1385,U_1384,U_1383,U_1382,U_1381,U_1380] :
( hAPP(U_1386,U_1386,hAPP(U_1386,fun(U_1386,U_1386),U_1383,hAPP(U_1387,U_1386,U_1381,U_1385)),hAPP(fun(U_1387,bool),U_1386,U_1380,U_1384)) = hAPP(fun(U_1387,bool),U_1386,U_1380,U_1384)
| ~ hBOOL(hAPP(fun(U_1387,bool),bool,hAPP(U_1387,fun(fun(U_1387,bool),bool),member(U_1387),U_1385),U_1384))
| ~ hBOOL(hAPP(fun(U_1387,bool),bool,finite_finite_1(U_1387),U_1384))
| ~ hBOOL(hAPP(fun(fun(U_1387,bool),U_1386),bool,hAPP(fun(U_1387,U_1386),fun(fun(fun(U_1387,bool),U_1386),bool),hAPP(U_1386,fun(fun(U_1387,U_1386),fun(fun(fun(U_1387,bool),U_1386),bool)),hAPP(fun(U_1386,fun(U_1386,U_1386)),fun(U_1386,fun(fun(U_1387,U_1386),fun(fun(fun(U_1387,bool),U_1386),bool))),finite908156982e_idem(U_1386,U_1387),U_1383),U_1382),U_1381),U_1380)) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
cnf(f_373_3,plain,
( hAPP(U_1386,U_1386,hAPP(U_1386,fun(U_1386,U_1386),U_1383,hAPP(U_1387,U_1386,U_1381,U_1385)),hAPP(fun(U_1387,bool),U_1386,U_1380,U_1384)) = hAPP(fun(U_1387,bool),U_1386,U_1380,U_1384)
| ~ hBOOL(hAPP(fun(U_1387,bool),bool,hAPP(U_1387,fun(fun(U_1387,bool),bool),member(U_1387),U_1385),U_1384))
| ~ hBOOL(hAPP(fun(U_1387,bool),bool,finite_finite_1(U_1387),U_1384))
| ~ hBOOL(hAPP(fun(fun(U_1387,bool),U_1386),bool,hAPP(fun(U_1387,U_1386),fun(fun(fun(U_1387,bool),U_1386),bool),hAPP(U_1386,fun(fun(U_1387,U_1386),fun(fun(fun(U_1387,bool),U_1386),bool)),hAPP(fun(U_1386,fun(U_1386,U_1386)),fun(U_1386,fun(fun(U_1387,U_1386),fun(fun(fun(U_1387,bool),U_1386),bool))),finite908156982e_idem(U_1386,U_1387),U_1383),U_1382),U_1381),U_1380)) ),
inference(clausify,[status(thm)],[f_373_2]) ).
fof(f_374_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_311_UNIV__Plus__UNIV]) ).
fof(f_374_2,plain,
! [U_1389,U_1388] : hAPP(fun(U_1389,bool),fun(sum_sum(U_1388,U_1389),bool),hAPP(fun(U_1388,bool),fun(fun(U_1389,bool),fun(sum_sum(U_1388,U_1389),bool)),sum_Plus(U_1388,U_1389),top_top(fun(U_1388,bool))),top_top(fun(U_1389,bool))) = top_top(fun(sum_sum(U_1388,U_1389),bool)),
inference(variable_rename,[status(thm)],[f_374_1]) ).
cnf(f_374_3,plain,
hAPP(fun(U_1389,bool),fun(sum_sum(U_1388,U_1389),bool),hAPP(fun(U_1388,bool),fun(fun(U_1389,bool),fun(sum_sum(U_1388,U_1389),bool)),sum_Plus(U_1388,U_1389),top_top(fun(U_1388,bool))),top_top(fun(U_1389,bool))) = top_top(fun(sum_sum(U_1388,U_1389),bool)),
inference(clausify,[status(thm)],[f_374_2]) ).
fof(f_375_1,plain,
! [Pa,I_1] : 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_1))))),
inference(fof_nnf,[status(thm)],[fact_312_finite__M__bounded__by__nat]) ).
fof(f_375_2,plain,
! [U_1391,U_1390] : 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_1391)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1390))))),
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(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_1391)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1390))))),
inference(clausify,[status(thm)],[f_375_2]) ).
fof(f_376_1,plain,
! [N_3] :
( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))
| ! [M] :
? [X_2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) ) )
& ( ? [M] :
! [X_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) ) ),
inference(fof_nnf,[status(thm)],[fact_313_finite__nat__set__iff__bounded__le]) ).
fof(f_376_2,plain,
! [U_1396] :
( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1396))
| ! [U_1395] :
? [U_1394] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1394),U_1395))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1394),U_1396)) ) )
& ( ? [U_1393] :
! [U_1392] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1392),U_1393))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1392),U_1396)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1396)) ) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
fof(f_376_3,plain,
( ! [U_1398] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1398))
| ! [U_1395] :
? [U_1394] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1394),U_1395))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1394),U_1398)) ) )
& ! [U_1397] :
( ? [U_1393] :
! [U_1392] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1392),U_1393))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1392),U_1397)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1397)) ) ),
inference(miniscope,[status(thm)],[f_376_2]) ).
fof(f_376_4,plain,
( ! [U_1398] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1398))
| ! [U_1395] :
? [U_1394] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1394),U_1395))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1394),U_1398)) ) )
& ! [U_1397] :
( ! [U_1392] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1392),sK81(U_1397)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1392),U_1397)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1397)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_1393,sK81(U_1397))],[f_376_3]) ).
fof(f_376_5,plain,
( ! [U_1398] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1398))
| ! [U_1395] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK82(U_1398,U_1395)),U_1395))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK82(U_1398,U_1395)),U_1398)) ) )
& ! [U_1397] :
( ! [U_1392] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1392),sK81(U_1397)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1392),U_1397)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1397)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_1394,sK82(U_1398,U_1395))],[f_376_4]) ).
cnf(f_376_6,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1392),sK81(U_1397)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1392),U_1397))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1397)) ),
inference(clausify,[status(thm)],[f_376_5]) ).
cnf(f_376_7,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK82(U_1398,U_1395)),U_1398))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1398)) ),
inference(clausify,[status(thm)],[f_376_5]) ).
cnf(f_376_8,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK82(U_1398,U_1395)),U_1395))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1398)) ),
inference(clausify,[status(thm)],[f_376_5]) ).
fof(f_377_1,plain,
! [N_3] :
( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))
| ! [M] :
? [X_2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) ) )
& ( ? [M] :
! [X_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) ) ),
inference(fof_nnf,[status(thm)],[fact_314_finite__nat__set__iff__bounded]) ).
fof(f_377_2,plain,
! [U_1403] :
( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1403))
| ! [U_1402] :
? [U_1401] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1401),U_1402))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1401),U_1403)) ) )
& ( ? [U_1400] :
! [U_1399] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1399),U_1400))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1399),U_1403)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1403)) ) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
( ! [U_1405] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1405))
| ! [U_1402] :
? [U_1401] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1401),U_1402))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1401),U_1405)) ) )
& ! [U_1404] :
( ? [U_1400] :
! [U_1399] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1399),U_1400))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1399),U_1404)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1404)) ) ),
inference(miniscope,[status(thm)],[f_377_2]) ).
fof(f_377_4,plain,
( ! [U_1405] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1405))
| ! [U_1402] :
? [U_1401] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1401),U_1402))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1401),U_1405)) ) )
& ! [U_1404] :
( ! [U_1399] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1399),sK83(U_1404)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1399),U_1404)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1404)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_1400,sK83(U_1404))],[f_377_3]) ).
fof(f_377_5,plain,
( ! [U_1405] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1405))
| ! [U_1402] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK84(U_1405,U_1402)),U_1402))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK84(U_1405,U_1402)),U_1405)) ) )
& ! [U_1404] :
( ! [U_1399] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1399),sK83(U_1404)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1399),U_1404)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1404)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_1401,sK84(U_1405,U_1402))],[f_377_4]) ).
cnf(f_377_6,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1399),sK83(U_1404)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1399),U_1404))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1404)) ),
inference(clausify,[status(thm)],[f_377_5]) ).
cnf(f_377_7,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK84(U_1405,U_1402)),U_1405))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1405)) ),
inference(clausify,[status(thm)],[f_377_5]) ).
cnf(f_377_8,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK84(U_1405,U_1402)),U_1402))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1405)) ),
inference(clausify,[status(thm)],[f_377_5]) ).
fof(f_378_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] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,F,N))) ),
inference(fof_nnf,[status(thm)],[fact_315_finite__less__ub]) ).
fof(f_378_2,plain,
! [U_1408,U_1407] :
( 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_1407)),U_1408))))
| ? [U_1406] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1406),hAPP(nat,nat,U_1407,U_1406))) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
! [U_1408,U_1407] :
( 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_1407)),U_1408))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK85(U_1408,U_1407)),hAPP(nat,nat,U_1407,sK85(U_1408,U_1407)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_1406,sK85(U_1408,U_1407))],[f_378_2]) ).
cnf(f_378_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_1407)),U_1408))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK85(U_1408,U_1407)),hAPP(nat,nat,U_1407,sK85(U_1408,U_1407)))) ),
inference(clausify,[status(thm)],[f_378_3]) ).
fof(f_379_1,plain,
! [Na,N_3] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3))
| ? [X_2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Na))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) ) ),
inference(fof_nnf,[status(thm)],[fact_316_bounded__nat__set__is__finite]) ).
fof(f_379_2,plain,
! [U_1411,U_1410] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1410))
| ? [U_1409] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1409),U_1411))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1409),U_1410)) ) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
! [U_1411,U_1410] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1410))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK86(U_1411,U_1410)),U_1411))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK86(U_1411,U_1410)),U_1410)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_1409,sK86(U_1411,U_1410))],[f_379_2]) ).
cnf(f_379_4,plain,
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK86(U_1411,U_1410)),U_1410))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1410)) ),
inference(clausify,[status(thm)],[f_379_3]) ).
cnf(f_379_5,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK86(U_1411,U_1410)),U_1411))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),U_1410)) ),
inference(clausify,[status(thm)],[f_379_3]) ).
fof(f_380_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_317_card__Plus__conv__if]) ).
fof(f_380_2,plain,
! [U_1415,U_1414,U_1413,U_1412] :
( ( hAPP(fun(sum_sum(U_1414,U_1415),bool),nat,finite_card(sum_sum(U_1414,U_1415)),hAPP(fun(U_1415,bool),fun(sum_sum(U_1414,U_1415),bool),hAPP(fun(U_1414,bool),fun(fun(U_1415,bool),fun(sum_sum(U_1414,U_1415),bool)),sum_Plus(U_1414,U_1415),U_1412),U_1413)) = zero_zero(nat)
| ( hBOOL(hAPP(fun(U_1415,bool),bool,finite_finite_1(U_1415),U_1413))
& hBOOL(hAPP(fun(U_1414,bool),bool,finite_finite_1(U_1414),U_1412)) ) )
& ( hAPP(fun(sum_sum(U_1414,U_1415),bool),nat,finite_card(sum_sum(U_1414,U_1415)),hAPP(fun(U_1415,bool),fun(sum_sum(U_1414,U_1415),bool),hAPP(fun(U_1414,bool),fun(fun(U_1415,bool),fun(sum_sum(U_1414,U_1415),bool)),sum_Plus(U_1414,U_1415),U_1412),U_1413)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1414,bool),nat,finite_card(U_1414),U_1412)),hAPP(fun(U_1415,bool),nat,finite_card(U_1415),U_1413))
| ~ hBOOL(hAPP(fun(U_1415,bool),bool,finite_finite_1(U_1415),U_1413))
| ~ hBOOL(hAPP(fun(U_1414,bool),bool,finite_finite_1(U_1414),U_1412)) ) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
fof(f_380_3,plain,
( ! [U_1423,U_1421,U_1419,U_1417] :
( hAPP(fun(sum_sum(U_1421,U_1423),bool),nat,finite_card(sum_sum(U_1421,U_1423)),hAPP(fun(U_1423,bool),fun(sum_sum(U_1421,U_1423),bool),hAPP(fun(U_1421,bool),fun(fun(U_1423,bool),fun(sum_sum(U_1421,U_1423),bool)),sum_Plus(U_1421,U_1423),U_1417),U_1419)) = zero_zero(nat)
| ( hBOOL(hAPP(fun(U_1423,bool),bool,finite_finite_1(U_1423),U_1419))
& hBOOL(hAPP(fun(U_1421,bool),bool,finite_finite_1(U_1421),U_1417)) ) )
& ! [U_1422,U_1420,U_1418,U_1416] :
( hAPP(fun(sum_sum(U_1420,U_1422),bool),nat,finite_card(sum_sum(U_1420,U_1422)),hAPP(fun(U_1422,bool),fun(sum_sum(U_1420,U_1422),bool),hAPP(fun(U_1420,bool),fun(fun(U_1422,bool),fun(sum_sum(U_1420,U_1422),bool)),sum_Plus(U_1420,U_1422),U_1416),U_1418)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1420,bool),nat,finite_card(U_1420),U_1416)),hAPP(fun(U_1422,bool),nat,finite_card(U_1422),U_1418))
| ~ hBOOL(hAPP(fun(U_1422,bool),bool,finite_finite_1(U_1422),U_1418))
| ~ hBOOL(hAPP(fun(U_1420,bool),bool,finite_finite_1(U_1420),U_1416)) ) ),
inference(miniscope,[status(thm)],[f_380_2]) ).
cnf(f_380_4,plain,
( hAPP(fun(sum_sum(U_1420,U_1422),bool),nat,finite_card(sum_sum(U_1420,U_1422)),hAPP(fun(U_1422,bool),fun(sum_sum(U_1420,U_1422),bool),hAPP(fun(U_1420,bool),fun(fun(U_1422,bool),fun(sum_sum(U_1420,U_1422),bool)),sum_Plus(U_1420,U_1422),U_1416),U_1418)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1420,bool),nat,finite_card(U_1420),U_1416)),hAPP(fun(U_1422,bool),nat,finite_card(U_1422),U_1418))
| ~ hBOOL(hAPP(fun(U_1422,bool),bool,finite_finite_1(U_1422),U_1418))
| ~ hBOOL(hAPP(fun(U_1420,bool),bool,finite_finite_1(U_1420),U_1416)) ),
inference(clausify,[status(thm)],[f_380_3]) ).
cnf(f_380_5,plain,
( hBOOL(hAPP(fun(U_1421,bool),bool,finite_finite_1(U_1421),U_1417))
| hAPP(fun(sum_sum(U_1421,U_1423),bool),nat,finite_card(sum_sum(U_1421,U_1423)),hAPP(fun(U_1423,bool),fun(sum_sum(U_1421,U_1423),bool),hAPP(fun(U_1421,bool),fun(fun(U_1423,bool),fun(sum_sum(U_1421,U_1423),bool)),sum_Plus(U_1421,U_1423),U_1417),U_1419)) = zero_zero(nat) ),
inference(clausify,[status(thm)],[f_380_3]) ).
cnf(f_380_6,plain,
( hBOOL(hAPP(fun(U_1423,bool),bool,finite_finite_1(U_1423),U_1419))
| hAPP(fun(sum_sum(U_1421,U_1423),bool),nat,finite_card(sum_sum(U_1421,U_1423)),hAPP(fun(U_1423,bool),fun(sum_sum(U_1421,U_1423),bool),hAPP(fun(U_1421,bool),fun(fun(U_1423,bool),fun(sum_sum(U_1421,U_1423),bool)),sum_Plus(U_1421,U_1423),U_1417),U_1419)) = zero_zero(nat) ),
inference(clausify,[status(thm)],[f_380_3]) ).
fof(f_381_1,plain,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))),
inference(fof_nnf,[status(thm)],[fact_318_less__zeroE]) ).
fof(f_381_2,plain,
! [U_1424] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1424),zero_zero(nat))),
inference(variable_rename,[status(thm)],[f_381_1]) ).
cnf(f_381_3,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1424),zero_zero(nat))),
inference(clausify,[status(thm)],[f_381_2]) ).
fof(f_382_1,plain,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1)),
inference(fof_nnf,[status(thm)],[fact_319_le0]) ).
fof(f_382_2,plain,
! [U_1425] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1425)),
inference(variable_rename,[status(thm)],[f_382_1]) ).
cnf(f_382_3,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1425)),
inference(clausify,[status(thm)],[f_382_2]) ).
fof(f_383_1,plain,
! [N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))
| N_1 = zero_zero(nat) ),
inference(fof_nnf,[status(thm)],[fact_320_gr0I]) ).
fof(f_383_2,plain,
! [U_1426] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1426))
| U_1426 = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
cnf(f_383_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1426))
| U_1426 = zero_zero(nat) ),
inference(clausify,[status(thm)],[f_383_2]) ).
fof(f_384_1,plain,
! [M_3,N_1] :
( N_1 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_321_gr__implies__not0]) ).
fof(f_384_2,plain,
! [U_1428,U_1427] :
( U_1427 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1428),U_1427)) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
cnf(f_384_3,plain,
( U_1427 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1428),U_1427)) ),
inference(clausify,[status(thm)],[f_384_2]) ).
fof(f_385_1,plain,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))),
inference(fof_nnf,[status(thm)],[fact_322_less__nat__zero__code]) ).
fof(f_385_2,plain,
! [U_1429] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1429),zero_zero(nat))),
inference(variable_rename,[status(thm)],[f_385_1]) ).
cnf(f_385_3,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1429),zero_zero(nat))),
inference(clausify,[status(thm)],[f_385_2]) ).
fof(f_386_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_323_neq0__conv]) ).
fof(f_386_2,plain,
! [U_1430] :
( ( U_1430 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1430)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1430))
| U_1430 = zero_zero(nat) ) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
( ! [U_1432] :
( U_1432 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1432)) )
& ! [U_1431] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1431))
| U_1431 = zero_zero(nat) ) ),
inference(miniscope,[status(thm)],[f_386_2]) ).
cnf(f_386_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1431))
| U_1431 = zero_zero(nat) ),
inference(clausify,[status(thm)],[f_386_3]) ).
cnf(f_386_5,plain,
( U_1432 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1432)) ),
inference(clausify,[status(thm)],[f_386_3]) ).
fof(f_387_1,plain,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat))),
inference(fof_nnf,[status(thm)],[fact_324_not__less0]) ).
fof(f_387_2,plain,
! [U_1433] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),zero_zero(nat))),
inference(variable_rename,[status(thm)],[f_387_1]) ).
cnf(f_387_3,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),zero_zero(nat))),
inference(clausify,[status(thm)],[f_387_2]) ).
fof(f_388_1,plain,
! [N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_1) = N_1,
inference(fof_nnf,[status(thm)],[fact_325_plus__nat_Oadd__0]) ).
fof(f_388_2,plain,
! [U_1434] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),U_1434) = U_1434,
inference(variable_rename,[status(thm)],[f_388_1]) ).
cnf(f_388_3,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),U_1434) = U_1434,
inference(clausify,[status(thm)],[f_388_2]) ).
fof(f_389_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_326_Nat_Oadd__0__right]) ).
fof(f_389_2,plain,
! [U_1435] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1435),zero_zero(nat)) = U_1435,
inference(variable_rename,[status(thm)],[f_389_1]) ).
cnf(f_389_3,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1435),zero_zero(nat)) = U_1435,
inference(clausify,[status(thm)],[f_389_2]) ).
fof(f_390_1,plain,
! [M_2,Na] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na) = zero_zero(nat)
| Na != zero_zero(nat)
| M_2 != zero_zero(nat) )
& ( ( Na = zero_zero(nat)
& M_2 = zero_zero(nat) )
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na) != zero_zero(nat) ) ),
inference(fof_nnf,[status(thm)],[fact_327_add__is__0]) ).
fof(f_390_2,plain,
! [U_1437,U_1436] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1437),U_1436) = zero_zero(nat)
| U_1436 != zero_zero(nat)
| U_1437 != zero_zero(nat) )
& ( ( U_1436 = zero_zero(nat)
& U_1437 = zero_zero(nat) )
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1437),U_1436) != zero_zero(nat) ) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
( ! [U_1441,U_1439] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1441),U_1439) = zero_zero(nat)
| U_1439 != zero_zero(nat)
| U_1441 != zero_zero(nat) )
& ! [U_1440,U_1438] :
( ( U_1438 = zero_zero(nat)
& U_1440 = zero_zero(nat) )
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1440),U_1438) != zero_zero(nat) ) ),
inference(miniscope,[status(thm)],[f_390_2]) ).
cnf(f_390_4,plain,
( U_1440 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1440),U_1438) != zero_zero(nat) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_5,plain,
( U_1438 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1440),U_1438) != zero_zero(nat) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_6,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1441),U_1439) = zero_zero(nat)
| U_1439 != zero_zero(nat)
| U_1441 != zero_zero(nat) ),
inference(clausify,[status(thm)],[f_390_3]) ).
fof(f_391_1,plain,
! [M_3,N_1] :
( N_1 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1) != M_3 ),
inference(fof_nnf,[status(thm)],[fact_328_add__eq__self__zero]) ).
fof(f_391_2,plain,
! [U_1443,U_1442] :
( U_1442 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1443),U_1442) != U_1443 ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
cnf(f_391_3,plain,
( U_1442 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1443),U_1442) != U_1443 ),
inference(clausify,[status(thm)],[f_391_2]) ).
fof(f_392_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_329_le__0__eq]) ).
fof(f_392_2,plain,
! [U_1444] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1444),zero_zero(nat)))
| U_1444 != zero_zero(nat) )
& ( U_1444 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1444),zero_zero(nat))) ) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
fof(f_392_3,plain,
( ! [U_1446] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1446),zero_zero(nat)))
| U_1446 != zero_zero(nat) )
& ! [U_1445] :
( U_1445 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1445),zero_zero(nat))) ) ),
inference(miniscope,[status(thm)],[f_392_2]) ).
cnf(f_392_4,plain,
( U_1445 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1445),zero_zero(nat))) ),
inference(clausify,[status(thm)],[f_392_3]) ).
cnf(f_392_5,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1446),zero_zero(nat)))
| U_1446 != zero_zero(nat) ),
inference(clausify,[status(thm)],[f_392_3]) ).
fof(f_393_1,plain,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1)),
inference(fof_nnf,[status(thm)],[fact_330_less__eq__nat_Osimps_I1_J]) ).
fof(f_393_2,plain,
! [U_1447] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1447)),
inference(variable_rename,[status(thm)],[f_393_1]) ).
cnf(f_393_3,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1447)),
inference(clausify,[status(thm)],[f_393_2]) ).
fof(f_394_1,plain,
! [X_a] :
( ! [X_1] :
( ( zero_zero(X_a) = ti(X_a,X_1)
| ti(X_a,X_1) != zero_zero(X_a) )
& ( ti(X_a,X_1) = zero_zero(X_a)
| zero_zero(X_a) != ti(X_a,X_1) ) )
| ~ zero(X_a) ),
inference(fof_nnf,[status(thm)],[fact_331_zero__reorient]) ).
fof(f_394_2,plain,
! [U_1449] :
( ! [U_1448] :
( ( zero_zero(U_1449) = ti(U_1449,U_1448)
| ti(U_1449,U_1448) != zero_zero(U_1449) )
& ( ti(U_1449,U_1448) = zero_zero(U_1449)
| zero_zero(U_1449) != ti(U_1449,U_1448) ) )
| ~ zero(U_1449) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
! [U_1449] :
( ( ! [U_1451] :
( zero_zero(U_1449) = ti(U_1449,U_1451)
| ti(U_1449,U_1451) != zero_zero(U_1449) )
& ! [U_1450] :
( ti(U_1449,U_1450) = zero_zero(U_1449)
| zero_zero(U_1449) != ti(U_1449,U_1450) ) )
| ~ zero(U_1449) ),
inference(miniscope,[status(thm)],[f_394_2]) ).
cnf(f_394_4,plain,
( ti(U_1449,U_1450) = zero_zero(U_1449)
| zero_zero(U_1449) != ti(U_1449,U_1450)
| ~ zero(U_1449) ),
inference(clausify,[status(thm)],[f_394_3]) ).
cnf(f_394_5,plain,
( zero_zero(U_1449) = ti(U_1449,U_1451)
| ti(U_1449,U_1451) != zero_zero(U_1449)
| ~ zero(U_1449) ),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_1,plain,
! [X_a] :
( zero_zero(X_a) != one_one(X_a)
| ~ zero_neq_one(X_a) ),
inference(fof_nnf,[status(thm)],[fact_332_zero__neq__one]) ).
fof(f_395_2,plain,
! [U_1452] :
( zero_zero(U_1452) != one_one(U_1452)
| ~ zero_neq_one(U_1452) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
cnf(f_395_3,plain,
( zero_zero(U_1452) != one_one(U_1452)
| ~ zero_neq_one(U_1452) ),
inference(clausify,[status(thm)],[f_395_2]) ).
fof(f_396_1,plain,
! [X_a] :
( one_one(X_a) != zero_zero(X_a)
| ~ zero_neq_one(X_a) ),
inference(fof_nnf,[status(thm)],[fact_333_one__neq__zero]) ).
fof(f_396_2,plain,
! [U_1453] :
( one_one(U_1453) != zero_zero(U_1453)
| ~ zero_neq_one(U_1453) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
cnf(f_396_3,plain,
( one_one(U_1453) != zero_zero(U_1453)
| ~ zero_neq_one(U_1453) ),
inference(clausify,[status(thm)],[f_396_2]) ).
fof(f_397_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_334_add_Ocomm__neutral]) ).
fof(f_397_2,plain,
! [U_1455] :
( ! [U_1454] : hAPP(U_1455,U_1455,hAPP(U_1455,fun(U_1455,U_1455),plus_plus(U_1455),U_1454),zero_zero(U_1455)) = ti(U_1455,U_1454)
| ~ comm_monoid_add(U_1455) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
cnf(f_397_3,plain,
( hAPP(U_1455,U_1455,hAPP(U_1455,fun(U_1455,U_1455),plus_plus(U_1455),U_1454),zero_zero(U_1455)) = ti(U_1455,U_1454)
| ~ comm_monoid_add(U_1455) ),
inference(clausify,[status(thm)],[f_397_2]) ).
fof(f_398_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_335_add__0__right]) ).
fof(f_398_2,plain,
! [U_1457] :
( ! [U_1456] : hAPP(U_1457,U_1457,hAPP(U_1457,fun(U_1457,U_1457),plus_plus(U_1457),U_1456),zero_zero(U_1457)) = ti(U_1457,U_1456)
| ~ monoid_add(U_1457) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
cnf(f_398_3,plain,
( hAPP(U_1457,U_1457,hAPP(U_1457,fun(U_1457,U_1457),plus_plus(U_1457),U_1456),zero_zero(U_1457)) = ti(U_1457,U_1456)
| ~ monoid_add(U_1457) ),
inference(clausify,[status(thm)],[f_398_2]) ).
fof(f_399_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_336_double__zero__sym]) ).
fof(f_399_2,plain,
! [U_1459] :
( ! [U_1458] :
( ( zero_zero(U_1459) = hAPP(U_1459,U_1459,hAPP(U_1459,fun(U_1459,U_1459),plus_plus(U_1459),U_1458),U_1458)
| ti(U_1459,U_1458) != zero_zero(U_1459) )
& ( ti(U_1459,U_1458) = zero_zero(U_1459)
| zero_zero(U_1459) != hAPP(U_1459,U_1459,hAPP(U_1459,fun(U_1459,U_1459),plus_plus(U_1459),U_1458),U_1458) ) )
| ~ linord219039673up_add(U_1459) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
fof(f_399_3,plain,
! [U_1459] :
( ( ! [U_1461] :
( zero_zero(U_1459) = hAPP(U_1459,U_1459,hAPP(U_1459,fun(U_1459,U_1459),plus_plus(U_1459),U_1461),U_1461)
| ti(U_1459,U_1461) != zero_zero(U_1459) )
& ! [U_1460] :
( ti(U_1459,U_1460) = zero_zero(U_1459)
| zero_zero(U_1459) != hAPP(U_1459,U_1459,hAPP(U_1459,fun(U_1459,U_1459),plus_plus(U_1459),U_1460),U_1460) ) )
| ~ linord219039673up_add(U_1459) ),
inference(miniscope,[status(thm)],[f_399_2]) ).
cnf(f_399_4,plain,
( ti(U_1459,U_1460) = zero_zero(U_1459)
| zero_zero(U_1459) != hAPP(U_1459,U_1459,hAPP(U_1459,fun(U_1459,U_1459),plus_plus(U_1459),U_1460),U_1460)
| ~ linord219039673up_add(U_1459) ),
inference(clausify,[status(thm)],[f_399_3]) ).
cnf(f_399_5,plain,
( zero_zero(U_1459) = hAPP(U_1459,U_1459,hAPP(U_1459,fun(U_1459,U_1459),plus_plus(U_1459),U_1461),U_1461)
| ti(U_1459,U_1461) != zero_zero(U_1459)
| ~ linord219039673up_add(U_1459) ),
inference(clausify,[status(thm)],[f_399_3]) ).
fof(f_400_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_337_add__0]) ).
fof(f_400_2,plain,
! [U_1463] :
( ! [U_1462] : hAPP(U_1463,U_1463,hAPP(U_1463,fun(U_1463,U_1463),plus_plus(U_1463),zero_zero(U_1463)),U_1462) = ti(U_1463,U_1462)
| ~ comm_monoid_add(U_1463) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
cnf(f_400_3,plain,
( hAPP(U_1463,U_1463,hAPP(U_1463,fun(U_1463,U_1463),plus_plus(U_1463),zero_zero(U_1463)),U_1462) = ti(U_1463,U_1462)
| ~ comm_monoid_add(U_1463) ),
inference(clausify,[status(thm)],[f_400_2]) ).
fof(f_401_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_338_add__0__left]) ).
fof(f_401_2,plain,
! [U_1465] :
( ! [U_1464] : hAPP(U_1465,U_1465,hAPP(U_1465,fun(U_1465,U_1465),plus_plus(U_1465),zero_zero(U_1465)),U_1464) = ti(U_1465,U_1464)
| ~ monoid_add(U_1465) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
cnf(f_401_3,plain,
( hAPP(U_1465,U_1465,hAPP(U_1465,fun(U_1465,U_1465),plus_plus(U_1465),zero_zero(U_1465)),U_1464) = ti(U_1465,U_1464)
| ~ monoid_add(U_1465) ),
inference(clausify,[status(thm)],[f_401_2]) ).
fof(f_402_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_339_add__nonpos__nonpos]) ).
fof(f_402_2,plain,
! [U_1468] :
( ! [U_1467,U_1466] :
( hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less_eq(U_1468),hAPP(U_1468,U_1468,hAPP(U_1468,fun(U_1468,U_1468),plus_plus(U_1468),U_1466),U_1467)),zero_zero(U_1468)))
| ~ hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less_eq(U_1468),U_1467),zero_zero(U_1468)))
| ~ hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less_eq(U_1468),U_1466),zero_zero(U_1468))) )
| ~ ordere216010020id_add(U_1468) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
cnf(f_402_3,plain,
( hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less_eq(U_1468),hAPP(U_1468,U_1468,hAPP(U_1468,fun(U_1468,U_1468),plus_plus(U_1468),U_1466),U_1467)),zero_zero(U_1468)))
| ~ hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less_eq(U_1468),U_1467),zero_zero(U_1468)))
| ~ hBOOL(hAPP(U_1468,bool,hAPP(U_1468,fun(U_1468,bool),ord_less_eq(U_1468),U_1466),zero_zero(U_1468)))
| ~ ordere216010020id_add(U_1468) ),
inference(clausify,[status(thm)],[f_402_2]) ).
fof(f_403_1,plain,
! [X_a] :
( ! [B_1,A_2,C] :
( 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)))
| ~ 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)) )
| ~ ordere216010020id_add(X_a) ),
inference(fof_nnf,[status(thm)],[fact_340_add__increasing2]) ).
fof(f_403_2,plain,
! [U_1472] :
( ! [U_1471,U_1470,U_1469] :
( hBOOL(hAPP(U_1472,bool,hAPP(U_1472,fun(U_1472,bool),ord_less_eq(U_1472),U_1471),hAPP(U_1472,U_1472,hAPP(U_1472,fun(U_1472,U_1472),plus_plus(U_1472),U_1470),U_1469)))
| ~ hBOOL(hAPP(U_1472,bool,hAPP(U_1472,fun(U_1472,bool),ord_less_eq(U_1472),U_1471),U_1470))
| ~ hBOOL(hAPP(U_1472,bool,hAPP(U_1472,fun(U_1472,bool),ord_less_eq(U_1472),zero_zero(U_1472)),U_1469)) )
| ~ ordere216010020id_add(U_1472) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
cnf(f_403_3,plain,
( hBOOL(hAPP(U_1472,bool,hAPP(U_1472,fun(U_1472,bool),ord_less_eq(U_1472),U_1471),hAPP(U_1472,U_1472,hAPP(U_1472,fun(U_1472,U_1472),plus_plus(U_1472),U_1470),U_1469)))
| ~ hBOOL(hAPP(U_1472,bool,hAPP(U_1472,fun(U_1472,bool),ord_less_eq(U_1472),U_1471),U_1470))
| ~ hBOOL(hAPP(U_1472,bool,hAPP(U_1472,fun(U_1472,bool),ord_less_eq(U_1472),zero_zero(U_1472)),U_1469))
| ~ ordere216010020id_add(U_1472) ),
inference(clausify,[status(thm)],[f_403_2]) ).
fof(f_404_1,plain,
! [X_a] :
( ! [B_1,C,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)))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C))
| ~ 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_341_add__increasing]) ).
fof(f_404_2,plain,
! [U_1476] :
( ! [U_1475,U_1474,U_1473] :
( hBOOL(hAPP(U_1476,bool,hAPP(U_1476,fun(U_1476,bool),ord_less_eq(U_1476),U_1475),hAPP(U_1476,U_1476,hAPP(U_1476,fun(U_1476,U_1476),plus_plus(U_1476),U_1473),U_1474)))
| ~ hBOOL(hAPP(U_1476,bool,hAPP(U_1476,fun(U_1476,bool),ord_less_eq(U_1476),U_1475),U_1474))
| ~ hBOOL(hAPP(U_1476,bool,hAPP(U_1476,fun(U_1476,bool),ord_less_eq(U_1476),zero_zero(U_1476)),U_1473)) )
| ~ ordere216010020id_add(U_1476) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
cnf(f_404_3,plain,
( hBOOL(hAPP(U_1476,bool,hAPP(U_1476,fun(U_1476,bool),ord_less_eq(U_1476),U_1475),hAPP(U_1476,U_1476,hAPP(U_1476,fun(U_1476,U_1476),plus_plus(U_1476),U_1473),U_1474)))
| ~ hBOOL(hAPP(U_1476,bool,hAPP(U_1476,fun(U_1476,bool),ord_less_eq(U_1476),U_1475),U_1474))
| ~ hBOOL(hAPP(U_1476,bool,hAPP(U_1476,fun(U_1476,bool),ord_less_eq(U_1476),zero_zero(U_1476)),U_1473))
| ~ ordere216010020id_add(U_1476) ),
inference(clausify,[status(thm)],[f_404_2]) ).
fof(f_405_1,plain,
! [X_a] :
( ! [Y_2,X_1] :
( ( ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_2) = zero_zero(X_a)
| ti(X_a,Y_2) != zero_zero(X_a)
| ti(X_a,X_1) != zero_zero(X_a) )
& ( ( ti(X_a,Y_2) = zero_zero(X_a)
& ti(X_a,X_1) = zero_zero(X_a) )
| hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_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)),Y_2))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) )
| ~ ordere216010020id_add(X_a) ),
inference(fof_nnf,[status(thm)],[fact_342_add__nonneg__eq__0__iff]) ).
fof(f_405_2,plain,
! [U_1479] :
( ! [U_1478,U_1477] :
( ( ( hAPP(U_1479,U_1479,hAPP(U_1479,fun(U_1479,U_1479),plus_plus(U_1479),U_1477),U_1478) = zero_zero(U_1479)
| ti(U_1479,U_1478) != zero_zero(U_1479)
| ti(U_1479,U_1477) != zero_zero(U_1479) )
& ( ( ti(U_1479,U_1478) = zero_zero(U_1479)
& ti(U_1479,U_1477) = zero_zero(U_1479) )
| hAPP(U_1479,U_1479,hAPP(U_1479,fun(U_1479,U_1479),plus_plus(U_1479),U_1477),U_1478) != zero_zero(U_1479) ) )
| ~ hBOOL(hAPP(U_1479,bool,hAPP(U_1479,fun(U_1479,bool),ord_less_eq(U_1479),zero_zero(U_1479)),U_1478))
| ~ hBOOL(hAPP(U_1479,bool,hAPP(U_1479,fun(U_1479,bool),ord_less_eq(U_1479),zero_zero(U_1479)),U_1477)) )
| ~ ordere216010020id_add(U_1479) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
cnf(f_405_3,plain,
( ti(U_1479,U_1477) = zero_zero(U_1479)
| hAPP(U_1479,U_1479,hAPP(U_1479,fun(U_1479,U_1479),plus_plus(U_1479),U_1477),U_1478) != zero_zero(U_1479)
| ~ hBOOL(hAPP(U_1479,bool,hAPP(U_1479,fun(U_1479,bool),ord_less_eq(U_1479),zero_zero(U_1479)),U_1478))
| ~ hBOOL(hAPP(U_1479,bool,hAPP(U_1479,fun(U_1479,bool),ord_less_eq(U_1479),zero_zero(U_1479)),U_1477))
| ~ ordere216010020id_add(U_1479) ),
inference(clausify,[status(thm)],[f_405_2]) ).
cnf(f_405_4,plain,
( ti(U_1479,U_1478) = zero_zero(U_1479)
| hAPP(U_1479,U_1479,hAPP(U_1479,fun(U_1479,U_1479),plus_plus(U_1479),U_1477),U_1478) != zero_zero(U_1479)
| ~ hBOOL(hAPP(U_1479,bool,hAPP(U_1479,fun(U_1479,bool),ord_less_eq(U_1479),zero_zero(U_1479)),U_1478))
| ~ hBOOL(hAPP(U_1479,bool,hAPP(U_1479,fun(U_1479,bool),ord_less_eq(U_1479),zero_zero(U_1479)),U_1477))
| ~ ordere216010020id_add(U_1479) ),
inference(clausify,[status(thm)],[f_405_2]) ).
cnf(f_405_5,plain,
( hAPP(U_1479,U_1479,hAPP(U_1479,fun(U_1479,U_1479),plus_plus(U_1479),U_1477),U_1478) = zero_zero(U_1479)
| ti(U_1479,U_1478) != zero_zero(U_1479)
| ti(U_1479,U_1477) != zero_zero(U_1479)
| ~ hBOOL(hAPP(U_1479,bool,hAPP(U_1479,fun(U_1479,bool),ord_less_eq(U_1479),zero_zero(U_1479)),U_1478))
| ~ hBOOL(hAPP(U_1479,bool,hAPP(U_1479,fun(U_1479,bool),ord_less_eq(U_1479),zero_zero(U_1479)),U_1477))
| ~ ordere216010020id_add(U_1479) ),
inference(clausify,[status(thm)],[f_405_2]) ).
fof(f_406_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_343_add__nonneg__nonneg]) ).
fof(f_406_2,plain,
! [U_1482] :
( ! [U_1481,U_1480] :
( hBOOL(hAPP(U_1482,bool,hAPP(U_1482,fun(U_1482,bool),ord_less_eq(U_1482),zero_zero(U_1482)),hAPP(U_1482,U_1482,hAPP(U_1482,fun(U_1482,U_1482),plus_plus(U_1482),U_1480),U_1481)))
| ~ hBOOL(hAPP(U_1482,bool,hAPP(U_1482,fun(U_1482,bool),ord_less_eq(U_1482),zero_zero(U_1482)),U_1481))
| ~ hBOOL(hAPP(U_1482,bool,hAPP(U_1482,fun(U_1482,bool),ord_less_eq(U_1482),zero_zero(U_1482)),U_1480)) )
| ~ ordere216010020id_add(U_1482) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
cnf(f_406_3,plain,
( hBOOL(hAPP(U_1482,bool,hAPP(U_1482,fun(U_1482,bool),ord_less_eq(U_1482),zero_zero(U_1482)),hAPP(U_1482,U_1482,hAPP(U_1482,fun(U_1482,U_1482),plus_plus(U_1482),U_1480),U_1481)))
| ~ hBOOL(hAPP(U_1482,bool,hAPP(U_1482,fun(U_1482,bool),ord_less_eq(U_1482),zero_zero(U_1482)),U_1481))
| ~ hBOOL(hAPP(U_1482,bool,hAPP(U_1482,fun(U_1482,bool),ord_less_eq(U_1482),zero_zero(U_1482)),U_1480))
| ~ ordere216010020id_add(U_1482) ),
inference(clausify,[status(thm)],[f_406_2]) ).
fof(f_407_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_344_double__add__le__zero__iff__single__add__le__zero]) ).
fof(f_407_2,plain,
! [U_1484] :
( ! [U_1483] :
( ( hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),hAPP(U_1484,U_1484,hAPP(U_1484,fun(U_1484,U_1484),plus_plus(U_1484),U_1483),U_1483)),zero_zero(U_1484)))
| ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1483),zero_zero(U_1484))) )
& ( hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1483),zero_zero(U_1484)))
| ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),hAPP(U_1484,U_1484,hAPP(U_1484,fun(U_1484,U_1484),plus_plus(U_1484),U_1483),U_1483)),zero_zero(U_1484))) ) )
| ~ linord219039673up_add(U_1484) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
fof(f_407_3,plain,
! [U_1484] :
( ( ! [U_1486] :
( hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),hAPP(U_1484,U_1484,hAPP(U_1484,fun(U_1484,U_1484),plus_plus(U_1484),U_1486),U_1486)),zero_zero(U_1484)))
| ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1486),zero_zero(U_1484))) )
& ! [U_1485] :
( hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1485),zero_zero(U_1484)))
| ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),hAPP(U_1484,U_1484,hAPP(U_1484,fun(U_1484,U_1484),plus_plus(U_1484),U_1485),U_1485)),zero_zero(U_1484))) ) )
| ~ linord219039673up_add(U_1484) ),
inference(miniscope,[status(thm)],[f_407_2]) ).
cnf(f_407_4,plain,
( hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1485),zero_zero(U_1484)))
| ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),hAPP(U_1484,U_1484,hAPP(U_1484,fun(U_1484,U_1484),plus_plus(U_1484),U_1485),U_1485)),zero_zero(U_1484)))
| ~ linord219039673up_add(U_1484) ),
inference(clausify,[status(thm)],[f_407_3]) ).
cnf(f_407_5,plain,
( hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),hAPP(U_1484,U_1484,hAPP(U_1484,fun(U_1484,U_1484),plus_plus(U_1484),U_1486),U_1486)),zero_zero(U_1484)))
| ~ hBOOL(hAPP(U_1484,bool,hAPP(U_1484,fun(U_1484,bool),ord_less_eq(U_1484),U_1486),zero_zero(U_1484)))
| ~ linord219039673up_add(U_1484) ),
inference(clausify,[status(thm)],[f_407_3]) ).
fof(f_408_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_345_zero__le__double__add__iff__zero__le__single__add]) ).
fof(f_408_2,plain,
! [U_1488] :
( ! [U_1487] :
( ( hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),hAPP(U_1488,U_1488,hAPP(U_1488,fun(U_1488,U_1488),plus_plus(U_1488),U_1487),U_1487)))
| ~ hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),U_1487)) )
& ( hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),U_1487))
| ~ hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),hAPP(U_1488,U_1488,hAPP(U_1488,fun(U_1488,U_1488),plus_plus(U_1488),U_1487),U_1487))) ) )
| ~ linord219039673up_add(U_1488) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
fof(f_408_3,plain,
! [U_1488] :
( ( ! [U_1490] :
( hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),hAPP(U_1488,U_1488,hAPP(U_1488,fun(U_1488,U_1488),plus_plus(U_1488),U_1490),U_1490)))
| ~ hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),U_1490)) )
& ! [U_1489] :
( hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),U_1489))
| ~ hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),hAPP(U_1488,U_1488,hAPP(U_1488,fun(U_1488,U_1488),plus_plus(U_1488),U_1489),U_1489))) ) )
| ~ linord219039673up_add(U_1488) ),
inference(miniscope,[status(thm)],[f_408_2]) ).
cnf(f_408_4,plain,
( hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),U_1489))
| ~ hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),hAPP(U_1488,U_1488,hAPP(U_1488,fun(U_1488,U_1488),plus_plus(U_1488),U_1489),U_1489)))
| ~ linord219039673up_add(U_1488) ),
inference(clausify,[status(thm)],[f_408_3]) ).
cnf(f_408_5,plain,
( hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),hAPP(U_1488,U_1488,hAPP(U_1488,fun(U_1488,U_1488),plus_plus(U_1488),U_1490),U_1490)))
| ~ hBOOL(hAPP(U_1488,bool,hAPP(U_1488,fun(U_1488,bool),ord_less_eq(U_1488),zero_zero(U_1488)),U_1490))
| ~ linord219039673up_add(U_1488) ),
inference(clausify,[status(thm)],[f_408_3]) ).
fof(f_409_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_346_add__neg__neg]) ).
fof(f_409_2,plain,
! [U_1493] :
( ! [U_1492,U_1491] :
( hBOOL(hAPP(U_1493,bool,hAPP(U_1493,fun(U_1493,bool),ord_less(U_1493),hAPP(U_1493,U_1493,hAPP(U_1493,fun(U_1493,U_1493),plus_plus(U_1493),U_1491),U_1492)),zero_zero(U_1493)))
| ~ hBOOL(hAPP(U_1493,bool,hAPP(U_1493,fun(U_1493,bool),ord_less(U_1493),U_1492),zero_zero(U_1493)))
| ~ hBOOL(hAPP(U_1493,bool,hAPP(U_1493,fun(U_1493,bool),ord_less(U_1493),U_1491),zero_zero(U_1493))) )
| ~ ordere216010020id_add(U_1493) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
cnf(f_409_3,plain,
( hBOOL(hAPP(U_1493,bool,hAPP(U_1493,fun(U_1493,bool),ord_less(U_1493),hAPP(U_1493,U_1493,hAPP(U_1493,fun(U_1493,U_1493),plus_plus(U_1493),U_1491),U_1492)),zero_zero(U_1493)))
| ~ hBOOL(hAPP(U_1493,bool,hAPP(U_1493,fun(U_1493,bool),ord_less(U_1493),U_1492),zero_zero(U_1493)))
| ~ hBOOL(hAPP(U_1493,bool,hAPP(U_1493,fun(U_1493,bool),ord_less(U_1493),U_1491),zero_zero(U_1493)))
| ~ ordere216010020id_add(U_1493) ),
inference(clausify,[status(thm)],[f_409_2]) ).
fof(f_410_1,plain,
! [X_a] :
( ! [B_1,C,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)))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C))
| ~ 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_347_pos__add__strict]) ).
fof(f_410_2,plain,
! [U_1497] :
( ! [U_1496,U_1495,U_1494] :
( hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1496),hAPP(U_1497,U_1497,hAPP(U_1497,fun(U_1497,U_1497),plus_plus(U_1497),U_1494),U_1495)))
| ~ hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1496),U_1495))
| ~ hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),zero_zero(U_1497)),U_1494)) )
| ~ linordered_semidom(U_1497) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
cnf(f_410_3,plain,
( hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1496),hAPP(U_1497,U_1497,hAPP(U_1497,fun(U_1497,U_1497),plus_plus(U_1497),U_1494),U_1495)))
| ~ hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1496),U_1495))
| ~ hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),zero_zero(U_1497)),U_1494))
| ~ linordered_semidom(U_1497) ),
inference(clausify,[status(thm)],[f_410_2]) ).
fof(f_411_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_348_add__pos__pos]) ).
fof(f_411_2,plain,
! [U_1500] :
( ! [U_1499,U_1498] :
( hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),zero_zero(U_1500)),hAPP(U_1500,U_1500,hAPP(U_1500,fun(U_1500,U_1500),plus_plus(U_1500),U_1498),U_1499)))
| ~ hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),zero_zero(U_1500)),U_1499))
| ~ hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),zero_zero(U_1500)),U_1498)) )
| ~ ordere216010020id_add(U_1500) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
cnf(f_411_3,plain,
( hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),zero_zero(U_1500)),hAPP(U_1500,U_1500,hAPP(U_1500,fun(U_1500,U_1500),plus_plus(U_1500),U_1498),U_1499)))
| ~ hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),zero_zero(U_1500)),U_1499))
| ~ hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),zero_zero(U_1500)),U_1498))
| ~ ordere216010020id_add(U_1500) ),
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_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_349_double__add__less__zero__iff__single__add__less__zero]) ).
fof(f_412_2,plain,
! [U_1502] :
( ! [U_1501] :
( ( hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),hAPP(U_1502,U_1502,hAPP(U_1502,fun(U_1502,U_1502),plus_plus(U_1502),U_1501),U_1501)),zero_zero(U_1502)))
| ~ hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),U_1501),zero_zero(U_1502))) )
& ( hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),U_1501),zero_zero(U_1502)))
| ~ hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),hAPP(U_1502,U_1502,hAPP(U_1502,fun(U_1502,U_1502),plus_plus(U_1502),U_1501),U_1501)),zero_zero(U_1502))) ) )
| ~ linord219039673up_add(U_1502) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
fof(f_412_3,plain,
! [U_1502] :
( ( ! [U_1504] :
( hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),hAPP(U_1502,U_1502,hAPP(U_1502,fun(U_1502,U_1502),plus_plus(U_1502),U_1504),U_1504)),zero_zero(U_1502)))
| ~ hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),U_1504),zero_zero(U_1502))) )
& ! [U_1503] :
( hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),U_1503),zero_zero(U_1502)))
| ~ hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),hAPP(U_1502,U_1502,hAPP(U_1502,fun(U_1502,U_1502),plus_plus(U_1502),U_1503),U_1503)),zero_zero(U_1502))) ) )
| ~ linord219039673up_add(U_1502) ),
inference(miniscope,[status(thm)],[f_412_2]) ).
cnf(f_412_4,plain,
( hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),U_1503),zero_zero(U_1502)))
| ~ hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),hAPP(U_1502,U_1502,hAPP(U_1502,fun(U_1502,U_1502),plus_plus(U_1502),U_1503),U_1503)),zero_zero(U_1502)))
| ~ linord219039673up_add(U_1502) ),
inference(clausify,[status(thm)],[f_412_3]) ).
cnf(f_412_5,plain,
( hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),hAPP(U_1502,U_1502,hAPP(U_1502,fun(U_1502,U_1502),plus_plus(U_1502),U_1504),U_1504)),zero_zero(U_1502)))
| ~ hBOOL(hAPP(U_1502,bool,hAPP(U_1502,fun(U_1502,bool),ord_less(U_1502),U_1504),zero_zero(U_1502)))
| ~ linord219039673up_add(U_1502) ),
inference(clausify,[status(thm)],[f_412_3]) ).
fof(f_413_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_350_zero__less__double__add__iff__zero__less__single__add]) ).
fof(f_413_2,plain,
! [U_1506] :
( ! [U_1505] :
( ( hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),hAPP(U_1506,U_1506,hAPP(U_1506,fun(U_1506,U_1506),plus_plus(U_1506),U_1505),U_1505)))
| ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),U_1505)) )
& ( hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),U_1505))
| ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),hAPP(U_1506,U_1506,hAPP(U_1506,fun(U_1506,U_1506),plus_plus(U_1506),U_1505),U_1505))) ) )
| ~ linord219039673up_add(U_1506) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
fof(f_413_3,plain,
! [U_1506] :
( ( ! [U_1508] :
( hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),hAPP(U_1506,U_1506,hAPP(U_1506,fun(U_1506,U_1506),plus_plus(U_1506),U_1508),U_1508)))
| ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),U_1508)) )
& ! [U_1507] :
( hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),U_1507))
| ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),hAPP(U_1506,U_1506,hAPP(U_1506,fun(U_1506,U_1506),plus_plus(U_1506),U_1507),U_1507))) ) )
| ~ linord219039673up_add(U_1506) ),
inference(miniscope,[status(thm)],[f_413_2]) ).
cnf(f_413_4,plain,
( hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),U_1507))
| ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),hAPP(U_1506,U_1506,hAPP(U_1506,fun(U_1506,U_1506),plus_plus(U_1506),U_1507),U_1507)))
| ~ linord219039673up_add(U_1506) ),
inference(clausify,[status(thm)],[f_413_3]) ).
cnf(f_413_5,plain,
( hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),hAPP(U_1506,U_1506,hAPP(U_1506,fun(U_1506,U_1506),plus_plus(U_1506),U_1508),U_1508)))
| ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),zero_zero(U_1506)),U_1508))
| ~ linord219039673up_add(U_1506) ),
inference(clausify,[status(thm)],[f_413_3]) ).
fof(f_414_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_351_zero__le__one]) ).
fof(f_414_2,plain,
! [U_1509] :
( hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less_eq(U_1509),zero_zero(U_1509)),one_one(U_1509)))
| ~ linordered_semidom(U_1509) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
cnf(f_414_3,plain,
( hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less_eq(U_1509),zero_zero(U_1509)),one_one(U_1509)))
| ~ linordered_semidom(U_1509) ),
inference(clausify,[status(thm)],[f_414_2]) ).
fof(f_415_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_352_not__one__le__zero]) ).
fof(f_415_2,plain,
! [U_1510] :
( ~ hBOOL(hAPP(U_1510,bool,hAPP(U_1510,fun(U_1510,bool),ord_less_eq(U_1510),one_one(U_1510)),zero_zero(U_1510)))
| ~ linordered_semidom(U_1510) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
cnf(f_415_3,plain,
( ~ hBOOL(hAPP(U_1510,bool,hAPP(U_1510,fun(U_1510,bool),ord_less_eq(U_1510),one_one(U_1510)),zero_zero(U_1510)))
| ~ linordered_semidom(U_1510) ),
inference(clausify,[status(thm)],[f_415_2]) ).
fof(f_416_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_353_zero__less__one]) ).
fof(f_416_2,plain,
! [U_1511] :
( hBOOL(hAPP(U_1511,bool,hAPP(U_1511,fun(U_1511,bool),ord_less(U_1511),zero_zero(U_1511)),one_one(U_1511)))
| ~ linordered_semidom(U_1511) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
cnf(f_416_3,plain,
( hBOOL(hAPP(U_1511,bool,hAPP(U_1511,fun(U_1511,bool),ord_less(U_1511),zero_zero(U_1511)),one_one(U_1511)))
| ~ linordered_semidom(U_1511) ),
inference(clausify,[status(thm)],[f_416_2]) ).
fof(f_417_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_354_not__one__less__zero]) ).
fof(f_417_2,plain,
! [U_1512] :
( ~ hBOOL(hAPP(U_1512,bool,hAPP(U_1512,fun(U_1512,bool),ord_less(U_1512),one_one(U_1512)),zero_zero(U_1512)))
| ~ linordered_semidom(U_1512) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
cnf(f_417_3,plain,
( ~ hBOOL(hAPP(U_1512,bool,hAPP(U_1512,fun(U_1512,bool),ord_less(U_1512),one_one(U_1512)),zero_zero(U_1512)))
| ~ linordered_semidom(U_1512) ),
inference(clausify,[status(thm)],[f_417_2]) ).
fof(f_418_1,plain,
! [M_2,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_2),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_2)) ) )
& ( 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_2))
| ~ 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_2),Na))) ) ),
inference(fof_nnf,[status(thm)],[fact_355_add__gr__0]) ).
fof(f_418_2,plain,
! [U_1514,U_1513] :
( ( 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_1514),U_1513)))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1513))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1514)) ) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1513))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1514))
| ~ 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_1514),U_1513))) ) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
fof(f_418_3,plain,
( ! [U_1518,U_1516] :
( 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_1518),U_1516)))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1516))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1518)) ) )
& ! [U_1517,U_1515] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1515))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1517))
| ~ 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_1517),U_1515))) ) ),
inference(miniscope,[status(thm)],[f_418_2]) ).
cnf(f_418_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1515))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1517))
| ~ 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_1517),U_1515))) ),
inference(clausify,[status(thm)],[f_418_3]) ).
cnf(f_418_5,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1518))
| 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_1518),U_1516))) ),
inference(clausify,[status(thm)],[f_418_3]) ).
cnf(f_418_6,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1516))
| 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_1518),U_1516))) ),
inference(clausify,[status(thm)],[f_418_3]) ).
fof(f_419_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_356_card__infinite]) ).
fof(f_419_2,plain,
! [U_1520,U_1519] :
( hAPP(fun(U_1520,bool),nat,finite_card(U_1520),U_1519) = zero_zero(nat)
| hBOOL(hAPP(fun(U_1520,bool),bool,finite_finite_1(U_1520),U_1519)) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
cnf(f_419_3,plain,
( hAPP(fun(U_1520,bool),nat,finite_card(U_1520),U_1519) = zero_zero(nat)
| hBOOL(hAPP(fun(U_1520,bool),bool,finite_finite_1(U_1520),U_1519)) ),
inference(clausify,[status(thm)],[f_419_2]) ).
fof(f_420_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_357_add__nonpos__neg]) ).
fof(f_420_2,plain,
! [U_1523] :
( ! [U_1522,U_1521] :
( hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less(U_1523),hAPP(U_1523,U_1523,hAPP(U_1523,fun(U_1523,U_1523),plus_plus(U_1523),U_1521),U_1522)),zero_zero(U_1523)))
| ~ hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less(U_1523),U_1522),zero_zero(U_1523)))
| ~ hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less_eq(U_1523),U_1521),zero_zero(U_1523))) )
| ~ ordere216010020id_add(U_1523) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
cnf(f_420_3,plain,
( hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less(U_1523),hAPP(U_1523,U_1523,hAPP(U_1523,fun(U_1523,U_1523),plus_plus(U_1523),U_1521),U_1522)),zero_zero(U_1523)))
| ~ hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less(U_1523),U_1522),zero_zero(U_1523)))
| ~ hBOOL(hAPP(U_1523,bool,hAPP(U_1523,fun(U_1523,bool),ord_less_eq(U_1523),U_1521),zero_zero(U_1523)))
| ~ ordere216010020id_add(U_1523) ),
inference(clausify,[status(thm)],[f_420_2]) ).
fof(f_421_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_358_add__neg__nonpos]) ).
fof(f_421_2,plain,
! [U_1526] :
( ! [U_1525,U_1524] :
( hBOOL(hAPP(U_1526,bool,hAPP(U_1526,fun(U_1526,bool),ord_less(U_1526),hAPP(U_1526,U_1526,hAPP(U_1526,fun(U_1526,U_1526),plus_plus(U_1526),U_1524),U_1525)),zero_zero(U_1526)))
| ~ hBOOL(hAPP(U_1526,bool,hAPP(U_1526,fun(U_1526,bool),ord_less_eq(U_1526),U_1525),zero_zero(U_1526)))
| ~ hBOOL(hAPP(U_1526,bool,hAPP(U_1526,fun(U_1526,bool),ord_less(U_1526),U_1524),zero_zero(U_1526))) )
| ~ ordere216010020id_add(U_1526) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
cnf(f_421_3,plain,
( hBOOL(hAPP(U_1526,bool,hAPP(U_1526,fun(U_1526,bool),ord_less(U_1526),hAPP(U_1526,U_1526,hAPP(U_1526,fun(U_1526,U_1526),plus_plus(U_1526),U_1524),U_1525)),zero_zero(U_1526)))
| ~ hBOOL(hAPP(U_1526,bool,hAPP(U_1526,fun(U_1526,bool),ord_less_eq(U_1526),U_1525),zero_zero(U_1526)))
| ~ hBOOL(hAPP(U_1526,bool,hAPP(U_1526,fun(U_1526,bool),ord_less(U_1526),U_1524),zero_zero(U_1526)))
| ~ ordere216010020id_add(U_1526) ),
inference(clausify,[status(thm)],[f_421_2]) ).
fof(f_422_1,plain,
! [X_a] :
( ! [B_1,C,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)))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C))
| ~ 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_359_add__strict__increasing2]) ).
fof(f_422_2,plain,
! [U_1530] :
( ! [U_1529,U_1528,U_1527] :
( hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less(U_1530),U_1529),hAPP(U_1530,U_1530,hAPP(U_1530,fun(U_1530,U_1530),plus_plus(U_1530),U_1527),U_1528)))
| ~ hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less(U_1530),U_1529),U_1528))
| ~ hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less_eq(U_1530),zero_zero(U_1530)),U_1527)) )
| ~ ordere216010020id_add(U_1530) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
cnf(f_422_3,plain,
( hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less(U_1530),U_1529),hAPP(U_1530,U_1530,hAPP(U_1530,fun(U_1530,U_1530),plus_plus(U_1530),U_1527),U_1528)))
| ~ hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less(U_1530),U_1529),U_1528))
| ~ hBOOL(hAPP(U_1530,bool,hAPP(U_1530,fun(U_1530,bool),ord_less_eq(U_1530),zero_zero(U_1530)),U_1527))
| ~ ordere216010020id_add(U_1530) ),
inference(clausify,[status(thm)],[f_422_2]) ).
fof(f_423_1,plain,
! [X_a] :
( ! [B_1,C,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)))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C))
| ~ 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_360_add__strict__increasing]) ).
fof(f_423_2,plain,
! [U_1534] :
( ! [U_1533,U_1532,U_1531] :
( hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less(U_1534),U_1533),hAPP(U_1534,U_1534,hAPP(U_1534,fun(U_1534,U_1534),plus_plus(U_1534),U_1531),U_1532)))
| ~ hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less_eq(U_1534),U_1533),U_1532))
| ~ hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less(U_1534),zero_zero(U_1534)),U_1531)) )
| ~ ordere216010020id_add(U_1534) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
cnf(f_423_3,plain,
( hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less(U_1534),U_1533),hAPP(U_1534,U_1534,hAPP(U_1534,fun(U_1534,U_1534),plus_plus(U_1534),U_1531),U_1532)))
| ~ hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less_eq(U_1534),U_1533),U_1532))
| ~ hBOOL(hAPP(U_1534,bool,hAPP(U_1534,fun(U_1534,bool),ord_less(U_1534),zero_zero(U_1534)),U_1531))
| ~ ordere216010020id_add(U_1534) ),
inference(clausify,[status(thm)],[f_423_2]) ).
fof(f_424_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_361_add__nonneg__pos]) ).
fof(f_424_2,plain,
! [U_1537] :
( ! [U_1536,U_1535] :
( hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less(U_1537),zero_zero(U_1537)),hAPP(U_1537,U_1537,hAPP(U_1537,fun(U_1537,U_1537),plus_plus(U_1537),U_1535),U_1536)))
| ~ hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less(U_1537),zero_zero(U_1537)),U_1536))
| ~ hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less_eq(U_1537),zero_zero(U_1537)),U_1535)) )
| ~ ordere216010020id_add(U_1537) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
cnf(f_424_3,plain,
( hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less(U_1537),zero_zero(U_1537)),hAPP(U_1537,U_1537,hAPP(U_1537,fun(U_1537,U_1537),plus_plus(U_1537),U_1535),U_1536)))
| ~ hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less(U_1537),zero_zero(U_1537)),U_1536))
| ~ hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less_eq(U_1537),zero_zero(U_1537)),U_1535))
| ~ ordere216010020id_add(U_1537) ),
inference(clausify,[status(thm)],[f_424_2]) ).
fof(f_425_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_362_add__pos__nonneg]) ).
fof(f_425_2,plain,
! [U_1540] :
( ! [U_1539,U_1538] :
( hBOOL(hAPP(U_1540,bool,hAPP(U_1540,fun(U_1540,bool),ord_less(U_1540),zero_zero(U_1540)),hAPP(U_1540,U_1540,hAPP(U_1540,fun(U_1540,U_1540),plus_plus(U_1540),U_1538),U_1539)))
| ~ hBOOL(hAPP(U_1540,bool,hAPP(U_1540,fun(U_1540,bool),ord_less_eq(U_1540),zero_zero(U_1540)),U_1539))
| ~ hBOOL(hAPP(U_1540,bool,hAPP(U_1540,fun(U_1540,bool),ord_less(U_1540),zero_zero(U_1540)),U_1538)) )
| ~ ordere216010020id_add(U_1540) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
cnf(f_425_3,plain,
( hBOOL(hAPP(U_1540,bool,hAPP(U_1540,fun(U_1540,bool),ord_less(U_1540),zero_zero(U_1540)),hAPP(U_1540,U_1540,hAPP(U_1540,fun(U_1540,U_1540),plus_plus(U_1540),U_1538),U_1539)))
| ~ hBOOL(hAPP(U_1540,bool,hAPP(U_1540,fun(U_1540,bool),ord_less_eq(U_1540),zero_zero(U_1540)),U_1539))
| ~ hBOOL(hAPP(U_1540,bool,hAPP(U_1540,fun(U_1540,bool),ord_less(U_1540),zero_zero(U_1540)),U_1538))
| ~ ordere216010020id_add(U_1540) ),
inference(clausify,[status(thm)],[f_425_2]) ).
fof(f_426_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_363_zero__less__two]) ).
fof(f_426_2,plain,
! [U_1541] :
( 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),one_one(U_1541)),one_one(U_1541))))
| ~ linordered_semidom(U_1541) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
cnf(f_426_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),one_one(U_1541)),one_one(U_1541))))
| ~ linordered_semidom(U_1541) ),
inference(clausify,[status(thm)],[f_426_2]) ).
fof(f_427_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_364_card__ge__0__finite]) ).
fof(f_427_2,plain,
! [U_1543,U_1542] :
( hBOOL(hAPP(fun(U_1543,bool),bool,finite_finite_1(U_1543),U_1542))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_1543,bool),nat,finite_card(U_1543),U_1542))) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
cnf(f_427_3,plain,
( hBOOL(hAPP(fun(U_1543,bool),bool,finite_finite_1(U_1543),U_1542))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_1543,bool),nat,finite_card(U_1543),U_1542))) ),
inference(clausify,[status(thm)],[f_427_2]) ).
fof(f_428_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_365_finite__UNIV__card__ge__0]) ).
fof(f_428_2,plain,
! [U_1544] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_1544,bool),nat,finite_card(U_1544),top_top(fun(U_1544,bool)))))
| ~ hBOOL(hAPP(fun(U_1544,bool),bool,finite_finite_1(U_1544),top_top(fun(U_1544,bool)))) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
cnf(f_428_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(U_1544,bool),nat,finite_card(U_1544),top_top(fun(U_1544,bool)))))
| ~ hBOOL(hAPP(fun(U_1544,bool),bool,finite_finite_1(U_1544),top_top(fun(U_1544,bool)))) ),
inference(clausify,[status(thm)],[f_428_2]) ).
fof(f_429_1,plain,
! [Na,Pa] :
( ? [K_2] :
( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),one_one(nat))))
& ! [I_2] :
( ~ hBOOL(hAPP(nat,bool,Pa,I_2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_2)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),Na)) )
| ~ hBOOL(hAPP(nat,bool,Pa,Na))
| hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ),
inference(fof_nnf,[status(thm)],[fact_366_ex__least__nat__less]) ).
fof(f_429_2,plain,
! [U_1548,U_1547] :
( ? [U_1546] :
( hBOOL(hAPP(nat,bool,U_1547,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1546),one_one(nat))))
& ! [U_1545] :
( ~ hBOOL(hAPP(nat,bool,U_1547,U_1545))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1545),U_1546)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1546),U_1548)) )
| ~ hBOOL(hAPP(nat,bool,U_1547,U_1548))
| hBOOL(hAPP(nat,bool,U_1547,zero_zero(nat))) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
fof(f_429_3,plain,
! [U_1548,U_1547] :
( ( hBOOL(hAPP(nat,bool,U_1547,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK87(U_1548,U_1547)),one_one(nat))))
& ! [U_1545] :
( ~ hBOOL(hAPP(nat,bool,U_1547,U_1545))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1545),sK87(U_1548,U_1547))) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK87(U_1548,U_1547)),U_1548)) )
| ~ hBOOL(hAPP(nat,bool,U_1547,U_1548))
| hBOOL(hAPP(nat,bool,U_1547,zero_zero(nat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_1546,sK87(U_1548,U_1547))],[f_429_2]) ).
cnf(f_429_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK87(U_1548,U_1547)),U_1548))
| ~ hBOOL(hAPP(nat,bool,U_1547,U_1548))
| hBOOL(hAPP(nat,bool,U_1547,zero_zero(nat))) ),
inference(clausify,[status(thm)],[f_429_3]) ).
cnf(f_429_5,plain,
( ~ hBOOL(hAPP(nat,bool,U_1547,U_1545))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1545),sK87(U_1548,U_1547)))
| ~ hBOOL(hAPP(nat,bool,U_1547,U_1548))
| hBOOL(hAPP(nat,bool,U_1547,zero_zero(nat))) ),
inference(clausify,[status(thm)],[f_429_3]) ).
cnf(f_429_6,plain,
( hBOOL(hAPP(nat,bool,U_1547,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sK87(U_1548,U_1547)),one_one(nat))))
| ~ hBOOL(hAPP(nat,bool,U_1547,U_1548))
| hBOOL(hAPP(nat,bool,U_1547,zero_zero(nat))) ),
inference(clausify,[status(thm)],[f_429_3]) ).
fof(f_430_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_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,finite_finite_1(X_a),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_367_card_Oneutral]) ).
fof(f_430_2,plain,
! [U_1551,U_1550] :
( hAPP(fun(U_1551,bool),nat,finite_card(U_1551),U_1550) = zero_zero(nat)
| ( one_one(nat) != zero_zero(nat)
& ? [U_1549] : hBOOL(hAPP(fun(U_1551,bool),bool,hAPP(U_1551,fun(fun(U_1551,bool),bool),member(U_1551),U_1549),U_1550)) )
| ~ hBOOL(hAPP(fun(U_1551,bool),bool,finite_finite_1(U_1551),U_1550)) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
fof(f_430_3,plain,
! [U_1551,U_1550] :
( hAPP(fun(U_1551,bool),nat,finite_card(U_1551),U_1550) = zero_zero(nat)
| ( one_one(nat) != zero_zero(nat)
& hBOOL(hAPP(fun(U_1551,bool),bool,hAPP(U_1551,fun(fun(U_1551,bool),bool),member(U_1551),sK88(U_1551,U_1550)),U_1550)) )
| ~ hBOOL(hAPP(fun(U_1551,bool),bool,finite_finite_1(U_1551),U_1550)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_1549,sK88(U_1551,U_1550))],[f_430_2]) ).
cnf(f_430_4,plain,
( hBOOL(hAPP(fun(U_1551,bool),bool,hAPP(U_1551,fun(fun(U_1551,bool),bool),member(U_1551),sK88(U_1551,U_1550)),U_1550))
| hAPP(fun(U_1551,bool),nat,finite_card(U_1551),U_1550) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(U_1551,bool),bool,finite_finite_1(U_1551),U_1550)) ),
inference(clausify,[status(thm)],[f_430_3]) ).
cnf(f_430_5,plain,
( one_one(nat) != zero_zero(nat)
| hAPP(fun(U_1551,bool),nat,finite_card(U_1551),U_1550) = zero_zero(nat)
| ~ hBOOL(hAPP(fun(U_1551,bool),bool,finite_finite_1(U_1551),U_1550)) ),
inference(clausify,[status(thm)],[f_430_3]) ).
fof(f_431_1,plain,
! [Na,Pa] :
( ? [K_2] :
( hBOOL(hAPP(nat,bool,Pa,K_2))
& ! [I_2] :
( ~ hBOOL(hAPP(nat,bool,Pa,I_2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_2)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na)) )
| ~ hBOOL(hAPP(nat,bool,Pa,Na))
| hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ),
inference(fof_nnf,[status(thm)],[fact_368_ex__least__nat__le]) ).
fof(f_431_2,plain,
! [U_1555,U_1554] :
( ? [U_1553] :
( hBOOL(hAPP(nat,bool,U_1554,U_1553))
& ! [U_1552] :
( ~ hBOOL(hAPP(nat,bool,U_1554,U_1552))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1552),U_1553)) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1553),U_1555)) )
| ~ hBOOL(hAPP(nat,bool,U_1554,U_1555))
| hBOOL(hAPP(nat,bool,U_1554,zero_zero(nat))) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
fof(f_431_3,plain,
! [U_1555,U_1554] :
( ( hBOOL(hAPP(nat,bool,U_1554,sK89(U_1555,U_1554)))
& ! [U_1552] :
( ~ hBOOL(hAPP(nat,bool,U_1554,U_1552))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1552),sK89(U_1555,U_1554))) )
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK89(U_1555,U_1554)),U_1555)) )
| ~ hBOOL(hAPP(nat,bool,U_1554,U_1555))
| hBOOL(hAPP(nat,bool,U_1554,zero_zero(nat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_1553,sK89(U_1555,U_1554))],[f_431_2]) ).
cnf(f_431_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK89(U_1555,U_1554)),U_1555))
| ~ hBOOL(hAPP(nat,bool,U_1554,U_1555))
| hBOOL(hAPP(nat,bool,U_1554,zero_zero(nat))) ),
inference(clausify,[status(thm)],[f_431_3]) ).
cnf(f_431_5,plain,
( ~ hBOOL(hAPP(nat,bool,U_1554,U_1552))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1552),sK89(U_1555,U_1554)))
| ~ hBOOL(hAPP(nat,bool,U_1554,U_1555))
| hBOOL(hAPP(nat,bool,U_1554,zero_zero(nat))) ),
inference(clausify,[status(thm)],[f_431_3]) ).
cnf(f_431_6,plain,
( hBOOL(hAPP(nat,bool,U_1554,sK89(U_1555,U_1554)))
| ~ hBOOL(hAPP(nat,bool,U_1554,U_1555))
| hBOOL(hAPP(nat,bool,U_1554,zero_zero(nat))) ),
inference(clausify,[status(thm)],[f_431_3]) ).
fof(f_432_1,plain,
! [I,J_2] :
( ? [K_2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2) = J_2
& hBOOL(hAPP(nat,bool,hAPP(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),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_369_less__imp__add__positive]) ).
fof(f_432_2,plain,
! [U_1558,U_1557] :
( ? [U_1556] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1558),U_1556) = U_1557
& 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),U_1558),U_1557)) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
fof(f_432_3,plain,
! [U_1558,U_1557] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1558),sK90(U_1558,U_1557)) = U_1557
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sK90(U_1558,U_1557))) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1558),U_1557)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_1556,sK90(U_1558,U_1557))],[f_432_2]) ).
cnf(f_432_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sK90(U_1558,U_1557)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1558),U_1557)) ),
inference(clausify,[status(thm)],[f_432_3]) ).
cnf(f_432_5,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1558),sK90(U_1558,U_1557)) = U_1557
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1558),U_1557)) ),
inference(clausify,[status(thm)],[f_432_3]) ).
fof(f_433_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_370_even__less__0__iff]) ).
fof(f_433_2,plain,
! [U_1560] :
( ! [U_1559] :
( ( hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),hAPP(U_1560,U_1560,hAPP(U_1560,fun(U_1560,U_1560),plus_plus(U_1560),U_1559),U_1559)),zero_zero(U_1560)))
| ~ hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),U_1559),zero_zero(U_1560))) )
& ( hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),U_1559),zero_zero(U_1560)))
| ~ hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),hAPP(U_1560,U_1560,hAPP(U_1560,fun(U_1560,U_1560),plus_plus(U_1560),U_1559),U_1559)),zero_zero(U_1560))) ) )
| ~ linordered_idom(U_1560) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
fof(f_433_3,plain,
! [U_1560] :
( ( ! [U_1562] :
( hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),hAPP(U_1560,U_1560,hAPP(U_1560,fun(U_1560,U_1560),plus_plus(U_1560),U_1562),U_1562)),zero_zero(U_1560)))
| ~ hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),U_1562),zero_zero(U_1560))) )
& ! [U_1561] :
( hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),U_1561),zero_zero(U_1560)))
| ~ hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),hAPP(U_1560,U_1560,hAPP(U_1560,fun(U_1560,U_1560),plus_plus(U_1560),U_1561),U_1561)),zero_zero(U_1560))) ) )
| ~ linordered_idom(U_1560) ),
inference(miniscope,[status(thm)],[f_433_2]) ).
cnf(f_433_4,plain,
( hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),U_1561),zero_zero(U_1560)))
| ~ hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),hAPP(U_1560,U_1560,hAPP(U_1560,fun(U_1560,U_1560),plus_plus(U_1560),U_1561),U_1561)),zero_zero(U_1560)))
| ~ linordered_idom(U_1560) ),
inference(clausify,[status(thm)],[f_433_3]) ).
cnf(f_433_5,plain,
( hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),hAPP(U_1560,U_1560,hAPP(U_1560,fun(U_1560,U_1560),plus_plus(U_1560),U_1562),U_1562)),zero_zero(U_1560)))
| ~ hBOOL(hAPP(U_1560,bool,hAPP(U_1560,fun(U_1560,bool),ord_less(U_1560),U_1562),zero_zero(U_1560)))
| ~ linordered_idom(U_1560) ),
inference(clausify,[status(thm)],[f_433_3]) ).
fof(f_434_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_371_double__eq__0__iff]) ).
fof(f_434_2,plain,
! [U_1564] :
( ! [U_1563] :
( ( hAPP(U_1564,U_1564,hAPP(U_1564,fun(U_1564,U_1564),plus_plus(U_1564),U_1563),U_1563) = zero_zero(U_1564)
| ti(U_1564,U_1563) != zero_zero(U_1564) )
& ( ti(U_1564,U_1563) = zero_zero(U_1564)
| hAPP(U_1564,U_1564,hAPP(U_1564,fun(U_1564,U_1564),plus_plus(U_1564),U_1563),U_1563) != zero_zero(U_1564) ) )
| ~ linord219039673up_add(U_1564) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
! [U_1564] :
( ( ! [U_1566] :
( hAPP(U_1564,U_1564,hAPP(U_1564,fun(U_1564,U_1564),plus_plus(U_1564),U_1566),U_1566) = zero_zero(U_1564)
| ti(U_1564,U_1566) != zero_zero(U_1564) )
& ! [U_1565] :
( ti(U_1564,U_1565) = zero_zero(U_1564)
| hAPP(U_1564,U_1564,hAPP(U_1564,fun(U_1564,U_1564),plus_plus(U_1564),U_1565),U_1565) != zero_zero(U_1564) ) )
| ~ linord219039673up_add(U_1564) ),
inference(miniscope,[status(thm)],[f_434_2]) ).
cnf(f_434_4,plain,
( ti(U_1564,U_1565) = zero_zero(U_1564)
| hAPP(U_1564,U_1564,hAPP(U_1564,fun(U_1564,U_1564),plus_plus(U_1564),U_1565),U_1565) != zero_zero(U_1564)
| ~ linord219039673up_add(U_1564) ),
inference(clausify,[status(thm)],[f_434_3]) ).
cnf(f_434_5,plain,
( hAPP(U_1564,U_1564,hAPP(U_1564,fun(U_1564,U_1564),plus_plus(U_1564),U_1566),U_1566) = zero_zero(U_1564)
| ti(U_1564,U_1566) != zero_zero(U_1564)
| ~ linord219039673up_add(U_1564) ),
inference(clausify,[status(thm)],[f_434_3]) ).
fof(f_435_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_435_2,plain,
! [U_1568,U_1567] :
( hBOOL(hAPP(fun(U_1568,bool),bool,finite_finite_1(U_1568),top_top(fun(U_1568,bool))))
| hAPP(fun(U_1567,bool),nat,finite_card(U_1567),top_top(fun(U_1567,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(fun(U_1568,U_1567),bool),bool,finite_finite_1(fun(U_1568,U_1567)),top_top(fun(fun(U_1568,U_1567),bool)))) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
cnf(f_435_3,plain,
( hBOOL(hAPP(fun(U_1568,bool),bool,finite_finite_1(U_1568),top_top(fun(U_1568,bool))))
| hAPP(fun(U_1567,bool),nat,finite_card(U_1567),top_top(fun(U_1567,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ hBOOL(hAPP(fun(fun(U_1568,U_1567),bool),bool,finite_finite_1(fun(U_1568,U_1567)),top_top(fun(fun(U_1568,U_1567),bool)))) ),
inference(clausify,[status(thm)],[f_435_2]) ).
fof(f_436_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_373_add__0__iff]) ).
fof(f_436_2,plain,
! [U_1571] :
( ! [U_1570,U_1569] :
( ( ti(U_1571,U_1570) = hAPP(U_1571,U_1571,hAPP(U_1571,fun(U_1571,U_1571),plus_plus(U_1571),U_1570),U_1569)
| ti(U_1571,U_1569) != zero_zero(U_1571) )
& ( ti(U_1571,U_1569) = zero_zero(U_1571)
| ti(U_1571,U_1570) != hAPP(U_1571,U_1571,hAPP(U_1571,fun(U_1571,U_1571),plus_plus(U_1571),U_1570),U_1569) ) )
| ~ semiri456707255roduct(U_1571) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
fof(f_436_3,plain,
! [U_1571] :
( ( ! [U_1575,U_1573] :
( ti(U_1571,U_1575) = hAPP(U_1571,U_1571,hAPP(U_1571,fun(U_1571,U_1571),plus_plus(U_1571),U_1575),U_1573)
| ti(U_1571,U_1573) != zero_zero(U_1571) )
& ! [U_1574,U_1572] :
( ti(U_1571,U_1572) = zero_zero(U_1571)
| ti(U_1571,U_1574) != hAPP(U_1571,U_1571,hAPP(U_1571,fun(U_1571,U_1571),plus_plus(U_1571),U_1574),U_1572) ) )
| ~ semiri456707255roduct(U_1571) ),
inference(miniscope,[status(thm)],[f_436_2]) ).
cnf(f_436_4,plain,
( ti(U_1571,U_1572) = zero_zero(U_1571)
| ti(U_1571,U_1574) != hAPP(U_1571,U_1571,hAPP(U_1571,fun(U_1571,U_1571),plus_plus(U_1571),U_1574),U_1572)
| ~ semiri456707255roduct(U_1571) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_5,plain,
( ti(U_1571,U_1575) = hAPP(U_1571,U_1571,hAPP(U_1571,fun(U_1571,U_1571),plus_plus(U_1571),U_1575),U_1573)
| ti(U_1571,U_1573) != zero_zero(U_1571)
| ~ semiri456707255roduct(U_1571) ),
inference(clausify,[status(thm)],[f_436_3]) ).
fof(f_437_1,plain,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,N_1))),
inference(fof_nnf,[status(thm)],[fact_374_lessI]) ).
fof(f_437_2,plain,
! [U_1576] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1576),hAPP(nat,nat,suc,U_1576))),
inference(variable_rename,[status(thm)],[f_437_1]) ).
cnf(f_437_3,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1576),hAPP(nat,nat,suc,U_1576))),
inference(clausify,[status(thm)],[f_437_2]) ).
fof(f_438_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),hAPP(nat,nat,suc,N_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_375_Suc__mono]) ).
fof(f_438_2,plain,
! [U_1578,U_1577] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1578)),hAPP(nat,nat,suc,U_1577)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1578),U_1577)) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
cnf(f_438_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1578)),hAPP(nat,nat,suc,U_1577)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1578),U_1577)) ),
inference(clausify,[status(thm)],[f_438_2]) ).
fof(f_439_1,plain,
! [N_1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))),
inference(fof_nnf,[status(thm)],[fact_376_zero__less__Suc]) ).
fof(f_439_2,plain,
! [U_1579] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,U_1579))),
inference(variable_rename,[status(thm)],[f_439_1]) ).
cnf(f_439_3,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,U_1579))),
inference(clausify,[status(thm)],[f_439_2]) ).
fof(f_440_1,plain,
! [N_1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1)),
inference(fof_nnf,[status(thm)],[fact_377_Suc__n__not__le__n]) ).
fof(f_440_2,plain,
! [U_1580] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1580)),U_1580)),
inference(variable_rename,[status(thm)],[f_440_1]) ).
cnf(f_440_3,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1580)),U_1580)),
inference(clausify,[status(thm)],[f_440_2]) ).
fof(f_441_1,plain,
! [M_2,Na] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_2)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) ) ),
inference(fof_nnf,[status(thm)],[fact_378_not__less__eq__eq]) ).
fof(f_441_2,plain,
! [U_1582,U_1581] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1582),U_1581))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1581)),U_1582)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1581)),U_1582))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1582),U_1581)) ) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
( ! [U_1586,U_1584] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1586),U_1584))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1584)),U_1586)) )
& ! [U_1585,U_1583] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1583)),U_1585))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1585),U_1583)) ) ),
inference(miniscope,[status(thm)],[f_441_2]) ).
cnf(f_441_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1583)),U_1585))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1585),U_1583)) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_5,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1586),U_1584))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1584)),U_1586)) ),
inference(clausify,[status(thm)],[f_441_3]) ).
fof(f_442_1,plain,
! [M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,Na)))
| ( M_2 != hAPP(nat,nat,suc,Na)
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) ) )
& ( M_2 = hAPP(nat,nat,suc,Na)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,Na))) ) ),
inference(fof_nnf,[status(thm)],[fact_379_le__Suc__eq]) ).
fof(f_442_2,plain,
! [U_1588,U_1587] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1588),hAPP(nat,nat,suc,U_1587)))
| ( U_1588 != hAPP(nat,nat,suc,U_1587)
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1588),U_1587)) ) )
& ( U_1588 = hAPP(nat,nat,suc,U_1587)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1588),U_1587))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1588),hAPP(nat,nat,suc,U_1587))) ) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
fof(f_442_3,plain,
( ! [U_1592,U_1590] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1592),hAPP(nat,nat,suc,U_1590)))
| ( U_1592 != hAPP(nat,nat,suc,U_1590)
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1592),U_1590)) ) )
& ! [U_1591,U_1589] :
( U_1591 = hAPP(nat,nat,suc,U_1589)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1591),U_1589))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1591),hAPP(nat,nat,suc,U_1589))) ) ),
inference(miniscope,[status(thm)],[f_442_2]) ).
cnf(f_442_4,plain,
( U_1591 = hAPP(nat,nat,suc,U_1589)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1591),U_1589))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1591),hAPP(nat,nat,suc,U_1589))) ),
inference(clausify,[status(thm)],[f_442_3]) ).
cnf(f_442_5,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1592),U_1590))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1592),hAPP(nat,nat,suc,U_1590))) ),
inference(clausify,[status(thm)],[f_442_3]) ).
cnf(f_442_6,plain,
( U_1592 != hAPP(nat,nat,suc,U_1590)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1592),hAPP(nat,nat,suc,U_1590))) ),
inference(clausify,[status(thm)],[f_442_3]) ).
fof(f_443_1,plain,
! [Na,M_2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_2)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_380_Suc__le__mono]) ).
fof(f_443_2,plain,
! [U_1594,U_1593] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1594)),hAPP(nat,nat,suc,U_1593)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1594),U_1593)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1594),U_1593))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1594)),hAPP(nat,nat,suc,U_1593))) ) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
( ! [U_1598,U_1596] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1598)),hAPP(nat,nat,suc,U_1596)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1598),U_1596)) )
& ! [U_1597,U_1595] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1597),U_1595))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1597)),hAPP(nat,nat,suc,U_1595))) ) ),
inference(miniscope,[status(thm)],[f_443_2]) ).
cnf(f_443_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1597),U_1595))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1597)),hAPP(nat,nat,suc,U_1595))) ),
inference(clausify,[status(thm)],[f_443_3]) ).
cnf(f_443_5,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1598)),hAPP(nat,nat,suc,U_1596)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1598),U_1596)) ),
inference(clausify,[status(thm)],[f_443_3]) ).
fof(f_444_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,N_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_381_le__SucI]) ).
fof(f_444_2,plain,
! [U_1600,U_1599] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1600),hAPP(nat,nat,suc,U_1599)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1600),U_1599)) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
cnf(f_444_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1600),hAPP(nat,nat,suc,U_1599)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1600),U_1599)) ),
inference(clausify,[status(thm)],[f_444_2]) ).
fof(f_445_1,plain,
! [M_3,N_1] :
( M_3 = hAPP(nat,nat,suc,N_1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,N_1))) ),
inference(fof_nnf,[status(thm)],[fact_382_le__SucE]) ).
fof(f_445_2,plain,
! [U_1602,U_1601] :
( U_1602 = hAPP(nat,nat,suc,U_1601)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1602),U_1601))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1602),hAPP(nat,nat,suc,U_1601))) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
cnf(f_445_3,plain,
( U_1602 = hAPP(nat,nat,suc,U_1601)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1602),U_1601))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1602),hAPP(nat,nat,suc,U_1601))) ),
inference(clausify,[status(thm)],[f_445_2]) ).
fof(f_446_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_383_Suc__leD]) ).
fof(f_446_2,plain,
! [U_1604,U_1603] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1604),U_1603))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1604)),U_1603)) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
cnf(f_446_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1604),U_1603))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1604)),U_1603)) ),
inference(clausify,[status(thm)],[f_446_2]) ).
fof(f_447_1,plain,
! [X,Y] :
( X = Y
| hAPP(nat,nat,suc,X) != hAPP(nat,nat,suc,Y) ),
inference(fof_nnf,[status(thm)],[fact_384_Suc__inject]) ).
fof(f_447_2,plain,
! [U_1606,U_1605] :
( U_1606 = U_1605
| hAPP(nat,nat,suc,U_1606) != hAPP(nat,nat,suc,U_1605) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
cnf(f_447_3,plain,
( U_1606 = U_1605
| hAPP(nat,nat,suc,U_1606) != hAPP(nat,nat,suc,U_1605) ),
inference(clausify,[status(thm)],[f_447_2]) ).
fof(f_448_1,plain,
! [Nat_4,Nat_3] :
( ( hAPP(nat,nat,suc,Nat_4) = hAPP(nat,nat,suc,Nat_3)
| Nat_4 != Nat_3 )
& ( Nat_4 = Nat_3
| hAPP(nat,nat,suc,Nat_4) != hAPP(nat,nat,suc,Nat_3) ) ),
inference(fof_nnf,[status(thm)],[fact_385_nat_Oinject]) ).
fof(f_448_2,plain,
! [U_1608,U_1607] :
( ( hAPP(nat,nat,suc,U_1608) = hAPP(nat,nat,suc,U_1607)
| U_1608 != U_1607 )
& ( U_1608 = U_1607
| hAPP(nat,nat,suc,U_1608) != hAPP(nat,nat,suc,U_1607) ) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
( ! [U_1612,U_1610] :
( hAPP(nat,nat,suc,U_1612) = hAPP(nat,nat,suc,U_1610)
| U_1612 != U_1610 )
& ! [U_1611,U_1609] :
( U_1611 = U_1609
| hAPP(nat,nat,suc,U_1611) != hAPP(nat,nat,suc,U_1609) ) ),
inference(miniscope,[status(thm)],[f_448_2]) ).
cnf(f_448_4,plain,
( U_1611 = U_1609
| hAPP(nat,nat,suc,U_1611) != hAPP(nat,nat,suc,U_1609) ),
inference(clausify,[status(thm)],[f_448_3]) ).
cnf(f_448_5,plain,
( hAPP(nat,nat,suc,U_1612) = hAPP(nat,nat,suc,U_1610)
| U_1612 != U_1610 ),
inference(clausify,[status(thm)],[f_448_3]) ).
fof(f_449_1,plain,
! [N_1] : hAPP(nat,nat,suc,N_1) != N_1,
inference(fof_nnf,[status(thm)],[fact_386_Suc__n__not__n]) ).
fof(f_449_2,plain,
! [U_1613] : hAPP(nat,nat,suc,U_1613) != U_1613,
inference(variable_rename,[status(thm)],[f_449_1]) ).
cnf(f_449_3,plain,
hAPP(nat,nat,suc,U_1613) != U_1613,
inference(clausify,[status(thm)],[f_449_2]) ).
fof(f_450_1,plain,
! [N_1] : N_1 != hAPP(nat,nat,suc,N_1),
inference(fof_nnf,[status(thm)],[fact_387_n__not__Suc__n]) ).
fof(f_450_2,plain,
! [U_1614] : U_1614 != hAPP(nat,nat,suc,U_1614),
inference(variable_rename,[status(thm)],[f_450_1]) ).
cnf(f_450_3,plain,
U_1614 != hAPP(nat,nat,suc,U_1614),
inference(clausify,[status(thm)],[f_450_2]) ).
fof(f_451_1,plain,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,suc,N_1)),
inference(fof_nnf,[status(thm)],[fact_388_add__Suc__shift]) ).
fof(f_451_2,plain,
! [U_1616,U_1615] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1616)),U_1615) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1616),hAPP(nat,nat,suc,U_1615)),
inference(variable_rename,[status(thm)],[f_451_1]) ).
cnf(f_451_3,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1616)),U_1615) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1616),hAPP(nat,nat,suc,U_1615)),
inference(clausify,[status(thm)],[f_451_2]) ).
fof(f_452_1,plain,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1)),
inference(fof_nnf,[status(thm)],[fact_389_add__Suc]) ).
fof(f_452_2,plain,
! [U_1618,U_1617] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1618)),U_1617) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1618),U_1617)),
inference(variable_rename,[status(thm)],[f_452_1]) ).
cnf(f_452_3,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1618)),U_1617) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1618),U_1617)),
inference(clausify,[status(thm)],[f_452_2]) ).
fof(f_453_1,plain,
! [M_3,N_1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),N_1)),
inference(fof_nnf,[status(thm)],[fact_390_add__Suc__right]) ).
fof(f_453_2,plain,
! [U_1620,U_1619] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1620),hAPP(nat,nat,suc,U_1619)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1620),U_1619)),
inference(variable_rename,[status(thm)],[f_453_1]) ).
cnf(f_453_3,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1620),hAPP(nat,nat,suc,U_1619)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1620),U_1619)),
inference(clausify,[status(thm)],[f_453_2]) ).
fof(f_454_1,plain,
! [M_2,Na] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) ),
inference(fof_nnf,[status(thm)],[fact_391_not__less__eq]) ).
fof(f_454_2,plain,
! [U_1622,U_1621] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1622),U_1621))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1621),hAPP(nat,nat,suc,U_1622))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1621),hAPP(nat,nat,suc,U_1622)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1622),U_1621)) ) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
fof(f_454_3,plain,
( ! [U_1626,U_1624] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1626),U_1624))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1624),hAPP(nat,nat,suc,U_1626))) )
& ! [U_1625,U_1623] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1623),hAPP(nat,nat,suc,U_1625)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1625),U_1623)) ) ),
inference(miniscope,[status(thm)],[f_454_2]) ).
cnf(f_454_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1623),hAPP(nat,nat,suc,U_1625)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1625),U_1623)) ),
inference(clausify,[status(thm)],[f_454_3]) ).
cnf(f_454_5,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1626),U_1624))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1624),hAPP(nat,nat,suc,U_1626))) ),
inference(clausify,[status(thm)],[f_454_3]) ).
fof(f_455_1,plain,
! [M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na)))
| ( M_2 != Na
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) )
& ( M_2 = Na
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na))) ) ),
inference(fof_nnf,[status(thm)],[fact_392_less__Suc__eq]) ).
fof(f_455_2,plain,
! [U_1628,U_1627] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1628),hAPP(nat,nat,suc,U_1627)))
| ( U_1628 != U_1627
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1628),U_1627)) ) )
& ( U_1628 = U_1627
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1628),U_1627))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1628),hAPP(nat,nat,suc,U_1627))) ) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
( ! [U_1632,U_1630] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1632),hAPP(nat,nat,suc,U_1630)))
| ( U_1632 != U_1630
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1632),U_1630)) ) )
& ! [U_1631,U_1629] :
( U_1631 = U_1629
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),U_1629))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),hAPP(nat,nat,suc,U_1629))) ) ),
inference(miniscope,[status(thm)],[f_455_2]) ).
cnf(f_455_4,plain,
( U_1631 = U_1629
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),U_1629))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1631),hAPP(nat,nat,suc,U_1629))) ),
inference(clausify,[status(thm)],[f_455_3]) ).
cnf(f_455_5,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1632),U_1630))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1632),hAPP(nat,nat,suc,U_1630))) ),
inference(clausify,[status(thm)],[f_455_3]) ).
cnf(f_455_6,plain,
( U_1632 != U_1630
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1632),hAPP(nat,nat,suc,U_1630))) ),
inference(clausify,[status(thm)],[f_455_3]) ).
fof(f_456_1,plain,
! [M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_2)),hAPP(nat,nat,suc,Na)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_2)),hAPP(nat,nat,suc,Na))) ) ),
inference(fof_nnf,[status(thm)],[fact_393_Suc__less__eq]) ).
fof(f_456_2,plain,
! [U_1634,U_1633] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1634)),hAPP(nat,nat,suc,U_1633)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1634),U_1633)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1634),U_1633))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1634)),hAPP(nat,nat,suc,U_1633))) ) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
fof(f_456_3,plain,
( ! [U_1638,U_1636] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1638)),hAPP(nat,nat,suc,U_1636)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1638),U_1636)) )
& ! [U_1637,U_1635] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1637),U_1635))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1637)),hAPP(nat,nat,suc,U_1635))) ) ),
inference(miniscope,[status(thm)],[f_456_2]) ).
cnf(f_456_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1637),U_1635))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1637)),hAPP(nat,nat,suc,U_1635))) ),
inference(clausify,[status(thm)],[f_456_3]) ).
cnf(f_456_5,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1638)),hAPP(nat,nat,suc,U_1636)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1638),U_1636)) ),
inference(clausify,[status(thm)],[f_456_3]) ).
fof(f_457_1,plain,
! [Na,M_2] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2)))
| Na != M_2 )
& ( Na = M_2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2))) ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2)) ),
inference(fof_nnf,[status(thm)],[fact_394_not__less__less__Suc__eq]) ).
fof(f_457_2,plain,
! [U_1640,U_1639] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1640),hAPP(nat,nat,suc,U_1639)))
| U_1640 != U_1639 )
& ( U_1640 = U_1639
| ~ 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_457_1]) ).
cnf(f_457_3,plain,
( U_1640 = U_1639
| ~ 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_457_2]) ).
cnf(f_457_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1640),hAPP(nat,nat,suc,U_1639)))
| U_1640 != U_1639
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1640),U_1639)) ),
inference(clausify,[status(thm)],[f_457_2]) ).
fof(f_458_1,plain,
! [N_1,M_3] :
( M_3 = N_1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_3)) ),
inference(fof_nnf,[status(thm)],[fact_395_less__antisym]) ).
fof(f_458_2,plain,
! [U_1642,U_1641] :
( U_1641 = U_1642
| ~ 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_458_1]) ).
cnf(f_458_3,plain,
( U_1641 = U_1642
| ~ 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_458_2]) ).
fof(f_459_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_396_less__SucI]) ).
fof(f_459_2,plain,
! [U_1644,U_1643] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),hAPP(nat,nat,suc,U_1643)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),U_1643)) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
cnf(f_459_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),hAPP(nat,nat,suc,U_1643)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1644),U_1643)) ),
inference(clausify,[status(thm)],[f_459_2]) ).
fof(f_460_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),N_1))
| hAPP(nat,nat,suc,M_3) = N_1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_397_Suc__lessI]) ).
fof(f_460_2,plain,
! [U_1646,U_1645] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1646)),U_1645))
| hAPP(nat,nat,suc,U_1646) = U_1645
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1646),U_1645)) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
cnf(f_460_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1646)),U_1645))
| hAPP(nat,nat,suc,U_1646) = U_1645
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1646),U_1645)) ),
inference(clausify,[status(thm)],[f_460_2]) ).
fof(f_461_1,plain,
! [K_1,I,J_2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_398_less__trans__Suc]) ).
fof(f_461_2,plain,
! [U_1649,U_1648,U_1647] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1648)),U_1649))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1647),U_1649))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1648),U_1647)) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
cnf(f_461_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1648)),U_1649))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1647),U_1649))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1648),U_1647)) ),
inference(clausify,[status(thm)],[f_461_2]) ).
fof(f_462_1,plain,
! [M_3,N_1] :
( M_3 = N_1
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N_1))) ),
inference(fof_nnf,[status(thm)],[fact_399_less__SucE]) ).
fof(f_462_2,plain,
! [U_1651,U_1650] :
( U_1651 = U_1650
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1651),U_1650))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1651),hAPP(nat,nat,suc,U_1650))) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
cnf(f_462_3,plain,
( U_1651 = U_1650
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1651),U_1650))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1651),hAPP(nat,nat,suc,U_1650))) ),
inference(clausify,[status(thm)],[f_462_2]) ).
fof(f_463_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_400_Suc__lessD]) ).
fof(f_463_2,plain,
! [U_1653,U_1652] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1653),U_1652))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1653)),U_1652)) ),
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_1653),U_1652))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1653)),U_1652)) ),
inference(clausify,[status(thm)],[f_463_2]) ).
fof(f_464_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_3)),hAPP(nat,nat,suc,N_1))) ),
inference(fof_nnf,[status(thm)],[fact_401_Suc__less__SucD]) ).
fof(f_464_2,plain,
! [U_1655,U_1654] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1655),U_1654))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1655)),hAPP(nat,nat,suc,U_1654))) ),
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),U_1655),U_1654))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1655)),hAPP(nat,nat,suc,U_1654))) ),
inference(clausify,[status(thm)],[f_464_2]) ).
fof(f_465_1,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(fof_nnf,[status(thm)],[fact_402_One__nat__def]) ).
cnf(f_465_2,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(clausify,[status(thm)],[f_465_1]) ).
fof(f_466_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_403_Suc__le__lessD]) ).
fof(f_466_2,plain,
! [U_1657,U_1656] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1657),U_1656))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1657)),U_1656)) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
cnf(f_466_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1657),U_1656))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1657)),U_1656)) ),
inference(clausify,[status(thm)],[f_466_2]) ).
fof(f_467_1,plain,
! [M_2,Na] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2)))
| Na != M_2 )
& ( Na = M_2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_2))) ) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) ),
inference(fof_nnf,[status(thm)],[fact_404_le__less__Suc__eq]) ).
fof(f_467_2,plain,
! [U_1659,U_1658] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1658),hAPP(nat,nat,suc,U_1659)))
| U_1658 != U_1659 )
& ( U_1658 = U_1659
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1658),hAPP(nat,nat,suc,U_1659))) ) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1659),U_1658)) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
cnf(f_467_3,plain,
( U_1658 = U_1659
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1658),hAPP(nat,nat,suc,U_1659)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1659),U_1658)) ),
inference(clausify,[status(thm)],[f_467_2]) ).
cnf(f_467_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1658),hAPP(nat,nat,suc,U_1659)))
| U_1658 != U_1659
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1659),U_1658)) ),
inference(clausify,[status(thm)],[f_467_2]) ).
fof(f_468_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_3)),N_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_405_Suc__leI]) ).
fof(f_468_2,plain,
! [U_1661,U_1660] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1661)),U_1660))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1661),U_1660)) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
cnf(f_468_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1661)),U_1660))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1661),U_1660)) ),
inference(clausify,[status(thm)],[f_468_2]) ).
fof(f_469_1,plain,
! [M_3,N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),hAPP(nat,nat,suc,N_1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_406_le__imp__less__Suc]) ).
fof(f_469_2,plain,
! [U_1663,U_1662] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1663),hAPP(nat,nat,suc,U_1662)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1663),U_1662)) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
cnf(f_469_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1663),hAPP(nat,nat,suc,U_1662)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1663),U_1662)) ),
inference(clausify,[status(thm)],[f_469_2]) ).
fof(f_470_1,plain,
! [M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),Na))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),Na)) ) ),
inference(fof_nnf,[status(thm)],[fact_407_Suc__le__eq]) ).
fof(f_470_2,plain,
! [U_1665,U_1664] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1665)),U_1664))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1665),U_1664)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1665),U_1664))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1665)),U_1664)) ) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
fof(f_470_3,plain,
( ! [U_1669,U_1667] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1669)),U_1667))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1669),U_1667)) )
& ! [U_1668,U_1666] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1668),U_1666))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1668)),U_1666)) ) ),
inference(miniscope,[status(thm)],[f_470_2]) ).
cnf(f_470_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1668),U_1666))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1668)),U_1666)) ),
inference(clausify,[status(thm)],[f_470_3]) ).
cnf(f_470_5,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1669)),U_1667))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1669),U_1667)) ),
inference(clausify,[status(thm)],[f_470_3]) ).
fof(f_471_1,plain,
! [M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na))) ) ),
inference(fof_nnf,[status(thm)],[fact_408_less__Suc__eq__le]) ).
fof(f_471_2,plain,
! [U_1671,U_1670] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1671),hAPP(nat,nat,suc,U_1670)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1671),U_1670)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1671),U_1670))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1671),hAPP(nat,nat,suc,U_1670))) ) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
fof(f_471_3,plain,
( ! [U_1675,U_1673] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1675),hAPP(nat,nat,suc,U_1673)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1675),U_1673)) )
& ! [U_1674,U_1672] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1674),U_1672))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1674),hAPP(nat,nat,suc,U_1672))) ) ),
inference(miniscope,[status(thm)],[f_471_2]) ).
cnf(f_471_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1674),U_1672))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1674),hAPP(nat,nat,suc,U_1672))) ),
inference(clausify,[status(thm)],[f_471_3]) ).
cnf(f_471_5,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1675),hAPP(nat,nat,suc,U_1673)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1675),U_1673)) ),
inference(clausify,[status(thm)],[f_471_3]) ).
fof(f_472_1,plain,
! [Na,M_2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_2)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_409_less__eq__Suc__le]) ).
fof(f_472_2,plain,
! [U_1677,U_1676] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1677),U_1676))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1677)),U_1676)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1677)),U_1676))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1677),U_1676)) ) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
fof(f_472_3,plain,
( ! [U_1681,U_1679] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1681),U_1679))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1681)),U_1679)) )
& ! [U_1680,U_1678] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1680)),U_1678))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1680),U_1678)) ) ),
inference(miniscope,[status(thm)],[f_472_2]) ).
cnf(f_472_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1680)),U_1678))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1680),U_1678)) ),
inference(clausify,[status(thm)],[f_472_3]) ).
cnf(f_472_5,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1681),U_1679))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1681)),U_1679)) ),
inference(clausify,[status(thm)],[f_472_3]) ).
fof(f_473_1,plain,
! [M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na))
| ! [K_2] : Na != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_2)) )
& ( ? [K_2] : Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),K_2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) ) ),
inference(fof_nnf,[status(thm)],[fact_410_less__iff__Suc__add]) ).
fof(f_473_2,plain,
! [U_1685,U_1684] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1685),U_1684))
| ! [U_1683] : U_1684 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1685),U_1683)) )
& ( ? [U_1682] : U_1684 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1685),U_1682))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1685),U_1684)) ) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
( ! [U_1689,U_1687] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1689),U_1687))
| ! [U_1683] : U_1687 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1689),U_1683)) )
& ! [U_1688,U_1686] :
( ? [U_1682] : U_1686 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1688),U_1682))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1688),U_1686)) ) ),
inference(miniscope,[status(thm)],[f_473_2]) ).
fof(f_473_4,plain,
( ! [U_1689,U_1687] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1689),U_1687))
| ! [U_1683] : U_1687 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1689),U_1683)) )
& ! [U_1688,U_1686] :
( U_1686 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1688),sK91(U_1688,U_1686)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1688),U_1686)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_1682,sK91(U_1688,U_1686))],[f_473_3]) ).
cnf(f_473_5,plain,
( U_1686 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1688),sK91(U_1688,U_1686)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1688),U_1686)) ),
inference(clausify,[status(thm)],[f_473_4]) ).
cnf(f_473_6,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1689),U_1687))
| U_1687 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1689),U_1683)) ),
inference(clausify,[status(thm)],[f_473_4]) ).
fof(f_474_1,plain,
! [I,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),I)))),
inference(fof_nnf,[status(thm)],[fact_411_less__add__Suc2]) ).
fof(f_474_2,plain,
! [U_1691,U_1690] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1691),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1690),U_1691)))),
inference(variable_rename,[status(thm)],[f_474_1]) ).
cnf(f_474_3,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1691),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1690),U_1691)))),
inference(clausify,[status(thm)],[f_474_2]) ).
fof(f_475_1,plain,
! [I,M_3] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M_3)))),
inference(fof_nnf,[status(thm)],[fact_412_less__add__Suc1]) ).
fof(f_475_2,plain,
! [U_1693,U_1692] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1693),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1693),U_1692)))),
inference(variable_rename,[status(thm)],[f_475_1]) ).
cnf(f_475_3,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1693),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1693),U_1692)))),
inference(clausify,[status(thm)],[f_475_2]) ).
fof(f_476_1,plain,
! [M_2,Na] :
( ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na)
| ( ( Na != hAPP(nat,nat,suc,zero_zero(nat))
| M_2 != zero_zero(nat) )
& ( Na != zero_zero(nat)
| M_2 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
& ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
& M_2 = zero_zero(nat) )
| ( Na = zero_zero(nat)
& M_2 = 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_2),Na) ) ),
inference(fof_nnf,[status(thm)],[fact_413_one__is__add]) ).
fof(f_476_2,plain,
! [U_1695,U_1694] :
( ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1695),U_1694)
| ( ( U_1694 != hAPP(nat,nat,suc,zero_zero(nat))
| U_1695 != zero_zero(nat) )
& ( U_1694 != zero_zero(nat)
| U_1695 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
& ( ( U_1694 = hAPP(nat,nat,suc,zero_zero(nat))
& U_1695 = zero_zero(nat) )
| ( U_1694 = zero_zero(nat)
& U_1695 = 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_1695),U_1694) ) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
fof(f_476_3,plain,
( ! [U_1699,U_1697] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1699),U_1697)
| ( ( U_1697 != hAPP(nat,nat,suc,zero_zero(nat))
| U_1699 != zero_zero(nat) )
& ( U_1697 != zero_zero(nat)
| U_1699 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
& ! [U_1698,U_1696] :
( ( U_1696 = hAPP(nat,nat,suc,zero_zero(nat))
& U_1698 = zero_zero(nat) )
| ( U_1696 = zero_zero(nat)
& U_1698 = 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_1698),U_1696) ) ),
inference(miniscope,[status(thm)],[f_476_2]) ).
cnf(f_476_4,plain,
( U_1698 = zero_zero(nat)
| U_1698 = 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_1698),U_1696) ),
inference(clausify,[status(thm)],[f_476_3]) ).
cnf(f_476_5,plain,
( U_1696 = hAPP(nat,nat,suc,zero_zero(nat))
| U_1698 = 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_1698),U_1696) ),
inference(clausify,[status(thm)],[f_476_3]) ).
cnf(f_476_6,plain,
( U_1698 = zero_zero(nat)
| U_1696 = zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1698),U_1696) ),
inference(clausify,[status(thm)],[f_476_3]) ).
cnf(f_476_7,plain,
( U_1696 = hAPP(nat,nat,suc,zero_zero(nat))
| U_1696 = zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1698),U_1696) ),
inference(clausify,[status(thm)],[f_476_3]) ).
cnf(f_476_8,plain,
( U_1697 != zero_zero(nat)
| U_1699 != 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_1699),U_1697) ),
inference(clausify,[status(thm)],[f_476_3]) ).
cnf(f_476_9,plain,
( U_1697 != hAPP(nat,nat,suc,zero_zero(nat))
| U_1699 != zero_zero(nat)
| hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1699),U_1697) ),
inference(clausify,[status(thm)],[f_476_3]) ).
fof(f_477_1,plain,
! [M_2,Na] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na) = hAPP(nat,nat,suc,zero_zero(nat))
| ( ( Na != hAPP(nat,nat,suc,zero_zero(nat))
| M_2 != zero_zero(nat) )
& ( Na != zero_zero(nat)
| M_2 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
& ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
& M_2 = zero_zero(nat) )
| ( Na = zero_zero(nat)
& M_2 = hAPP(nat,nat,suc,zero_zero(nat)) )
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_2),Na) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
inference(fof_nnf,[status(thm)],[fact_414_add__is__1]) ).
fof(f_477_2,plain,
! [U_1701,U_1700] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1701),U_1700) = hAPP(nat,nat,suc,zero_zero(nat))
| ( ( U_1700 != hAPP(nat,nat,suc,zero_zero(nat))
| U_1701 != zero_zero(nat) )
& ( U_1700 != zero_zero(nat)
| U_1701 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
& ( ( U_1700 = hAPP(nat,nat,suc,zero_zero(nat))
& U_1701 = zero_zero(nat) )
| ( U_1700 = zero_zero(nat)
& U_1701 = hAPP(nat,nat,suc,zero_zero(nat)) )
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1701),U_1700) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
( ! [U_1705,U_1703] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1705),U_1703) = hAPP(nat,nat,suc,zero_zero(nat))
| ( ( U_1703 != hAPP(nat,nat,suc,zero_zero(nat))
| U_1705 != zero_zero(nat) )
& ( U_1703 != zero_zero(nat)
| U_1705 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
& ! [U_1704,U_1702] :
( ( U_1702 = hAPP(nat,nat,suc,zero_zero(nat))
& U_1704 = zero_zero(nat) )
| ( U_1702 = zero_zero(nat)
& U_1704 = hAPP(nat,nat,suc,zero_zero(nat)) )
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1704),U_1702) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
inference(miniscope,[status(thm)],[f_477_2]) ).
cnf(f_477_4,plain,
( U_1704 = zero_zero(nat)
| U_1704 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1704),U_1702) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_5,plain,
( U_1702 = hAPP(nat,nat,suc,zero_zero(nat))
| U_1704 = hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1704),U_1702) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_6,plain,
( U_1704 = zero_zero(nat)
| U_1702 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1704),U_1702) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_7,plain,
( U_1702 = hAPP(nat,nat,suc,zero_zero(nat))
| U_1702 = zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1704),U_1702) != hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_8,plain,
( U_1703 != zero_zero(nat)
| U_1705 != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1705),U_1703) = hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_9,plain,
( U_1703 != hAPP(nat,nat,suc,zero_zero(nat))
| U_1705 != zero_zero(nat)
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1705),U_1703) = hAPP(nat,nat,suc,zero_zero(nat)) ),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_1,plain,
! [Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))
| ! [M] : Na != hAPP(nat,nat,suc,M) )
& ( ? [M] : Na = hAPP(nat,nat,suc,M)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) ) ),
inference(fof_nnf,[status(thm)],[fact_415_gr0__conv__Suc]) ).
fof(f_478_2,plain,
! [U_1708] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1708))
| ! [U_1707] : U_1708 != hAPP(nat,nat,suc,U_1707) )
& ( ? [U_1706] : U_1708 = hAPP(nat,nat,suc,U_1706)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1708)) ) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
fof(f_478_3,plain,
( ! [U_1710] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1710))
| ! [U_1707] : U_1710 != hAPP(nat,nat,suc,U_1707) )
& ! [U_1709] :
( ? [U_1706] : U_1709 = hAPP(nat,nat,suc,U_1706)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1709)) ) ),
inference(miniscope,[status(thm)],[f_478_2]) ).
fof(f_478_4,plain,
( ! [U_1710] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1710))
| ! [U_1707] : U_1710 != hAPP(nat,nat,suc,U_1707) )
& ! [U_1709] :
( U_1709 = hAPP(nat,nat,suc,sK92(U_1709))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1709)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_1706,sK92(U_1709))],[f_478_3]) ).
cnf(f_478_5,plain,
( U_1709 = hAPP(nat,nat,suc,sK92(U_1709))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1709)) ),
inference(clausify,[status(thm)],[f_478_4]) ).
cnf(f_478_6,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1710))
| U_1710 != hAPP(nat,nat,suc,U_1707) ),
inference(clausify,[status(thm)],[f_478_4]) ).
fof(f_479_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_416_less__Suc0]) ).
fof(f_479_2,plain,
! [U_1711] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1711),hAPP(nat,nat,suc,zero_zero(nat))))
| U_1711 != zero_zero(nat) )
& ( U_1711 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1711),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
( ! [U_1713] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1713),hAPP(nat,nat,suc,zero_zero(nat))))
| U_1713 != zero_zero(nat) )
& ! [U_1712] :
( U_1712 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1712),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
inference(miniscope,[status(thm)],[f_479_2]) ).
cnf(f_479_4,plain,
( U_1712 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1712),hAPP(nat,nat,suc,zero_zero(nat)))) ),
inference(clausify,[status(thm)],[f_479_3]) ).
cnf(f_479_5,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1713),hAPP(nat,nat,suc,zero_zero(nat))))
| U_1713 != zero_zero(nat) ),
inference(clausify,[status(thm)],[f_479_3]) ).
fof(f_480_1,plain,
! [M_2,Na] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na)))
| ( ! [J] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),Na))
| M_2 != hAPP(nat,nat,suc,J) )
& M_2 != zero_zero(nat) ) )
& ( ? [J] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),Na))
& M_2 = hAPP(nat,nat,suc,J) )
| M_2 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),hAPP(nat,nat,suc,Na))) ) ),
inference(fof_nnf,[status(thm)],[fact_417_less__Suc__eq__0__disj]) ).
fof(f_480_2,plain,
! [U_1717,U_1716] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1717),hAPP(nat,nat,suc,U_1716)))
| ( ! [U_1715] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1715),U_1716))
| U_1717 != hAPP(nat,nat,suc,U_1715) )
& U_1717 != zero_zero(nat) ) )
& ( ? [U_1714] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),U_1716))
& U_1717 = hAPP(nat,nat,suc,U_1714) )
| U_1717 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1717),hAPP(nat,nat,suc,U_1716))) ) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
fof(f_480_3,plain,
( ! [U_1721,U_1719] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1721),hAPP(nat,nat,suc,U_1719)))
| ( ! [U_1715] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1715),U_1719))
| U_1721 != hAPP(nat,nat,suc,U_1715) )
& U_1721 != zero_zero(nat) ) )
& ! [U_1720,U_1718] :
( ? [U_1714] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),U_1718))
& U_1720 = hAPP(nat,nat,suc,U_1714) )
| U_1720 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1720),hAPP(nat,nat,suc,U_1718))) ) ),
inference(miniscope,[status(thm)],[f_480_2]) ).
fof(f_480_4,plain,
( ! [U_1721,U_1719] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1721),hAPP(nat,nat,suc,U_1719)))
| ( ! [U_1715] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1715),U_1719))
| U_1721 != hAPP(nat,nat,suc,U_1715) )
& U_1721 != zero_zero(nat) ) )
& ! [U_1720,U_1718] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK93(U_1720,U_1718)),U_1718))
& U_1720 = hAPP(nat,nat,suc,sK93(U_1720,U_1718)) )
| U_1720 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1720),hAPP(nat,nat,suc,U_1718))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_1714,sK93(U_1720,U_1718))],[f_480_3]) ).
cnf(f_480_5,plain,
( U_1720 = hAPP(nat,nat,suc,sK93(U_1720,U_1718))
| U_1720 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1720),hAPP(nat,nat,suc,U_1718))) ),
inference(clausify,[status(thm)],[f_480_4]) ).
cnf(f_480_6,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK93(U_1720,U_1718)),U_1718))
| U_1720 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1720),hAPP(nat,nat,suc,U_1718))) ),
inference(clausify,[status(thm)],[f_480_4]) ).
cnf(f_480_7,plain,
( U_1721 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1721),hAPP(nat,nat,suc,U_1719))) ),
inference(clausify,[status(thm)],[f_480_4]) ).
cnf(f_480_8,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1715),U_1719))
| U_1721 != hAPP(nat,nat,suc,U_1715)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1721),hAPP(nat,nat,suc,U_1719))) ),
inference(clausify,[status(thm)],[f_480_4]) ).
fof(f_481_1,plain,
! [N_3] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),N_3)),
inference(fof_nnf,[status(thm)],[fact_418_inj__Suc]) ).
fof(f_481_2,plain,
! [U_1722] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),U_1722)),
inference(variable_rename,[status(thm)],[f_481_1]) ).
cnf(f_481_3,plain,
hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),U_1722)),
inference(clausify,[status(thm)],[f_481_2]) ).
fof(f_482_1,plain,
! [M_3] : hAPP(nat,nat,suc,M_3) != zero_zero(nat),
inference(fof_nnf,[status(thm)],[fact_419_Suc__neq__Zero]) ).
fof(f_482_2,plain,
! [U_1723] : hAPP(nat,nat,suc,U_1723) != zero_zero(nat),
inference(variable_rename,[status(thm)],[f_482_1]) ).
cnf(f_482_3,plain,
hAPP(nat,nat,suc,U_1723) != zero_zero(nat),
inference(clausify,[status(thm)],[f_482_2]) ).
fof(f_483_1,plain,
! [M_3] : zero_zero(nat) != hAPP(nat,nat,suc,M_3),
inference(fof_nnf,[status(thm)],[fact_420_Zero__neq__Suc]) ).
fof(f_483_2,plain,
! [U_1724] : zero_zero(nat) != hAPP(nat,nat,suc,U_1724),
inference(variable_rename,[status(thm)],[f_483_1]) ).
cnf(f_483_3,plain,
zero_zero(nat) != hAPP(nat,nat,suc,U_1724),
inference(clausify,[status(thm)],[f_483_2]) ).
fof(f_484_1,plain,
! [Nat_2] : hAPP(nat,nat,suc,Nat_2) != zero_zero(nat),
inference(fof_nnf,[status(thm)],[fact_421_nat_Osimps_I3_J]) ).
fof(f_484_2,plain,
! [U_1725] : hAPP(nat,nat,suc,U_1725) != zero_zero(nat),
inference(variable_rename,[status(thm)],[f_484_1]) ).
cnf(f_484_3,plain,
hAPP(nat,nat,suc,U_1725) != zero_zero(nat),
inference(clausify,[status(thm)],[f_484_2]) ).
fof(f_485_1,plain,
! [M_3] : hAPP(nat,nat,suc,M_3) != zero_zero(nat),
inference(fof_nnf,[status(thm)],[fact_422_Suc__not__Zero]) ).
fof(f_485_2,plain,
! [U_1726] : hAPP(nat,nat,suc,U_1726) != zero_zero(nat),
inference(variable_rename,[status(thm)],[f_485_1]) ).
cnf(f_485_3,plain,
hAPP(nat,nat,suc,U_1726) != zero_zero(nat),
inference(clausify,[status(thm)],[f_485_2]) ).
fof(f_486_1,plain,
! [Nat_1] : zero_zero(nat) != hAPP(nat,nat,suc,Nat_1),
inference(fof_nnf,[status(thm)],[fact_423_nat_Osimps_I2_J]) ).
fof(f_486_2,plain,
! [U_1727] : zero_zero(nat) != hAPP(nat,nat,suc,U_1727),
inference(variable_rename,[status(thm)],[f_486_1]) ).
cnf(f_486_3,plain,
zero_zero(nat) != hAPP(nat,nat,suc,U_1727),
inference(clausify,[status(thm)],[f_486_2]) ).
fof(f_487_1,plain,
! [M_3] : zero_zero(nat) != hAPP(nat,nat,suc,M_3),
inference(fof_nnf,[status(thm)],[fact_424_Zero__not__Suc]) ).
fof(f_487_2,plain,
! [U_1728] : zero_zero(nat) != hAPP(nat,nat,suc,U_1728),
inference(variable_rename,[status(thm)],[f_487_1]) ).
cnf(f_487_3,plain,
zero_zero(nat) != hAPP(nat,nat,suc,U_1728),
inference(clausify,[status(thm)],[f_487_2]) ).
fof(f_488_1,plain,
! [X_2] : hAPP(nat,fun(nat,bool),ord_less(nat),X_2) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2)),
inference(fof_nnf,[status(thm)],[fact_425_less__eq__Suc__le__raw]) ).
fof(f_488_2,plain,
! [U_1729] : hAPP(nat,fun(nat,bool),ord_less(nat),U_1729) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1729)),
inference(variable_rename,[status(thm)],[f_488_1]) ).
cnf(f_488_3,plain,
hAPP(nat,fun(nat,bool),ord_less(nat),U_1729) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1729)),
inference(clausify,[status(thm)],[f_488_2]) ).
fof(f_489_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_426_card__Collect__le__nat]) ).
fof(f_489_2,plain,
! [U_1730] : 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_1730))) = hAPP(nat,nat,suc,U_1730),
inference(variable_rename,[status(thm)],[f_489_1]) ).
cnf(f_489_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_1730))) = hAPP(nat,nat,suc,U_1730),
inference(clausify,[status(thm)],[f_489_2]) ).
fof(f_490_1,plain,
! [X_a] :
( ! [A_2,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_2)
| ~ comm_semiring_1(X_a) ),
inference(fof_nnf,[status(thm)],[fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_490_2,plain,
! [U_1733] :
( ! [U_1732,U_1731] : hAPP(U_1733,U_1733,hAPP(U_1733,fun(U_1733,U_1733),plus_plus(U_1733),U_1732),U_1731) = hAPP(U_1733,U_1733,hAPP(U_1733,fun(U_1733,U_1733),plus_plus(U_1733),U_1731),U_1732)
| ~ comm_semiring_1(U_1733) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
cnf(f_490_3,plain,
( hAPP(U_1733,U_1733,hAPP(U_1733,fun(U_1733,U_1733),plus_plus(U_1733),U_1732),U_1731) = hAPP(U_1733,U_1733,hAPP(U_1733,fun(U_1733,U_1733),plus_plus(U_1733),U_1731),U_1732)
| ~ comm_semiring_1(U_1733) ),
inference(clausify,[status(thm)],[f_490_2]) ).
fof(f_491_1,plain,
! [X_a] :
( ! [A_2,C,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),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),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_428_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_491_2,plain,
! [U_1737] :
( ! [U_1736,U_1735,U_1734] : hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1736),hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1735),U_1734)) = hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1735),hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1736),U_1734))
| ~ comm_semiring_1(U_1737) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
cnf(f_491_3,plain,
( hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1736),hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1735),U_1734)) = hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1735),hAPP(U_1737,U_1737,hAPP(U_1737,fun(U_1737,U_1737),plus_plus(U_1737),U_1736),U_1734))
| ~ comm_semiring_1(U_1737) ),
inference(clausify,[status(thm)],[f_491_2]) ).
fof(f_492_1,plain,
! [X_a] :
( ! [A_2,C,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),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)),D)
| ~ comm_semiring_1(X_a) ),
inference(fof_nnf,[status(thm)],[fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_492_2,plain,
! [U_1741] :
( ! [U_1740,U_1739,U_1738] : hAPP(U_1741,U_1741,hAPP(U_1741,fun(U_1741,U_1741),plus_plus(U_1741),U_1740),hAPP(U_1741,U_1741,hAPP(U_1741,fun(U_1741,U_1741),plus_plus(U_1741),U_1739),U_1738)) = hAPP(U_1741,U_1741,hAPP(U_1741,fun(U_1741,U_1741),plus_plus(U_1741),hAPP(U_1741,U_1741,hAPP(U_1741,fun(U_1741,U_1741),plus_plus(U_1741),U_1740),U_1739)),U_1738)
| ~ comm_semiring_1(U_1741) ),
inference(variable_rename,[status(thm)],[f_492_1]) ).
cnf(f_492_3,plain,
( hAPP(U_1741,U_1741,hAPP(U_1741,fun(U_1741,U_1741),plus_plus(U_1741),U_1740),hAPP(U_1741,U_1741,hAPP(U_1741,fun(U_1741,U_1741),plus_plus(U_1741),U_1739),U_1738)) = hAPP(U_1741,U_1741,hAPP(U_1741,fun(U_1741,U_1741),plus_plus(U_1741),hAPP(U_1741,U_1741,hAPP(U_1741,fun(U_1741,U_1741),plus_plus(U_1741),U_1740),U_1739)),U_1738)
| ~ comm_semiring_1(U_1741) ),
inference(clausify,[status(thm)],[f_492_2]) ).
fof(f_493_1,plain,
! [X_a] :
( ! [A_2,B_1,C] : 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) = 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))
| ~ comm_semiring_1(X_a) ),
inference(fof_nnf,[status(thm)],[fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_493_2,plain,
! [U_1745] :
( ! [U_1744,U_1743,U_1742] : hAPP(U_1745,U_1745,hAPP(U_1745,fun(U_1745,U_1745),plus_plus(U_1745),hAPP(U_1745,U_1745,hAPP(U_1745,fun(U_1745,U_1745),plus_plus(U_1745),U_1744),U_1743)),U_1742) = hAPP(U_1745,U_1745,hAPP(U_1745,fun(U_1745,U_1745),plus_plus(U_1745),U_1744),hAPP(U_1745,U_1745,hAPP(U_1745,fun(U_1745,U_1745),plus_plus(U_1745),U_1743),U_1742))
| ~ comm_semiring_1(U_1745) ),
inference(variable_rename,[status(thm)],[f_493_1]) ).
cnf(f_493_3,plain,
( hAPP(U_1745,U_1745,hAPP(U_1745,fun(U_1745,U_1745),plus_plus(U_1745),hAPP(U_1745,U_1745,hAPP(U_1745,fun(U_1745,U_1745),plus_plus(U_1745),U_1744),U_1743)),U_1742) = hAPP(U_1745,U_1745,hAPP(U_1745,fun(U_1745,U_1745),plus_plus(U_1745),U_1744),hAPP(U_1745,U_1745,hAPP(U_1745,fun(U_1745,U_1745),plus_plus(U_1745),U_1743),U_1742))
| ~ comm_semiring_1(U_1745) ),
inference(clausify,[status(thm)],[f_493_2]) ).
fof(f_494_1,plain,
! [X_a] :
( ! [A_2,B_1,C] : 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) = 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)),B_1)
| ~ comm_semiring_1(X_a) ),
inference(fof_nnf,[status(thm)],[fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_494_2,plain,
! [U_1749] :
( ! [U_1748,U_1747,U_1746] : hAPP(U_1749,U_1749,hAPP(U_1749,fun(U_1749,U_1749),plus_plus(U_1749),hAPP(U_1749,U_1749,hAPP(U_1749,fun(U_1749,U_1749),plus_plus(U_1749),U_1748),U_1747)),U_1746) = hAPP(U_1749,U_1749,hAPP(U_1749,fun(U_1749,U_1749),plus_plus(U_1749),hAPP(U_1749,U_1749,hAPP(U_1749,fun(U_1749,U_1749),plus_plus(U_1749),U_1748),U_1746)),U_1747)
| ~ comm_semiring_1(U_1749) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
cnf(f_494_3,plain,
( hAPP(U_1749,U_1749,hAPP(U_1749,fun(U_1749,U_1749),plus_plus(U_1749),hAPP(U_1749,U_1749,hAPP(U_1749,fun(U_1749,U_1749),plus_plus(U_1749),U_1748),U_1747)),U_1746) = hAPP(U_1749,U_1749,hAPP(U_1749,fun(U_1749,U_1749),plus_plus(U_1749),hAPP(U_1749,U_1749,hAPP(U_1749,fun(U_1749,U_1749),plus_plus(U_1749),U_1748),U_1746)),U_1747)
| ~ comm_semiring_1(U_1749) ),
inference(clausify,[status(thm)],[f_494_2]) ).
fof(f_495_1,plain,
! [X_a] :
( ! [A_2,B_1,C,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),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)),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_432_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_495_2,plain,
! [U_1754] :
( ! [U_1753,U_1752,U_1751,U_1750] : hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),U_1753),U_1752)),hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),U_1751),U_1750)) = hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),U_1753),U_1751)),hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),U_1752),U_1750))
| ~ comm_semiring_1(U_1754) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
cnf(f_495_3,plain,
( hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),U_1753),U_1752)),hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),U_1751),U_1750)) = hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),U_1753),U_1751)),hAPP(U_1754,U_1754,hAPP(U_1754,fun(U_1754,U_1754),plus_plus(U_1754),U_1752),U_1750))
| ~ comm_semiring_1(U_1754) ),
inference(clausify,[status(thm)],[f_495_2]) ).
fof(f_496_1,plain,
! [I_1,M_4] :
( 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_4))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))) = 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_4))),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_1)))))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_4)) ),
inference(fof_nnf,[status(thm)],[fact_433_card__less__Suc]) ).
fof(f_496_2,plain,
! [U_1756,U_1755] :
( 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_1755))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1756))))) = 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_1755))),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_1756)))))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1755)) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
cnf(f_496_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_1755))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1756))))) = 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_1755))),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_1756)))))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1755)) ),
inference(clausify,[status(thm)],[f_496_2]) ).
fof(f_497_1,plain,
! [I_1,M_4] :
( 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_4))),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_1))))) != zero_zero(nat)
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_4)) ),
inference(fof_nnf,[status(thm)],[fact_434_card__less]) ).
fof(f_497_2,plain,
! [U_1758,U_1757] :
( 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_1757))),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_1758))))) != zero_zero(nat)
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1757)) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
cnf(f_497_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_1757))),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_1758))))) != zero_zero(nat)
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1757)) ),
inference(clausify,[status(thm)],[f_497_2]) ).
fof(f_498_1,plain,
! [I_1,M_4] :
( 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_4))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))) = 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_4))),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_1)))))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_4)) ),
inference(fof_nnf,[status(thm)],[fact_435_card__less__Suc2]) ).
fof(f_498_2,plain,
! [U_1760,U_1759] :
( 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_1759))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1760)))) = 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_1759))),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_1760)))))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1759)) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
cnf(f_498_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_1759))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1760)))) = 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_1759))),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_1760)))))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),U_1759)) ),
inference(clausify,[status(thm)],[f_498_2]) ).
fof(f_499_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_436_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_499_2,plain,
! [U_1762] :
( ! [U_1761] : hAPP(U_1762,U_1762,hAPP(U_1762,fun(U_1762,U_1762),plus_plus(U_1762),zero_zero(U_1762)),U_1761) = ti(U_1762,U_1761)
| ~ comm_semiring_1(U_1762) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
cnf(f_499_3,plain,
( hAPP(U_1762,U_1762,hAPP(U_1762,fun(U_1762,U_1762),plus_plus(U_1762),zero_zero(U_1762)),U_1761) = ti(U_1762,U_1761)
| ~ comm_semiring_1(U_1762) ),
inference(clausify,[status(thm)],[f_499_2]) ).
fof(f_500_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_437_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_500_2,plain,
! [U_1764] :
( ! [U_1763] : hAPP(U_1764,U_1764,hAPP(U_1764,fun(U_1764,U_1764),plus_plus(U_1764),U_1763),zero_zero(U_1764)) = ti(U_1764,U_1763)
| ~ comm_semiring_1(U_1764) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
cnf(f_500_3,plain,
( hAPP(U_1764,U_1764,hAPP(U_1764,fun(U_1764,U_1764),plus_plus(U_1764),U_1763),zero_zero(U_1764)) = ti(U_1764,U_1763)
| ~ comm_semiring_1(U_1764) ),
inference(clausify,[status(thm)],[f_500_2]) ).
fof(f_501_1,plain,
! [Pa,I_1,J_1] :
( hBOOL(hAPP(nat,bool,Pa,I_1))
| ? [I_2] :
( ~ hBOOL(hAPP(nat,bool,Pa,I_2))
& hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I_2)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) )
| ~ hBOOL(hAPP(nat,bool,Pa,J_1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_438_inc__induct]) ).
fof(f_501_2,plain,
! [U_1768,U_1767,U_1766] :
( hBOOL(hAPP(nat,bool,U_1768,U_1767))
| ? [U_1765] :
( ~ hBOOL(hAPP(nat,bool,U_1768,U_1765))
& hBOOL(hAPP(nat,bool,U_1768,hAPP(nat,nat,suc,U_1765)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1765),U_1766)) )
| ~ hBOOL(hAPP(nat,bool,U_1768,U_1766))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1767),U_1766)) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
fof(f_501_3,plain,
! [U_1768,U_1767,U_1766] :
( hBOOL(hAPP(nat,bool,U_1768,U_1767))
| ( ~ hBOOL(hAPP(nat,bool,U_1768,sK94(U_1768,U_1767,U_1766)))
& hBOOL(hAPP(nat,bool,U_1768,hAPP(nat,nat,suc,sK94(U_1768,U_1767,U_1766))))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK94(U_1768,U_1767,U_1766)),U_1766)) )
| ~ hBOOL(hAPP(nat,bool,U_1768,U_1766))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1767),U_1766)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_1765,sK94(U_1768,U_1767,U_1766))],[f_501_2]) ).
cnf(f_501_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK94(U_1768,U_1767,U_1766)),U_1766))
| hBOOL(hAPP(nat,bool,U_1768,U_1767))
| ~ hBOOL(hAPP(nat,bool,U_1768,U_1766))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1767),U_1766)) ),
inference(clausify,[status(thm)],[f_501_3]) ).
cnf(f_501_5,plain,
( hBOOL(hAPP(nat,bool,U_1768,hAPP(nat,nat,suc,sK94(U_1768,U_1767,U_1766))))
| hBOOL(hAPP(nat,bool,U_1768,U_1767))
| ~ hBOOL(hAPP(nat,bool,U_1768,U_1766))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1767),U_1766)) ),
inference(clausify,[status(thm)],[f_501_3]) ).
cnf(f_501_6,plain,
( ~ hBOOL(hAPP(nat,bool,U_1768,sK94(U_1768,U_1767,U_1766)))
| hBOOL(hAPP(nat,bool,U_1768,U_1767))
| ~ hBOOL(hAPP(nat,bool,U_1768,U_1766))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1767),U_1766)) ),
inference(clausify,[status(thm)],[f_501_3]) ).
fof(f_502_1,plain,
! [M_3,N_1] :
( ? [K_2] : N_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_3),K_2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_439_less__imp__Suc__add]) ).
fof(f_502_2,plain,
! [U_1771,U_1770] :
( ? [U_1769] : U_1770 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1771),U_1769))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1771),U_1770)) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
! [U_1771,U_1770] :
( U_1770 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1771),sK95(U_1771,U_1770)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1771),U_1770)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_1769,sK95(U_1771,U_1770))],[f_502_2]) ).
cnf(f_502_4,plain,
( U_1770 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1771),sK95(U_1771,U_1770)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1771),U_1770)) ),
inference(clausify,[status(thm)],[f_502_3]) ).
fof(f_503_1,plain,
! [N_1] :
( ? [M] : N_1 = hAPP(nat,nat,suc,M)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_440_gr0__implies__Suc]) ).
fof(f_503_2,plain,
! [U_1773] :
( ? [U_1772] : U_1773 = hAPP(nat,nat,suc,U_1772)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1773)) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
fof(f_503_3,plain,
! [U_1773] :
( U_1773 = hAPP(nat,nat,suc,sK96(U_1773))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1773)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_1772,sK96(U_1773))],[f_503_2]) ).
cnf(f_503_4,plain,
( U_1773 = hAPP(nat,nat,suc,sK96(U_1773))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),U_1773)) ),
inference(clausify,[status(thm)],[f_503_3]) ).
fof(f_504_1,plain,
! [X_a] :
( ! [Na,N_2,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_2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_2))
| ? [N] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N)))) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_441_lift__Suc__mono__le]) ).
fof(f_504_2,plain,
! [U_1778] :
( ! [U_1777,U_1776,U_1775] :
( hBOOL(hAPP(U_1778,bool,hAPP(U_1778,fun(U_1778,bool),ord_less_eq(U_1778),hAPP(nat,U_1778,U_1775,U_1777)),hAPP(nat,U_1778,U_1775,U_1776)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1777),U_1776))
| ? [U_1774] : ~ hBOOL(hAPP(U_1778,bool,hAPP(U_1778,fun(U_1778,bool),ord_less_eq(U_1778),hAPP(nat,U_1778,U_1775,U_1774)),hAPP(nat,U_1778,U_1775,hAPP(nat,nat,suc,U_1774)))) )
| ~ order(U_1778) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
fof(f_504_3,plain,
! [U_1778] :
( ! [U_1777,U_1776,U_1775] :
( hBOOL(hAPP(U_1778,bool,hAPP(U_1778,fun(U_1778,bool),ord_less_eq(U_1778),hAPP(nat,U_1778,U_1775,U_1777)),hAPP(nat,U_1778,U_1775,U_1776)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1777),U_1776))
| ~ hBOOL(hAPP(U_1778,bool,hAPP(U_1778,fun(U_1778,bool),ord_less_eq(U_1778),hAPP(nat,U_1778,U_1775,sK97(U_1778,U_1777,U_1776,U_1775))),hAPP(nat,U_1778,U_1775,hAPP(nat,nat,suc,sK97(U_1778,U_1777,U_1776,U_1775))))) )
| ~ order(U_1778) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_1774,sK97(U_1778,U_1777,U_1776,U_1775))],[f_504_2]) ).
cnf(f_504_4,plain,
( hBOOL(hAPP(U_1778,bool,hAPP(U_1778,fun(U_1778,bool),ord_less_eq(U_1778),hAPP(nat,U_1778,U_1775,U_1777)),hAPP(nat,U_1778,U_1775,U_1776)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1777),U_1776))
| ~ hBOOL(hAPP(U_1778,bool,hAPP(U_1778,fun(U_1778,bool),ord_less_eq(U_1778),hAPP(nat,U_1778,U_1775,sK97(U_1778,U_1777,U_1776,U_1775))),hAPP(nat,U_1778,U_1775,hAPP(nat,nat,suc,sK97(U_1778,U_1777,U_1776,U_1775)))))
| ~ order(U_1778) ),
inference(clausify,[status(thm)],[f_504_3]) ).
fof(f_505_1,plain,
! [X_a] :
( ! [Na,N_2,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_2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_2))
| ? [N] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N)))) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_442_lift__Suc__mono__less]) ).
fof(f_505_2,plain,
! [U_1783] :
( ! [U_1782,U_1781,U_1780] :
( hBOOL(hAPP(U_1783,bool,hAPP(U_1783,fun(U_1783,bool),ord_less(U_1783),hAPP(nat,U_1783,U_1780,U_1782)),hAPP(nat,U_1783,U_1780,U_1781)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1782),U_1781))
| ? [U_1779] : ~ hBOOL(hAPP(U_1783,bool,hAPP(U_1783,fun(U_1783,bool),ord_less(U_1783),hAPP(nat,U_1783,U_1780,U_1779)),hAPP(nat,U_1783,U_1780,hAPP(nat,nat,suc,U_1779)))) )
| ~ order(U_1783) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
fof(f_505_3,plain,
! [U_1783] :
( ! [U_1782,U_1781,U_1780] :
( hBOOL(hAPP(U_1783,bool,hAPP(U_1783,fun(U_1783,bool),ord_less(U_1783),hAPP(nat,U_1783,U_1780,U_1782)),hAPP(nat,U_1783,U_1780,U_1781)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1782),U_1781))
| ~ hBOOL(hAPP(U_1783,bool,hAPP(U_1783,fun(U_1783,bool),ord_less(U_1783),hAPP(nat,U_1783,U_1780,sK98(U_1783,U_1782,U_1781,U_1780))),hAPP(nat,U_1783,U_1780,hAPP(nat,nat,suc,sK98(U_1783,U_1782,U_1781,U_1780))))) )
| ~ order(U_1783) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_1779,sK98(U_1783,U_1782,U_1781,U_1780))],[f_505_2]) ).
cnf(f_505_4,plain,
( hBOOL(hAPP(U_1783,bool,hAPP(U_1783,fun(U_1783,bool),ord_less(U_1783),hAPP(nat,U_1783,U_1780,U_1782)),hAPP(nat,U_1783,U_1780,U_1781)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1782),U_1781))
| ~ hBOOL(hAPP(U_1783,bool,hAPP(U_1783,fun(U_1783,bool),ord_less(U_1783),hAPP(nat,U_1783,U_1780,sK98(U_1783,U_1782,U_1781,U_1780))),hAPP(nat,U_1783,U_1780,hAPP(nat,nat,suc,sK98(U_1783,U_1782,U_1781,U_1780)))))
| ~ order(U_1783) ),
inference(clausify,[status(thm)],[f_505_3]) ).
fof(f_506_1,plain,
! [X_a] :
( ! [Na,M_2,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_2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_2)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_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_2))) ) )
| ? [N] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N)))) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_443_lift__Suc__mono__less__iff]) ).
fof(f_506_2,plain,
! [U_1788] :
( ! [U_1787,U_1786,U_1785] :
( ( ( hBOOL(hAPP(U_1788,bool,hAPP(U_1788,fun(U_1788,bool),ord_less(U_1788),hAPP(nat,U_1788,U_1785,U_1787)),hAPP(nat,U_1788,U_1785,U_1786)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1787),U_1786)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1787),U_1786))
| ~ hBOOL(hAPP(U_1788,bool,hAPP(U_1788,fun(U_1788,bool),ord_less(U_1788),hAPP(nat,U_1788,U_1785,U_1787)),hAPP(nat,U_1788,U_1785,U_1786))) ) )
| ? [U_1784] : ~ hBOOL(hAPP(U_1788,bool,hAPP(U_1788,fun(U_1788,bool),ord_less(U_1788),hAPP(nat,U_1788,U_1785,U_1784)),hAPP(nat,U_1788,U_1785,hAPP(nat,nat,suc,U_1784)))) )
| ~ order(U_1788) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
fof(f_506_3,plain,
! [U_1788] :
( ! [U_1787,U_1786,U_1785] :
( ( ( hBOOL(hAPP(U_1788,bool,hAPP(U_1788,fun(U_1788,bool),ord_less(U_1788),hAPP(nat,U_1788,U_1785,U_1787)),hAPP(nat,U_1788,U_1785,U_1786)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1787),U_1786)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1787),U_1786))
| ~ hBOOL(hAPP(U_1788,bool,hAPP(U_1788,fun(U_1788,bool),ord_less(U_1788),hAPP(nat,U_1788,U_1785,U_1787)),hAPP(nat,U_1788,U_1785,U_1786))) ) )
| ~ hBOOL(hAPP(U_1788,bool,hAPP(U_1788,fun(U_1788,bool),ord_less(U_1788),hAPP(nat,U_1788,U_1785,sK99(U_1788,U_1787,U_1786,U_1785))),hAPP(nat,U_1788,U_1785,hAPP(nat,nat,suc,sK99(U_1788,U_1787,U_1786,U_1785))))) )
| ~ order(U_1788) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_1784,sK99(U_1788,U_1787,U_1786,U_1785))],[f_506_2]) ).
cnf(f_506_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1787),U_1786))
| ~ hBOOL(hAPP(U_1788,bool,hAPP(U_1788,fun(U_1788,bool),ord_less(U_1788),hAPP(nat,U_1788,U_1785,U_1787)),hAPP(nat,U_1788,U_1785,U_1786)))
| ~ hBOOL(hAPP(U_1788,bool,hAPP(U_1788,fun(U_1788,bool),ord_less(U_1788),hAPP(nat,U_1788,U_1785,sK99(U_1788,U_1787,U_1786,U_1785))),hAPP(nat,U_1788,U_1785,hAPP(nat,nat,suc,sK99(U_1788,U_1787,U_1786,U_1785)))))
| ~ order(U_1788) ),
inference(clausify,[status(thm)],[f_506_3]) ).
cnf(f_506_5,plain,
( hBOOL(hAPP(U_1788,bool,hAPP(U_1788,fun(U_1788,bool),ord_less(U_1788),hAPP(nat,U_1788,U_1785,U_1787)),hAPP(nat,U_1788,U_1785,U_1786)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1787),U_1786))
| ~ hBOOL(hAPP(U_1788,bool,hAPP(U_1788,fun(U_1788,bool),ord_less(U_1788),hAPP(nat,U_1788,U_1785,sK99(U_1788,U_1787,U_1786,U_1785))),hAPP(nat,U_1788,U_1785,hAPP(nat,nat,suc,sK99(U_1788,U_1787,U_1786,U_1785)))))
| ~ order(U_1788) ),
inference(clausify,[status(thm)],[f_506_3]) ).
fof(f_507_1,plain,
! [N_1] : hAPP(nat,nat,suc,N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1),
inference(fof_nnf,[status(thm)],[fact_444_Suc__eq__plus1__left]) ).
fof(f_507_2,plain,
! [U_1789] : hAPP(nat,nat,suc,U_1789) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_1789),
inference(variable_rename,[status(thm)],[f_507_1]) ).
cnf(f_507_3,plain,
hAPP(nat,nat,suc,U_1789) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_1789),
inference(clausify,[status(thm)],[f_507_2]) ).
fof(f_508_1,plain,
! [N_1] : hAPP(nat,nat,suc,N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)),
inference(fof_nnf,[status(thm)],[fact_445_Suc__eq__plus1]) ).
fof(f_508_2,plain,
! [U_1790] : hAPP(nat,nat,suc,U_1790) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1790),one_one(nat)),
inference(variable_rename,[status(thm)],[f_508_1]) ).
cnf(f_508_3,plain,
hAPP(nat,nat,suc,U_1790) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1790),one_one(nat)),
inference(clausify,[status(thm)],[f_508_2]) ).
fof(f_509_1,plain,
! [N_1,M_1] :
( ? [M] : M_1 = hAPP(nat,nat,suc,M)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_1)) ),
inference(fof_nnf,[status(thm)],[fact_446_Suc__le__D]) ).
fof(f_509_2,plain,
! [U_1793,U_1792] :
( ? [U_1791] : U_1792 = hAPP(nat,nat,suc,U_1791)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1793)),U_1792)) ),
inference(variable_rename,[status(thm)],[f_509_1]) ).
fof(f_509_3,plain,
! [U_1793,U_1792] :
( U_1792 = hAPP(nat,nat,suc,sK100(U_1793,U_1792))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1793)),U_1792)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_1791,sK100(U_1793,U_1792))],[f_509_2]) ).
cnf(f_509_4,plain,
( U_1792 = hAPP(nat,nat,suc,sK100(U_1793,U_1792))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1793)),U_1792)) ),
inference(clausify,[status(thm)],[f_509_3]) ).
fof(f_510_1,plain,
! [I,K_1] :
( ? [J] :
( K_1 = hAPP(nat,nat,suc,J)
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) )
| K_1 = hAPP(nat,nat,suc,I)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_1)) ),
inference(fof_nnf,[status(thm)],[fact_447_lessE]) ).
fof(f_510_2,plain,
! [U_1796,U_1795] :
( ? [U_1794] :
( U_1795 = hAPP(nat,nat,suc,U_1794)
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1796),U_1794)) )
| U_1795 = hAPP(nat,nat,suc,U_1796)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1796),U_1795)) ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
fof(f_510_3,plain,
! [U_1796,U_1795] :
( ( U_1795 = hAPP(nat,nat,suc,sK101(U_1796,U_1795))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1796),sK101(U_1796,U_1795))) )
| U_1795 = hAPP(nat,nat,suc,U_1796)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1796),U_1795)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_1794,sK101(U_1796,U_1795))],[f_510_2]) ).
cnf(f_510_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1796),sK101(U_1796,U_1795)))
| U_1795 = hAPP(nat,nat,suc,U_1796)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1796),U_1795)) ),
inference(clausify,[status(thm)],[f_510_3]) ).
cnf(f_510_5,plain,
( U_1795 = hAPP(nat,nat,suc,sK101(U_1796,U_1795))
| U_1795 = hAPP(nat,nat,suc,U_1796)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1796),U_1795)) ),
inference(clausify,[status(thm)],[f_510_3]) ).
fof(f_511_1,plain,
! [I,K_1] :
( ? [J] :
( K_1 = hAPP(nat,nat,suc,J)
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K_1)) ),
inference(fof_nnf,[status(thm)],[fact_448_Suc__lessE]) ).
fof(f_511_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(nat),U_1799),U_1797)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1799)),U_1798)) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
fof(f_511_3,plain,
! [U_1799,U_1798] :
( ( U_1798 = hAPP(nat,nat,suc,sK102(U_1799,U_1798))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1799),sK102(U_1799,U_1798))) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1799)),U_1798)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_1797,sK102(U_1799,U_1798))],[f_511_2]) ).
cnf(f_511_4,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1799),sK102(U_1799,U_1798)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1799)),U_1798)) ),
inference(clausify,[status(thm)],[f_511_3]) ).
cnf(f_511_5,plain,
( U_1798 = hAPP(nat,nat,suc,sK102(U_1799,U_1798))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1799)),U_1798)) ),
inference(clausify,[status(thm)],[f_511_3]) ).
fof(f_512_1,plain,
! [N_1] :
( ? [M] : N_1 = hAPP(nat,nat,suc,M)
| N_1 = zero_zero(nat) ),
inference(fof_nnf,[status(thm)],[fact_449_not0__implies__Suc]) ).
fof(f_512_2,plain,
! [U_1801] :
( ? [U_1800] : U_1801 = hAPP(nat,nat,suc,U_1800)
| U_1801 = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
fof(f_512_3,plain,
! [U_1801] :
( U_1801 = hAPP(nat,nat,suc,sK103(U_1801))
| U_1801 = zero_zero(nat) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_1800,sK103(U_1801))],[f_512_2]) ).
cnf(f_512_4,plain,
( U_1801 = hAPP(nat,nat,suc,sK103(U_1801))
| U_1801 = zero_zero(nat) ),
inference(clausify,[status(thm)],[f_512_3]) ).
fof(f_513_1,plain,
! [Y] :
( ? [Nat] : Y = hAPP(nat,nat,suc,Nat)
| Y = zero_zero(nat) ),
inference(fof_nnf,[status(thm)],[fact_450_nat_Oexhaust]) ).
fof(f_513_2,plain,
! [U_1803] :
( ? [U_1802] : U_1803 = hAPP(nat,nat,suc,U_1802)
| U_1803 = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
fof(f_513_3,plain,
! [U_1803] :
( U_1803 = hAPP(nat,nat,suc,sK104(U_1803))
| U_1803 = zero_zero(nat) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_1802,sK104(U_1803))],[f_513_2]) ).
cnf(f_513_4,plain,
( U_1803 = hAPP(nat,nat,suc,sK104(U_1803))
| U_1803 = zero_zero(nat) ),
inference(clausify,[status(thm)],[f_513_3]) ).
fof(f_514_1,plain,
! [Pa,K] :
( hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))
| ? [N] :
( ~ hBOOL(hAPP(nat,bool,Pa,N))
& hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N))) )
| ~ hBOOL(hAPP(nat,bool,Pa,K)) ),
inference(fof_nnf,[status(thm)],[fact_451_zero__induct]) ).
fof(f_514_2,plain,
! [U_1806,U_1805] :
( hBOOL(hAPP(nat,bool,U_1806,zero_zero(nat)))
| ? [U_1804] :
( ~ hBOOL(hAPP(nat,bool,U_1806,U_1804))
& hBOOL(hAPP(nat,bool,U_1806,hAPP(nat,nat,suc,U_1804))) )
| ~ hBOOL(hAPP(nat,bool,U_1806,U_1805)) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
fof(f_514_3,plain,
! [U_1806] :
( ! [U_1805] : ~ hBOOL(hAPP(nat,bool,U_1806,U_1805))
| hBOOL(hAPP(nat,bool,U_1806,zero_zero(nat)))
| ? [U_1804] :
( ~ hBOOL(hAPP(nat,bool,U_1806,U_1804))
& hBOOL(hAPP(nat,bool,U_1806,hAPP(nat,nat,suc,U_1804))) ) ),
inference(miniscope,[status(thm)],[f_514_2]) ).
fof(f_514_4,plain,
! [U_1806] :
( ! [U_1805] : ~ hBOOL(hAPP(nat,bool,U_1806,U_1805))
| hBOOL(hAPP(nat,bool,U_1806,zero_zero(nat)))
| ( ~ hBOOL(hAPP(nat,bool,U_1806,sK105(U_1806)))
& hBOOL(hAPP(nat,bool,U_1806,hAPP(nat,nat,suc,sK105(U_1806)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_1804,sK105(U_1806))],[f_514_3]) ).
cnf(f_514_5,plain,
( hBOOL(hAPP(nat,bool,U_1806,hAPP(nat,nat,suc,sK105(U_1806))))
| hBOOL(hAPP(nat,bool,U_1806,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,U_1806,U_1805)) ),
inference(clausify,[status(thm)],[f_514_4]) ).
cnf(f_514_6,plain,
( ~ hBOOL(hAPP(nat,bool,U_1806,sK105(U_1806)))
| hBOOL(hAPP(nat,bool,U_1806,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,U_1806,U_1805)) ),
inference(clausify,[status(thm)],[f_514_4]) ).
fof(f_515_1,plain,
! [Na,Pa] :
( hBOOL(hAPP(nat,bool,Pa,Na))
| ? [N] :
( ~ hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N)))
& hBOOL(hAPP(nat,bool,Pa,N)) )
| ~ hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) ),
inference(fof_nnf,[status(thm)],[fact_452_nat__induct]) ).
fof(f_515_2,plain,
! [U_1809,U_1808] :
( hBOOL(hAPP(nat,bool,U_1808,U_1809))
| ? [U_1807] :
( ~ hBOOL(hAPP(nat,bool,U_1808,hAPP(nat,nat,suc,U_1807)))
& hBOOL(hAPP(nat,bool,U_1808,U_1807)) )
| ~ hBOOL(hAPP(nat,bool,U_1808,zero_zero(nat))) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
fof(f_515_3,plain,
! [U_1809,U_1808] :
( hBOOL(hAPP(nat,bool,U_1808,U_1809))
| ( ~ hBOOL(hAPP(nat,bool,U_1808,hAPP(nat,nat,suc,sK106(U_1809,U_1808))))
& hBOOL(hAPP(nat,bool,U_1808,sK106(U_1809,U_1808))) )
| ~ hBOOL(hAPP(nat,bool,U_1808,zero_zero(nat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_1807,sK106(U_1809,U_1808))],[f_515_2]) ).
cnf(f_515_4,plain,
( hBOOL(hAPP(nat,bool,U_1808,sK106(U_1809,U_1808)))
| hBOOL(hAPP(nat,bool,U_1808,U_1809))
| ~ hBOOL(hAPP(nat,bool,U_1808,zero_zero(nat))) ),
inference(clausify,[status(thm)],[f_515_3]) ).
cnf(f_515_5,plain,
( ~ hBOOL(hAPP(nat,bool,U_1808,hAPP(nat,nat,suc,sK106(U_1809,U_1808))))
| hBOOL(hAPP(nat,bool,U_1808,U_1809))
| ~ hBOOL(hAPP(nat,bool,U_1808,zero_zero(nat))) ),
inference(clausify,[status(thm)],[f_515_3]) ).
fof(f_516_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] :
( ~ 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)))
& hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E)) ) )
| ~ linordered_field(X_a) ),
inference(fof_nnf,[status(thm)],[fact_453_field__le__epsilon]) ).
fof(f_516_2,plain,
! [U_1813] :
( ! [U_1812,U_1811] :
( hBOOL(hAPP(U_1813,bool,hAPP(U_1813,fun(U_1813,bool),ord_less_eq(U_1813),U_1812),U_1811))
| ? [U_1810] :
( ~ hBOOL(hAPP(U_1813,bool,hAPP(U_1813,fun(U_1813,bool),ord_less_eq(U_1813),U_1812),hAPP(U_1813,U_1813,hAPP(U_1813,fun(U_1813,U_1813),plus_plus(U_1813),U_1811),U_1810)))
& hBOOL(hAPP(U_1813,bool,hAPP(U_1813,fun(U_1813,bool),ord_less(U_1813),zero_zero(U_1813)),U_1810)) ) )
| ~ linordered_field(U_1813) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
fof(f_516_3,plain,
! [U_1813] :
( ! [U_1812,U_1811] :
( hBOOL(hAPP(U_1813,bool,hAPP(U_1813,fun(U_1813,bool),ord_less_eq(U_1813),U_1812),U_1811))
| ( ~ hBOOL(hAPP(U_1813,bool,hAPP(U_1813,fun(U_1813,bool),ord_less_eq(U_1813),U_1812),hAPP(U_1813,U_1813,hAPP(U_1813,fun(U_1813,U_1813),plus_plus(U_1813),U_1811),sK107(U_1813,U_1812,U_1811))))
& hBOOL(hAPP(U_1813,bool,hAPP(U_1813,fun(U_1813,bool),ord_less(U_1813),zero_zero(U_1813)),sK107(U_1813,U_1812,U_1811))) ) )
| ~ linordered_field(U_1813) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_1810,sK107(U_1813,U_1812,U_1811))],[f_516_2]) ).
cnf(f_516_4,plain,
( hBOOL(hAPP(U_1813,bool,hAPP(U_1813,fun(U_1813,bool),ord_less(U_1813),zero_zero(U_1813)),sK107(U_1813,U_1812,U_1811)))
| hBOOL(hAPP(U_1813,bool,hAPP(U_1813,fun(U_1813,bool),ord_less_eq(U_1813),U_1812),U_1811))
| ~ linordered_field(U_1813) ),
inference(clausify,[status(thm)],[f_516_3]) ).
cnf(f_516_5,plain,
( ~ hBOOL(hAPP(U_1813,bool,hAPP(U_1813,fun(U_1813,bool),ord_less_eq(U_1813),U_1812),hAPP(U_1813,U_1813,hAPP(U_1813,fun(U_1813,U_1813),plus_plus(U_1813),U_1811),sK107(U_1813,U_1812,U_1811))))
| hBOOL(hAPP(U_1813,bool,hAPP(U_1813,fun(U_1813,bool),ord_less_eq(U_1813),U_1812),U_1811))
| ~ linordered_field(U_1813) ),
inference(clausify,[status(thm)],[f_516_3]) ).
fof(f_517_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_454_card_Oeq__fold__g]) ).
fof(f_517_2,plain,
! [U_1815,U_1814] :
( hAPP(fun(U_1815,bool),nat,finite_card(U_1815),U_1814) = hAPP(fun(U_1815,bool),nat,hAPP(nat,fun(fun(U_1815,bool),nat),hAPP(fun(U_1815,nat),fun(nat,fun(fun(U_1815,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_1815,nat),fun(nat,fun(fun(U_1815,bool),nat))),finite_fold_image(nat,U_1815),plus_plus(nat)),hAPP(nat,fun(U_1815,nat),combk(nat,U_1815),one_one(nat))),zero_zero(nat)),U_1814)
| ~ hBOOL(hAPP(fun(U_1815,bool),bool,finite_finite_1(U_1815),U_1814)) ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
cnf(f_517_3,plain,
( hAPP(fun(U_1815,bool),nat,finite_card(U_1815),U_1814) = hAPP(fun(U_1815,bool),nat,hAPP(nat,fun(fun(U_1815,bool),nat),hAPP(fun(U_1815,nat),fun(nat,fun(fun(U_1815,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_1815,nat),fun(nat,fun(fun(U_1815,bool),nat))),finite_fold_image(nat,U_1815),plus_plus(nat)),hAPP(nat,fun(U_1815,nat),combk(nat,U_1815),one_one(nat))),zero_zero(nat)),U_1814)
| ~ hBOOL(hAPP(fun(U_1815,bool),bool,finite_finite_1(U_1815),U_1814)) ),
inference(clausify,[status(thm)],[f_517_2]) ).
fof(f_518_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_518_2,plain,
! [U_1817,U_1816] :
( ( hAPP(fun(U_1817,bool),nat,finite_card(U_1817),U_1816) = zero_zero(nat)
| hBOOL(hAPP(fun(U_1817,bool),bool,finite_finite_1(U_1817),U_1816)) )
& ( hAPP(fun(U_1817,bool),nat,finite_card(U_1817),U_1816) = hAPP(fun(U_1817,bool),nat,hAPP(nat,fun(fun(U_1817,bool),nat),hAPP(fun(U_1817,nat),fun(nat,fun(fun(U_1817,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_1817,nat),fun(nat,fun(fun(U_1817,bool),nat))),finite_fold_image(nat,U_1817),plus_plus(nat)),hAPP(nat,fun(U_1817,nat),combk(nat,U_1817),one_one(nat))),zero_zero(nat)),U_1816)
| ~ hBOOL(hAPP(fun(U_1817,bool),bool,finite_finite_1(U_1817),U_1816)) ) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
fof(f_518_3,plain,
( ! [U_1821,U_1819] :
( hAPP(fun(U_1821,bool),nat,finite_card(U_1821),U_1819) = zero_zero(nat)
| hBOOL(hAPP(fun(U_1821,bool),bool,finite_finite_1(U_1821),U_1819)) )
& ! [U_1820,U_1818] :
( hAPP(fun(U_1820,bool),nat,finite_card(U_1820),U_1818) = hAPP(fun(U_1820,bool),nat,hAPP(nat,fun(fun(U_1820,bool),nat),hAPP(fun(U_1820,nat),fun(nat,fun(fun(U_1820,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_1820,nat),fun(nat,fun(fun(U_1820,bool),nat))),finite_fold_image(nat,U_1820),plus_plus(nat)),hAPP(nat,fun(U_1820,nat),combk(nat,U_1820),one_one(nat))),zero_zero(nat)),U_1818)
| ~ hBOOL(hAPP(fun(U_1820,bool),bool,finite_finite_1(U_1820),U_1818)) ) ),
inference(miniscope,[status(thm)],[f_518_2]) ).
cnf(f_518_4,plain,
( hAPP(fun(U_1820,bool),nat,finite_card(U_1820),U_1818) = hAPP(fun(U_1820,bool),nat,hAPP(nat,fun(fun(U_1820,bool),nat),hAPP(fun(U_1820,nat),fun(nat,fun(fun(U_1820,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(U_1820,nat),fun(nat,fun(fun(U_1820,bool),nat))),finite_fold_image(nat,U_1820),plus_plus(nat)),hAPP(nat,fun(U_1820,nat),combk(nat,U_1820),one_one(nat))),zero_zero(nat)),U_1818)
| ~ hBOOL(hAPP(fun(U_1820,bool),bool,finite_finite_1(U_1820),U_1818)) ),
inference(clausify,[status(thm)],[f_518_3]) ).
cnf(f_518_5,plain,
( hAPP(fun(U_1821,bool),nat,finite_card(U_1821),U_1819) = zero_zero(nat)
| hBOOL(hAPP(fun(U_1821,bool),bool,finite_finite_1(U_1821),U_1819)) ),
inference(clausify,[status(thm)],[f_518_3]) ).
fof(f_519_1,plain,
hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
inference(fof_nnf,[status(thm)],[fact_456_surjh]) ).
cnf(f_519_2,plain,
hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
inference(clausify,[status(thm)],[f_519_1]) ).
fof(f_520_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_457_Ints__odd__less__0]) ).
fof(f_520_2,plain,
! [U_1823] :
( ! [U_1822] :
( ( ( hBOOL(hAPP(U_1823,bool,hAPP(U_1823,fun(U_1823,bool),ord_less(U_1823),hAPP(U_1823,U_1823,hAPP(U_1823,fun(U_1823,U_1823),plus_plus(U_1823),hAPP(U_1823,U_1823,hAPP(U_1823,fun(U_1823,U_1823),plus_plus(U_1823),one_one(U_1823)),U_1822)),U_1822)),zero_zero(U_1823)))
| ~ hBOOL(hAPP(U_1823,bool,hAPP(U_1823,fun(U_1823,bool),ord_less(U_1823),U_1822),zero_zero(U_1823))) )
& ( hBOOL(hAPP(U_1823,bool,hAPP(U_1823,fun(U_1823,bool),ord_less(U_1823),U_1822),zero_zero(U_1823)))
| ~ hBOOL(hAPP(U_1823,bool,hAPP(U_1823,fun(U_1823,bool),ord_less(U_1823),hAPP(U_1823,U_1823,hAPP(U_1823,fun(U_1823,U_1823),plus_plus(U_1823),hAPP(U_1823,U_1823,hAPP(U_1823,fun(U_1823,U_1823),plus_plus(U_1823),one_one(U_1823)),U_1822)),U_1822)),zero_zero(U_1823))) ) )
| ~ hBOOL(hAPP(fun(U_1823,bool),bool,hAPP(U_1823,fun(fun(U_1823,bool),bool),member(U_1823),U_1822),ring_1_Ints(U_1823))) )
| ~ linordered_idom(U_1823) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
cnf(f_520_3,plain,
( hBOOL(hAPP(U_1823,bool,hAPP(U_1823,fun(U_1823,bool),ord_less(U_1823),U_1822),zero_zero(U_1823)))
| ~ hBOOL(hAPP(U_1823,bool,hAPP(U_1823,fun(U_1823,bool),ord_less(U_1823),hAPP(U_1823,U_1823,hAPP(U_1823,fun(U_1823,U_1823),plus_plus(U_1823),hAPP(U_1823,U_1823,hAPP(U_1823,fun(U_1823,U_1823),plus_plus(U_1823),one_one(U_1823)),U_1822)),U_1822)),zero_zero(U_1823)))
| ~ hBOOL(hAPP(fun(U_1823,bool),bool,hAPP(U_1823,fun(fun(U_1823,bool),bool),member(U_1823),U_1822),ring_1_Ints(U_1823)))
| ~ linordered_idom(U_1823) ),
inference(clausify,[status(thm)],[f_520_2]) ).
cnf(f_520_4,plain,
( hBOOL(hAPP(U_1823,bool,hAPP(U_1823,fun(U_1823,bool),ord_less(U_1823),hAPP(U_1823,U_1823,hAPP(U_1823,fun(U_1823,U_1823),plus_plus(U_1823),hAPP(U_1823,U_1823,hAPP(U_1823,fun(U_1823,U_1823),plus_plus(U_1823),one_one(U_1823)),U_1822)),U_1822)),zero_zero(U_1823)))
| ~ hBOOL(hAPP(U_1823,bool,hAPP(U_1823,fun(U_1823,bool),ord_less(U_1823),U_1822),zero_zero(U_1823)))
| ~ hBOOL(hAPP(fun(U_1823,bool),bool,hAPP(U_1823,fun(fun(U_1823,bool),bool),member(U_1823),U_1822),ring_1_Ints(U_1823)))
| ~ linordered_idom(U_1823) ),
inference(clausify,[status(thm)],[f_520_2]) ).
fof(f_521_1,plain,
! [X_a,X_b,A_1,Ba,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)))
| ~ 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) ),
inference(fof_nnf,[status(thm)],[fact_458_image__eqI]) ).
fof(f_521_2,plain,
! [U_1829,U_1828,U_1827,U_1826,U_1825,U_1824] :
( hBOOL(hAPP(fun(U_1829,bool),bool,hAPP(U_1829,fun(fun(U_1829,bool),bool),member(U_1829),U_1826),hAPP(fun(U_1828,bool),fun(U_1829,bool),hAPP(fun(U_1828,U_1829),fun(fun(U_1828,bool),fun(U_1829,bool)),image(U_1828,U_1829),U_1825),U_1827)))
| ~ hBOOL(hAPP(fun(U_1828,bool),bool,hAPP(U_1828,fun(fun(U_1828,bool),bool),member(U_1828),U_1824),U_1827))
| ti(U_1829,U_1826) != hAPP(U_1828,U_1829,U_1825,U_1824) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
cnf(f_521_3,plain,
( hBOOL(hAPP(fun(U_1829,bool),bool,hAPP(U_1829,fun(fun(U_1829,bool),bool),member(U_1829),U_1826),hAPP(fun(U_1828,bool),fun(U_1829,bool),hAPP(fun(U_1828,U_1829),fun(fun(U_1828,bool),fun(U_1829,bool)),image(U_1828,U_1829),U_1825),U_1827)))
| ~ hBOOL(hAPP(fun(U_1828,bool),bool,hAPP(U_1828,fun(fun(U_1828,bool),bool),member(U_1828),U_1824),U_1827))
| ti(U_1829,U_1826) != hAPP(U_1828,U_1829,U_1825,U_1824) ),
inference(clausify,[status(thm)],[f_521_2]) ).
fof(f_522_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_522_2,plain,
! [U_1833,U_1832,U_1831,U_1830] :
( hBOOL(hAPP(fun(U_1833,bool),bool,finite_finite_1(U_1833),hAPP(fun(U_1832,bool),fun(U_1833,bool),hAPP(fun(U_1832,U_1833),fun(fun(U_1832,bool),fun(U_1833,bool)),image(U_1832,U_1833),U_1831),U_1830)))
| ~ hBOOL(hAPP(fun(U_1832,bool),bool,finite_finite_1(U_1832),U_1830)) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
cnf(f_522_3,plain,
( hBOOL(hAPP(fun(U_1833,bool),bool,finite_finite_1(U_1833),hAPP(fun(U_1832,bool),fun(U_1833,bool),hAPP(fun(U_1832,U_1833),fun(fun(U_1832,bool),fun(U_1833,bool)),image(U_1832,U_1833),U_1831),U_1830)))
| ~ hBOOL(hAPP(fun(U_1832,bool),bool,finite_finite_1(U_1832),U_1830)) ),
inference(clausify,[status(thm)],[f_522_2]) ).
fof(f_523_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_523_2,plain,
! [U_1835,U_1834] : 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_1835),U_1834))),
inference(variable_rename,[status(thm)],[f_523_1]) ).
cnf(f_523_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_1835),U_1834))),
inference(clausify,[status(thm)],[f_523_2]) ).
fof(f_524_1,plain,
? [H] :
( hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),H),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))
& hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),H),top_top(fun(arrow_660593299e_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_524_2,plain,
? [U_1836] :
( hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),U_1836),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))
& hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),U_1836),top_top(fun(arrow_660593299e_indi,bool)))) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
fof(f_524_3,plain,
( hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),sK108),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))
& hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),sK108),top_top(fun(arrow_660593299e_indi,bool)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_1836,sK108)],[f_524_2]) ).
cnf(f_524_4,plain,
hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),sK108),top_top(fun(arrow_660593299e_indi,bool)))),
inference(clausify,[status(thm)],[f_524_3]) ).
cnf(f_524_5,plain,
hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),sK108),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
inference(clausify,[status(thm)],[f_524_3]) ).
fof(f_525_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_462_atLeastLessThan__subset__iff]) ).
fof(f_525_2,plain,
! [U_1841] :
( ! [U_1840,U_1839,U_1838,U_1837] :
( ( hBOOL(hAPP(U_1841,bool,hAPP(U_1841,fun(U_1841,bool),ord_less_eq(U_1841),U_1839),U_1837))
& hBOOL(hAPP(U_1841,bool,hAPP(U_1841,fun(U_1841,bool),ord_less_eq(U_1841),U_1838),U_1840)) )
| hBOOL(hAPP(U_1841,bool,hAPP(U_1841,fun(U_1841,bool),ord_less_eq(U_1841),U_1839),U_1840))
| ~ hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less_eq(fun(U_1841,bool)),hAPP(U_1841,fun(U_1841,bool),hAPP(U_1841,fun(U_1841,fun(U_1841,bool)),ord_atLeastLessThan(U_1841),U_1840),U_1839)),hAPP(U_1841,fun(U_1841,bool),hAPP(U_1841,fun(U_1841,fun(U_1841,bool)),ord_atLeastLessThan(U_1841),U_1838),U_1837))) )
| ~ linorder(U_1841) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
cnf(f_525_3,plain,
( hBOOL(hAPP(U_1841,bool,hAPP(U_1841,fun(U_1841,bool),ord_less_eq(U_1841),U_1838),U_1840))
| hBOOL(hAPP(U_1841,bool,hAPP(U_1841,fun(U_1841,bool),ord_less_eq(U_1841),U_1839),U_1840))
| ~ hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less_eq(fun(U_1841,bool)),hAPP(U_1841,fun(U_1841,bool),hAPP(U_1841,fun(U_1841,fun(U_1841,bool)),ord_atLeastLessThan(U_1841),U_1840),U_1839)),hAPP(U_1841,fun(U_1841,bool),hAPP(U_1841,fun(U_1841,fun(U_1841,bool)),ord_atLeastLessThan(U_1841),U_1838),U_1837)))
| ~ linorder(U_1841) ),
inference(clausify,[status(thm)],[f_525_2]) ).
cnf(f_525_4,plain,
( hBOOL(hAPP(U_1841,bool,hAPP(U_1841,fun(U_1841,bool),ord_less_eq(U_1841),U_1839),U_1837))
| hBOOL(hAPP(U_1841,bool,hAPP(U_1841,fun(U_1841,bool),ord_less_eq(U_1841),U_1839),U_1840))
| ~ hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less_eq(fun(U_1841,bool)),hAPP(U_1841,fun(U_1841,bool),hAPP(U_1841,fun(U_1841,fun(U_1841,bool)),ord_atLeastLessThan(U_1841),U_1840),U_1839)),hAPP(U_1841,fun(U_1841,bool),hAPP(U_1841,fun(U_1841,fun(U_1841,bool)),ord_atLeastLessThan(U_1841),U_1838),U_1837)))
| ~ linorder(U_1841) ),
inference(clausify,[status(thm)],[f_525_2]) ).
fof(f_526_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_463_funcset__image]) ).
fof(f_526_2,plain,
! [U_1846,U_1845,U_1844,U_1843,U_1842] :
( hBOOL(hAPP(fun(U_1845,bool),bool,hAPP(fun(U_1845,bool),fun(fun(U_1845,bool),bool),ord_less_eq(fun(U_1845,bool)),hAPP(fun(U_1846,bool),fun(U_1845,bool),hAPP(fun(U_1846,U_1845),fun(fun(U_1846,bool),fun(U_1845,bool)),image(U_1846,U_1845),U_1844),U_1843)),U_1842))
| ~ hBOOL(hAPP(fun(fun(U_1846,U_1845),bool),bool,hAPP(fun(U_1846,U_1845),fun(fun(fun(U_1846,U_1845),bool),bool),member(fun(U_1846,U_1845)),U_1844),hAPP(fun(U_1846,fun(U_1845,bool)),fun(fun(U_1846,U_1845),bool),hAPP(fun(U_1846,bool),fun(fun(U_1846,fun(U_1845,bool)),fun(fun(U_1846,U_1845),bool)),pi(U_1846,U_1845),U_1843),hAPP(fun(U_1845,bool),fun(U_1846,fun(U_1845,bool)),combk(fun(U_1845,bool),U_1846),U_1842)))) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
cnf(f_526_3,plain,
( hBOOL(hAPP(fun(U_1845,bool),bool,hAPP(fun(U_1845,bool),fun(fun(U_1845,bool),bool),ord_less_eq(fun(U_1845,bool)),hAPP(fun(U_1846,bool),fun(U_1845,bool),hAPP(fun(U_1846,U_1845),fun(fun(U_1846,bool),fun(U_1845,bool)),image(U_1846,U_1845),U_1844),U_1843)),U_1842))
| ~ hBOOL(hAPP(fun(fun(U_1846,U_1845),bool),bool,hAPP(fun(U_1846,U_1845),fun(fun(fun(U_1846,U_1845),bool),bool),member(fun(U_1846,U_1845)),U_1844),hAPP(fun(U_1846,fun(U_1845,bool)),fun(fun(U_1846,U_1845),bool),hAPP(fun(U_1846,bool),fun(fun(U_1846,fun(U_1845,bool)),fun(fun(U_1846,U_1845),bool)),pi(U_1846,U_1845),U_1843),hAPP(fun(U_1845,bool),fun(U_1846,fun(U_1845,bool)),combk(fun(U_1845,bool),U_1846),U_1842)))) ),
inference(clausify,[status(thm)],[f_526_2]) ).
fof(f_527_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_464_finite__surj__inj]) ).
fof(f_527_2,plain,
! [U_1849,U_1848,U_1847] :
( hBOOL(hAPP(fun(U_1849,bool),bool,hAPP(fun(U_1849,U_1849),fun(fun(U_1849,bool),bool),inj_on(U_1849,U_1849),U_1848),U_1847))
| ~ hBOOL(hAPP(fun(U_1849,bool),bool,hAPP(fun(U_1849,bool),fun(fun(U_1849,bool),bool),ord_less_eq(fun(U_1849,bool)),U_1847),hAPP(fun(U_1849,bool),fun(U_1849,bool),hAPP(fun(U_1849,U_1849),fun(fun(U_1849,bool),fun(U_1849,bool)),image(U_1849,U_1849),U_1848),U_1847)))
| ~ hBOOL(hAPP(fun(U_1849,bool),bool,finite_finite_1(U_1849),U_1847)) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
cnf(f_527_3,plain,
( hBOOL(hAPP(fun(U_1849,bool),bool,hAPP(fun(U_1849,U_1849),fun(fun(U_1849,bool),bool),inj_on(U_1849,U_1849),U_1848),U_1847))
| ~ hBOOL(hAPP(fun(U_1849,bool),bool,hAPP(fun(U_1849,bool),fun(fun(U_1849,bool),bool),ord_less_eq(fun(U_1849,bool)),U_1847),hAPP(fun(U_1849,bool),fun(U_1849,bool),hAPP(fun(U_1849,U_1849),fun(fun(U_1849,bool),fun(U_1849,bool)),image(U_1849,U_1849),U_1848),U_1847)))
| ~ hBOOL(hAPP(fun(U_1849,bool),bool,finite_finite_1(U_1849),U_1847)) ),
inference(clausify,[status(thm)],[f_527_2]) ).
fof(f_528_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_465_endo__inj__surj]) ).
fof(f_528_2,plain,
! [U_1852,U_1851,U_1850] :
( hAPP(fun(U_1852,bool),fun(U_1852,bool),hAPP(fun(U_1852,U_1852),fun(fun(U_1852,bool),fun(U_1852,bool)),image(U_1852,U_1852),U_1851),U_1850) = ti(fun(U_1852,bool),U_1850)
| ~ hBOOL(hAPP(fun(U_1852,bool),bool,hAPP(fun(U_1852,U_1852),fun(fun(U_1852,bool),bool),inj_on(U_1852,U_1852),U_1851),U_1850))
| ~ hBOOL(hAPP(fun(U_1852,bool),bool,hAPP(fun(U_1852,bool),fun(fun(U_1852,bool),bool),ord_less_eq(fun(U_1852,bool)),hAPP(fun(U_1852,bool),fun(U_1852,bool),hAPP(fun(U_1852,U_1852),fun(fun(U_1852,bool),fun(U_1852,bool)),image(U_1852,U_1852),U_1851),U_1850)),U_1850))
| ~ hBOOL(hAPP(fun(U_1852,bool),bool,finite_finite_1(U_1852),U_1850)) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
cnf(f_528_3,plain,
( hAPP(fun(U_1852,bool),fun(U_1852,bool),hAPP(fun(U_1852,U_1852),fun(fun(U_1852,bool),fun(U_1852,bool)),image(U_1852,U_1852),U_1851),U_1850) = ti(fun(U_1852,bool),U_1850)
| ~ hBOOL(hAPP(fun(U_1852,bool),bool,hAPP(fun(U_1852,U_1852),fun(fun(U_1852,bool),bool),inj_on(U_1852,U_1852),U_1851),U_1850))
| ~ hBOOL(hAPP(fun(U_1852,bool),bool,hAPP(fun(U_1852,bool),fun(fun(U_1852,bool),bool),ord_less_eq(fun(U_1852,bool)),hAPP(fun(U_1852,bool),fun(U_1852,bool),hAPP(fun(U_1852,U_1852),fun(fun(U_1852,bool),fun(U_1852,bool)),image(U_1852,U_1852),U_1851),U_1850)),U_1850))
| ~ hBOOL(hAPP(fun(U_1852,bool),bool,finite_finite_1(U_1852),U_1850)) ),
inference(clausify,[status(thm)],[f_528_2]) ).
fof(f_529_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_466_finite__UNIV__inj__surj]) ).
fof(f_529_2,plain,
! [U_1854,U_1853] :
( hAPP(fun(U_1854,bool),fun(U_1854,bool),hAPP(fun(U_1854,U_1854),fun(fun(U_1854,bool),fun(U_1854,bool)),image(U_1854,U_1854),U_1853),top_top(fun(U_1854,bool))) = top_top(fun(U_1854,bool))
| ~ hBOOL(hAPP(fun(U_1854,bool),bool,hAPP(fun(U_1854,U_1854),fun(fun(U_1854,bool),bool),inj_on(U_1854,U_1854),U_1853),top_top(fun(U_1854,bool))))
| ~ hBOOL(hAPP(fun(U_1854,bool),bool,finite_finite_1(U_1854),top_top(fun(U_1854,bool)))) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
! [U_1854] :
( ! [U_1853] :
( hAPP(fun(U_1854,bool),fun(U_1854,bool),hAPP(fun(U_1854,U_1854),fun(fun(U_1854,bool),fun(U_1854,bool)),image(U_1854,U_1854),U_1853),top_top(fun(U_1854,bool))) = top_top(fun(U_1854,bool))
| ~ hBOOL(hAPP(fun(U_1854,bool),bool,hAPP(fun(U_1854,U_1854),fun(fun(U_1854,bool),bool),inj_on(U_1854,U_1854),U_1853),top_top(fun(U_1854,bool)))) )
| ~ hBOOL(hAPP(fun(U_1854,bool),bool,finite_finite_1(U_1854),top_top(fun(U_1854,bool)))) ),
inference(miniscope,[status(thm)],[f_529_2]) ).
cnf(f_529_4,plain,
( hAPP(fun(U_1854,bool),fun(U_1854,bool),hAPP(fun(U_1854,U_1854),fun(fun(U_1854,bool),fun(U_1854,bool)),image(U_1854,U_1854),U_1853),top_top(fun(U_1854,bool))) = top_top(fun(U_1854,bool))
| ~ hBOOL(hAPP(fun(U_1854,bool),bool,hAPP(fun(U_1854,U_1854),fun(fun(U_1854,bool),bool),inj_on(U_1854,U_1854),U_1853),top_top(fun(U_1854,bool))))
| ~ hBOOL(hAPP(fun(U_1854,bool),bool,finite_finite_1(U_1854),top_top(fun(U_1854,bool)))) ),
inference(clausify,[status(thm)],[f_529_3]) ).
fof(f_530_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_467_finite__UNIV__surj__inj]) ).
fof(f_530_2,plain,
! [U_1856,U_1855] :
( hBOOL(hAPP(fun(U_1856,bool),bool,hAPP(fun(U_1856,U_1856),fun(fun(U_1856,bool),bool),inj_on(U_1856,U_1856),U_1855),top_top(fun(U_1856,bool))))
| hAPP(fun(U_1856,bool),fun(U_1856,bool),hAPP(fun(U_1856,U_1856),fun(fun(U_1856,bool),fun(U_1856,bool)),image(U_1856,U_1856),U_1855),top_top(fun(U_1856,bool))) != top_top(fun(U_1856,bool))
| ~ hBOOL(hAPP(fun(U_1856,bool),bool,finite_finite_1(U_1856),top_top(fun(U_1856,bool)))) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
! [U_1856] :
( ! [U_1855] :
( hBOOL(hAPP(fun(U_1856,bool),bool,hAPP(fun(U_1856,U_1856),fun(fun(U_1856,bool),bool),inj_on(U_1856,U_1856),U_1855),top_top(fun(U_1856,bool))))
| hAPP(fun(U_1856,bool),fun(U_1856,bool),hAPP(fun(U_1856,U_1856),fun(fun(U_1856,bool),fun(U_1856,bool)),image(U_1856,U_1856),U_1855),top_top(fun(U_1856,bool))) != top_top(fun(U_1856,bool)) )
| ~ hBOOL(hAPP(fun(U_1856,bool),bool,finite_finite_1(U_1856),top_top(fun(U_1856,bool)))) ),
inference(miniscope,[status(thm)],[f_530_2]) ).
cnf(f_530_4,plain,
( hBOOL(hAPP(fun(U_1856,bool),bool,hAPP(fun(U_1856,U_1856),fun(fun(U_1856,bool),bool),inj_on(U_1856,U_1856),U_1855),top_top(fun(U_1856,bool))))
| hAPP(fun(U_1856,bool),fun(U_1856,bool),hAPP(fun(U_1856,U_1856),fun(fun(U_1856,bool),fun(U_1856,bool)),image(U_1856,U_1856),U_1855),top_top(fun(U_1856,bool))) != top_top(fun(U_1856,bool))
| ~ hBOOL(hAPP(fun(U_1856,bool),bool,finite_finite_1(U_1856),top_top(fun(U_1856,bool)))) ),
inference(clausify,[status(thm)],[f_530_3]) ).
fof(f_531_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_468_inj__image__subset__iff]) ).
fof(f_531_2,plain,
! [U_1861,U_1860,U_1859,U_1858,U_1857] :
( ( ( hBOOL(hAPP(fun(U_1860,bool),bool,hAPP(fun(U_1860,bool),fun(fun(U_1860,bool),bool),ord_less_eq(fun(U_1860,bool)),hAPP(fun(U_1861,bool),fun(U_1860,bool),hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),fun(U_1860,bool)),image(U_1861,U_1860),U_1857),U_1859)),hAPP(fun(U_1861,bool),fun(U_1860,bool),hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),fun(U_1860,bool)),image(U_1861,U_1860),U_1857),U_1858)))
| ~ hBOOL(hAPP(fun(U_1861,bool),bool,hAPP(fun(U_1861,bool),fun(fun(U_1861,bool),bool),ord_less_eq(fun(U_1861,bool)),U_1859),U_1858)) )
& ( hBOOL(hAPP(fun(U_1861,bool),bool,hAPP(fun(U_1861,bool),fun(fun(U_1861,bool),bool),ord_less_eq(fun(U_1861,bool)),U_1859),U_1858))
| ~ hBOOL(hAPP(fun(U_1860,bool),bool,hAPP(fun(U_1860,bool),fun(fun(U_1860,bool),bool),ord_less_eq(fun(U_1860,bool)),hAPP(fun(U_1861,bool),fun(U_1860,bool),hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),fun(U_1860,bool)),image(U_1861,U_1860),U_1857),U_1859)),hAPP(fun(U_1861,bool),fun(U_1860,bool),hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),fun(U_1860,bool)),image(U_1861,U_1860),U_1857),U_1858))) ) )
| ~ hBOOL(hAPP(fun(U_1861,bool),bool,hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),bool),inj_on(U_1861,U_1860),U_1857),top_top(fun(U_1861,bool)))) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
cnf(f_531_3,plain,
( hBOOL(hAPP(fun(U_1861,bool),bool,hAPP(fun(U_1861,bool),fun(fun(U_1861,bool),bool),ord_less_eq(fun(U_1861,bool)),U_1859),U_1858))
| ~ hBOOL(hAPP(fun(U_1860,bool),bool,hAPP(fun(U_1860,bool),fun(fun(U_1860,bool),bool),ord_less_eq(fun(U_1860,bool)),hAPP(fun(U_1861,bool),fun(U_1860,bool),hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),fun(U_1860,bool)),image(U_1861,U_1860),U_1857),U_1859)),hAPP(fun(U_1861,bool),fun(U_1860,bool),hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),fun(U_1860,bool)),image(U_1861,U_1860),U_1857),U_1858)))
| ~ hBOOL(hAPP(fun(U_1861,bool),bool,hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),bool),inj_on(U_1861,U_1860),U_1857),top_top(fun(U_1861,bool)))) ),
inference(clausify,[status(thm)],[f_531_2]) ).
cnf(f_531_4,plain,
( hBOOL(hAPP(fun(U_1860,bool),bool,hAPP(fun(U_1860,bool),fun(fun(U_1860,bool),bool),ord_less_eq(fun(U_1860,bool)),hAPP(fun(U_1861,bool),fun(U_1860,bool),hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),fun(U_1860,bool)),image(U_1861,U_1860),U_1857),U_1859)),hAPP(fun(U_1861,bool),fun(U_1860,bool),hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),fun(U_1860,bool)),image(U_1861,U_1860),U_1857),U_1858)))
| ~ hBOOL(hAPP(fun(U_1861,bool),bool,hAPP(fun(U_1861,bool),fun(fun(U_1861,bool),bool),ord_less_eq(fun(U_1861,bool)),U_1859),U_1858))
| ~ hBOOL(hAPP(fun(U_1861,bool),bool,hAPP(fun(U_1861,U_1860),fun(fun(U_1861,bool),bool),inj_on(U_1861,U_1860),U_1857),top_top(fun(U_1861,bool)))) ),
inference(clausify,[status(thm)],[f_531_2]) ).
fof(f_532_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_469_card__image__le]) ).
fof(f_532_2,plain,
! [U_1865,U_1864,U_1863,U_1862] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1865,bool),nat,finite_card(U_1865),hAPP(fun(U_1864,bool),fun(U_1865,bool),hAPP(fun(U_1864,U_1865),fun(fun(U_1864,bool),fun(U_1865,bool)),image(U_1864,U_1865),U_1863),U_1862))),hAPP(fun(U_1864,bool),nat,finite_card(U_1864),U_1862)))
| ~ hBOOL(hAPP(fun(U_1864,bool),bool,finite_finite_1(U_1864),U_1862)) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
cnf(f_532_3,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_1865,bool),nat,finite_card(U_1865),hAPP(fun(U_1864,bool),fun(U_1865,bool),hAPP(fun(U_1864,U_1865),fun(fun(U_1864,bool),fun(U_1865,bool)),image(U_1864,U_1865),U_1863),U_1862))),hAPP(fun(U_1864,bool),nat,finite_card(U_1864),U_1862)))
| ~ hBOOL(hAPP(fun(U_1864,bool),bool,finite_finite_1(U_1864),U_1862)) ),
inference(clausify,[status(thm)],[f_532_2]) ).
fof(f_533_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_470_eq__card__imp__inj__on]) ).
fof(f_533_2,plain,
! [U_1869,U_1868,U_1867,U_1866] :
( hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(fun(U_1868,U_1869),fun(fun(U_1868,bool),bool),inj_on(U_1868,U_1869),U_1867),U_1866))
| hAPP(fun(U_1869,bool),nat,finite_card(U_1869),hAPP(fun(U_1868,bool),fun(U_1869,bool),hAPP(fun(U_1868,U_1869),fun(fun(U_1868,bool),fun(U_1869,bool)),image(U_1868,U_1869),U_1867),U_1866)) != hAPP(fun(U_1868,bool),nat,finite_card(U_1868),U_1866)
| ~ hBOOL(hAPP(fun(U_1868,bool),bool,finite_finite_1(U_1868),U_1866)) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
cnf(f_533_3,plain,
( hBOOL(hAPP(fun(U_1868,bool),bool,hAPP(fun(U_1868,U_1869),fun(fun(U_1868,bool),bool),inj_on(U_1868,U_1869),U_1867),U_1866))
| hAPP(fun(U_1869,bool),nat,finite_card(U_1869),hAPP(fun(U_1868,bool),fun(U_1869,bool),hAPP(fun(U_1868,U_1869),fun(fun(U_1868,bool),fun(U_1869,bool)),image(U_1868,U_1869),U_1867),U_1866)) != hAPP(fun(U_1868,bool),nat,finite_card(U_1868),U_1866)
| ~ hBOOL(hAPP(fun(U_1868,bool),bool,finite_finite_1(U_1868),U_1866)) ),
inference(clausify,[status(thm)],[f_533_2]) ).
fof(f_534_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_471_inj__on__iff__eq__card]) ).
fof(f_534_2,plain,
! [U_1873,U_1872,U_1871,U_1870] :
( ( ( hBOOL(hAPP(fun(U_1872,bool),bool,hAPP(fun(U_1872,U_1873),fun(fun(U_1872,bool),bool),inj_on(U_1872,U_1873),U_1871),U_1870))
| hAPP(fun(U_1873,bool),nat,finite_card(U_1873),hAPP(fun(U_1872,bool),fun(U_1873,bool),hAPP(fun(U_1872,U_1873),fun(fun(U_1872,bool),fun(U_1873,bool)),image(U_1872,U_1873),U_1871),U_1870)) != hAPP(fun(U_1872,bool),nat,finite_card(U_1872),U_1870) )
& ( hAPP(fun(U_1873,bool),nat,finite_card(U_1873),hAPP(fun(U_1872,bool),fun(U_1873,bool),hAPP(fun(U_1872,U_1873),fun(fun(U_1872,bool),fun(U_1873,bool)),image(U_1872,U_1873),U_1871),U_1870)) = hAPP(fun(U_1872,bool),nat,finite_card(U_1872),U_1870)
| ~ hBOOL(hAPP(fun(U_1872,bool),bool,hAPP(fun(U_1872,U_1873),fun(fun(U_1872,bool),bool),inj_on(U_1872,U_1873),U_1871),U_1870)) ) )
| ~ hBOOL(hAPP(fun(U_1872,bool),bool,finite_finite_1(U_1872),U_1870)) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
cnf(f_534_3,plain,
( hAPP(fun(U_1873,bool),nat,finite_card(U_1873),hAPP(fun(U_1872,bool),fun(U_1873,bool),hAPP(fun(U_1872,U_1873),fun(fun(U_1872,bool),fun(U_1873,bool)),image(U_1872,U_1873),U_1871),U_1870)) = hAPP(fun(U_1872,bool),nat,finite_card(U_1872),U_1870)
| ~ hBOOL(hAPP(fun(U_1872,bool),bool,hAPP(fun(U_1872,U_1873),fun(fun(U_1872,bool),bool),inj_on(U_1872,U_1873),U_1871),U_1870))
| ~ hBOOL(hAPP(fun(U_1872,bool),bool,finite_finite_1(U_1872),U_1870)) ),
inference(clausify,[status(thm)],[f_534_2]) ).
cnf(f_534_4,plain,
( hBOOL(hAPP(fun(U_1872,bool),bool,hAPP(fun(U_1872,U_1873),fun(fun(U_1872,bool),bool),inj_on(U_1872,U_1873),U_1871),U_1870))
| hAPP(fun(U_1873,bool),nat,finite_card(U_1873),hAPP(fun(U_1872,bool),fun(U_1873,bool),hAPP(fun(U_1872,U_1873),fun(fun(U_1872,bool),fun(U_1873,bool)),image(U_1872,U_1873),U_1871),U_1870)) != hAPP(fun(U_1872,bool),nat,finite_card(U_1872),U_1870)
| ~ hBOOL(hAPP(fun(U_1872,bool),bool,finite_finite_1(U_1872),U_1870)) ),
inference(clausify,[status(thm)],[f_534_2]) ).
fof(f_535_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_472_pigeonhole]) ).
fof(f_535_2,plain,
! [U_1877,U_1876,U_1875,U_1874] :
( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,U_1877),fun(fun(U_1876,bool),bool),inj_on(U_1876,U_1877),U_1875),U_1874))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1877,bool),nat,finite_card(U_1877),hAPP(fun(U_1876,bool),fun(U_1877,bool),hAPP(fun(U_1876,U_1877),fun(fun(U_1876,bool),fun(U_1877,bool)),image(U_1876,U_1877),U_1875),U_1874))),hAPP(fun(U_1876,bool),nat,finite_card(U_1876),U_1874))) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
cnf(f_535_3,plain,
( ~ hBOOL(hAPP(fun(U_1876,bool),bool,hAPP(fun(U_1876,U_1877),fun(fun(U_1876,bool),bool),inj_on(U_1876,U_1877),U_1875),U_1874))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1877,bool),nat,finite_card(U_1877),hAPP(fun(U_1876,bool),fun(U_1877,bool),hAPP(fun(U_1876,U_1877),fun(fun(U_1876,bool),fun(U_1877,bool)),image(U_1876,U_1877),U_1875),U_1874))),hAPP(fun(U_1876,bool),nat,finite_card(U_1876),U_1874))) ),
inference(clausify,[status(thm)],[f_535_2]) ).
fof(f_536_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_473_Ints__double__eq__0__iff]) ).
fof(f_536_2,plain,
! [U_1879] :
( ! [U_1878] :
( ( ( hAPP(U_1879,U_1879,hAPP(U_1879,fun(U_1879,U_1879),plus_plus(U_1879),U_1878),U_1878) = zero_zero(U_1879)
| ti(U_1879,U_1878) != zero_zero(U_1879) )
& ( ti(U_1879,U_1878) = zero_zero(U_1879)
| hAPP(U_1879,U_1879,hAPP(U_1879,fun(U_1879,U_1879),plus_plus(U_1879),U_1878),U_1878) != zero_zero(U_1879) ) )
| ~ hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(U_1879,fun(fun(U_1879,bool),bool),member(U_1879),U_1878),ring_1_Ints(U_1879))) )
| ~ ring_char_0(U_1879) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
cnf(f_536_3,plain,
( ti(U_1879,U_1878) = zero_zero(U_1879)
| hAPP(U_1879,U_1879,hAPP(U_1879,fun(U_1879,U_1879),plus_plus(U_1879),U_1878),U_1878) != zero_zero(U_1879)
| ~ hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(U_1879,fun(fun(U_1879,bool),bool),member(U_1879),U_1878),ring_1_Ints(U_1879)))
| ~ ring_char_0(U_1879) ),
inference(clausify,[status(thm)],[f_536_2]) ).
cnf(f_536_4,plain,
( hAPP(U_1879,U_1879,hAPP(U_1879,fun(U_1879,U_1879),plus_plus(U_1879),U_1878),U_1878) = zero_zero(U_1879)
| ti(U_1879,U_1878) != zero_zero(U_1879)
| ~ hBOOL(hAPP(fun(U_1879,bool),bool,hAPP(U_1879,fun(fun(U_1879,bool),bool),member(U_1879),U_1878),ring_1_Ints(U_1879)))
| ~ ring_char_0(U_1879) ),
inference(clausify,[status(thm)],[f_536_2]) ).
fof(f_537_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_474_Ints__0]) ).
fof(f_537_2,plain,
! [U_1880] :
( hBOOL(hAPP(fun(U_1880,bool),bool,hAPP(U_1880,fun(fun(U_1880,bool),bool),member(U_1880),zero_zero(U_1880)),ring_1_Ints(U_1880)))
| ~ ring_1(U_1880) ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
cnf(f_537_3,plain,
( hBOOL(hAPP(fun(U_1880,bool),bool,hAPP(U_1880,fun(fun(U_1880,bool),bool),member(U_1880),zero_zero(U_1880)),ring_1_Ints(U_1880)))
| ~ ring_1(U_1880) ),
inference(clausify,[status(thm)],[f_537_2]) ).
fof(f_538_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_475_Ints__1]) ).
fof(f_538_2,plain,
! [U_1881] :
( hBOOL(hAPP(fun(U_1881,bool),bool,hAPP(U_1881,fun(fun(U_1881,bool),bool),member(U_1881),one_one(U_1881)),ring_1_Ints(U_1881)))
| ~ ring_1(U_1881) ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
cnf(f_538_3,plain,
( hBOOL(hAPP(fun(U_1881,bool),bool,hAPP(U_1881,fun(fun(U_1881,bool),bool),member(U_1881),one_one(U_1881)),ring_1_Ints(U_1881)))
| ~ ring_1(U_1881) ),
inference(clausify,[status(thm)],[f_538_2]) ).
fof(f_539_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_476_Ints__add]) ).
fof(f_539_2,plain,
! [U_1884] :
( ! [U_1883,U_1882] :
( hBOOL(hAPP(fun(U_1884,bool),bool,hAPP(U_1884,fun(fun(U_1884,bool),bool),member(U_1884),hAPP(U_1884,U_1884,hAPP(U_1884,fun(U_1884,U_1884),plus_plus(U_1884),U_1882),U_1883)),ring_1_Ints(U_1884)))
| ~ hBOOL(hAPP(fun(U_1884,bool),bool,hAPP(U_1884,fun(fun(U_1884,bool),bool),member(U_1884),U_1883),ring_1_Ints(U_1884)))
| ~ hBOOL(hAPP(fun(U_1884,bool),bool,hAPP(U_1884,fun(fun(U_1884,bool),bool),member(U_1884),U_1882),ring_1_Ints(U_1884))) )
| ~ ring_1(U_1884) ),
inference(variable_rename,[status(thm)],[f_539_1]) ).
cnf(f_539_3,plain,
( hBOOL(hAPP(fun(U_1884,bool),bool,hAPP(U_1884,fun(fun(U_1884,bool),bool),member(U_1884),hAPP(U_1884,U_1884,hAPP(U_1884,fun(U_1884,U_1884),plus_plus(U_1884),U_1882),U_1883)),ring_1_Ints(U_1884)))
| ~ hBOOL(hAPP(fun(U_1884,bool),bool,hAPP(U_1884,fun(fun(U_1884,bool),bool),member(U_1884),U_1883),ring_1_Ints(U_1884)))
| ~ hBOOL(hAPP(fun(U_1884,bool),bool,hAPP(U_1884,fun(fun(U_1884,bool),bool),member(U_1884),U_1882),ring_1_Ints(U_1884)))
| ~ ring_1(U_1884) ),
inference(clausify,[status(thm)],[f_539_2]) ).
fof(f_540_1,plain,
! [X_b,X_a,A_1,F,X_1,Y_2] :
( ti(X_b,X_1) = ti(X_b,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),A_1)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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),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_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_2) ),
inference(fof_nnf,[status(thm)],[fact_477_inv__into__injective]) ).
fof(f_540_2,plain,
! [U_1890,U_1889,U_1888,U_1887,U_1886,U_1885] :
( ti(U_1890,U_1886) = ti(U_1890,U_1885)
| ~ hBOOL(hAPP(fun(U_1890,bool),bool,hAPP(U_1890,fun(fun(U_1890,bool),bool),member(U_1890),U_1885),hAPP(fun(U_1889,bool),fun(U_1890,bool),hAPP(fun(U_1889,U_1890),fun(fun(U_1889,bool),fun(U_1890,bool)),image(U_1889,U_1890),U_1887),U_1888)))
| ~ hBOOL(hAPP(fun(U_1890,bool),bool,hAPP(U_1890,fun(fun(U_1890,bool),bool),member(U_1890),U_1886),hAPP(fun(U_1889,bool),fun(U_1890,bool),hAPP(fun(U_1889,U_1890),fun(fun(U_1889,bool),fun(U_1890,bool)),image(U_1889,U_1890),U_1887),U_1888)))
| hAPP(U_1890,U_1889,hAPP(fun(U_1889,U_1890),fun(U_1890,U_1889),hAPP(fun(U_1889,bool),fun(fun(U_1889,U_1890),fun(U_1890,U_1889)),hilbert_inv_into(U_1889,U_1890),U_1888),U_1887),U_1886) != hAPP(U_1890,U_1889,hAPP(fun(U_1889,U_1890),fun(U_1890,U_1889),hAPP(fun(U_1889,bool),fun(fun(U_1889,U_1890),fun(U_1890,U_1889)),hilbert_inv_into(U_1889,U_1890),U_1888),U_1887),U_1885) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
cnf(f_540_3,plain,
( ti(U_1890,U_1886) = ti(U_1890,U_1885)
| ~ hBOOL(hAPP(fun(U_1890,bool),bool,hAPP(U_1890,fun(fun(U_1890,bool),bool),member(U_1890),U_1885),hAPP(fun(U_1889,bool),fun(U_1890,bool),hAPP(fun(U_1889,U_1890),fun(fun(U_1889,bool),fun(U_1890,bool)),image(U_1889,U_1890),U_1887),U_1888)))
| ~ hBOOL(hAPP(fun(U_1890,bool),bool,hAPP(U_1890,fun(fun(U_1890,bool),bool),member(U_1890),U_1886),hAPP(fun(U_1889,bool),fun(U_1890,bool),hAPP(fun(U_1889,U_1890),fun(fun(U_1889,bool),fun(U_1890,bool)),image(U_1889,U_1890),U_1887),U_1888)))
| hAPP(U_1890,U_1889,hAPP(fun(U_1889,U_1890),fun(U_1890,U_1889),hAPP(fun(U_1889,bool),fun(fun(U_1889,U_1890),fun(U_1890,U_1889)),hilbert_inv_into(U_1889,U_1890),U_1888),U_1887),U_1886) != hAPP(U_1890,U_1889,hAPP(fun(U_1889,U_1890),fun(U_1890,U_1889),hAPP(fun(U_1889,bool),fun(fun(U_1889,U_1890),fun(U_1890,U_1889)),hilbert_inv_into(U_1889,U_1890),U_1888),U_1887),U_1885) ),
inference(clausify,[status(thm)],[f_540_2]) ).
fof(f_541_1,plain,
! [X_a,X_b,X_1,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_1)),A_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_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_478_inv__into__into]) ).
fof(f_541_2,plain,
! [U_1895,U_1894,U_1893,U_1892,U_1891] :
( hBOOL(hAPP(fun(U_1894,bool),bool,hAPP(U_1894,fun(fun(U_1894,bool),bool),member(U_1894),hAPP(U_1895,U_1894,hAPP(fun(U_1894,U_1895),fun(U_1895,U_1894),hAPP(fun(U_1894,bool),fun(fun(U_1894,U_1895),fun(U_1895,U_1894)),hilbert_inv_into(U_1894,U_1895),U_1891),U_1892),U_1893)),U_1891))
| ~ hBOOL(hAPP(fun(U_1895,bool),bool,hAPP(U_1895,fun(fun(U_1895,bool),bool),member(U_1895),U_1893),hAPP(fun(U_1894,bool),fun(U_1895,bool),hAPP(fun(U_1894,U_1895),fun(fun(U_1894,bool),fun(U_1895,bool)),image(U_1894,U_1895),U_1892),U_1891))) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
cnf(f_541_3,plain,
( hBOOL(hAPP(fun(U_1894,bool),bool,hAPP(U_1894,fun(fun(U_1894,bool),bool),member(U_1894),hAPP(U_1895,U_1894,hAPP(fun(U_1894,U_1895),fun(U_1895,U_1894),hAPP(fun(U_1894,bool),fun(fun(U_1894,U_1895),fun(U_1895,U_1894)),hilbert_inv_into(U_1894,U_1895),U_1891),U_1892),U_1893)),U_1891))
| ~ hBOOL(hAPP(fun(U_1895,bool),bool,hAPP(U_1895,fun(fun(U_1895,bool),bool),member(U_1895),U_1893),hAPP(fun(U_1894,bool),fun(U_1895,bool),hAPP(fun(U_1894,U_1895),fun(fun(U_1894,bool),fun(U_1895,bool)),image(U_1894,U_1895),U_1892),U_1891))) ),
inference(clausify,[status(thm)],[f_541_2]) ).
fof(f_542_1,plain,
! [X_a,X_b,Y_2,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_2)) = ti(X_a,Y_2)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_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_479_f__inv__into__f]) ).
fof(f_542_2,plain,
! [U_1900,U_1899,U_1898,U_1897,U_1896] :
( hAPP(U_1899,U_1900,U_1897,hAPP(U_1900,U_1899,hAPP(fun(U_1899,U_1900),fun(U_1900,U_1899),hAPP(fun(U_1899,bool),fun(fun(U_1899,U_1900),fun(U_1900,U_1899)),hilbert_inv_into(U_1899,U_1900),U_1896),U_1897),U_1898)) = ti(U_1900,U_1898)
| ~ hBOOL(hAPP(fun(U_1900,bool),bool,hAPP(U_1900,fun(fun(U_1900,bool),bool),member(U_1900),U_1898),hAPP(fun(U_1899,bool),fun(U_1900,bool),hAPP(fun(U_1899,U_1900),fun(fun(U_1899,bool),fun(U_1900,bool)),image(U_1899,U_1900),U_1897),U_1896))) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
cnf(f_542_3,plain,
( hAPP(U_1899,U_1900,U_1897,hAPP(U_1900,U_1899,hAPP(fun(U_1899,U_1900),fun(U_1900,U_1899),hAPP(fun(U_1899,bool),fun(fun(U_1899,U_1900),fun(U_1900,U_1899)),hilbert_inv_into(U_1899,U_1900),U_1896),U_1897),U_1898)) = ti(U_1900,U_1898)
| ~ hBOOL(hAPP(fun(U_1900,bool),bool,hAPP(U_1900,fun(fun(U_1900,bool),bool),member(U_1900),U_1898),hAPP(fun(U_1899,bool),fun(U_1900,bool),hAPP(fun(U_1899,U_1900),fun(fun(U_1899,bool),fun(U_1900,bool)),image(U_1899,U_1900),U_1897),U_1896))) ),
inference(clausify,[status(thm)],[f_542_2]) ).
fof(f_543_1,plain,
! [X_b,X_a,Ba,F,X_1,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_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_480_rev__image__eqI]) ).
fof(f_543_2,plain,
! [U_1906,U_1905,U_1904,U_1903,U_1902,U_1901] :
( 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),U_1901)))
| ti(U_1906,U_1904) != hAPP(U_1905,U_1906,U_1903,U_1902)
| ~ hBOOL(hAPP(fun(U_1905,bool),bool,hAPP(U_1905,fun(fun(U_1905,bool),bool),member(U_1905),U_1902),U_1901)) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
cnf(f_543_3,plain,
( 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),U_1901)))
| ti(U_1906,U_1904) != hAPP(U_1905,U_1906,U_1903,U_1902)
| ~ hBOOL(hAPP(fun(U_1905,bool),bool,hAPP(U_1905,fun(fun(U_1905,bool),bool),member(U_1905),U_1902),U_1901)) ),
inference(clausify,[status(thm)],[f_543_2]) ).
fof(f_544_1,plain,
! [X_b,X_a,F,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(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_1),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_481_imageI]) ).
fof(f_544_2,plain,
! [U_1911,U_1910,U_1909,U_1908,U_1907] :
( hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(U_1911,fun(fun(U_1911,bool),bool),member(U_1911),hAPP(U_1910,U_1911,U_1909,U_1908)),hAPP(fun(U_1910,bool),fun(U_1911,bool),hAPP(fun(U_1910,U_1911),fun(fun(U_1910,bool),fun(U_1911,bool)),image(U_1910,U_1911),U_1909),U_1907)))
| ~ hBOOL(hAPP(fun(U_1910,bool),bool,hAPP(U_1910,fun(fun(U_1910,bool),bool),member(U_1910),U_1908),U_1907)) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
cnf(f_544_3,plain,
( hBOOL(hAPP(fun(U_1911,bool),bool,hAPP(U_1911,fun(fun(U_1911,bool),bool),member(U_1911),hAPP(U_1910,U_1911,U_1909,U_1908)),hAPP(fun(U_1910,bool),fun(U_1911,bool),hAPP(fun(U_1910,U_1911),fun(fun(U_1910,bool),fun(U_1911,bool)),image(U_1910,U_1911),U_1909),U_1907)))
| ~ hBOOL(hAPP(fun(U_1910,bool),bool,hAPP(U_1910,fun(fun(U_1910,bool),bool),member(U_1910),U_1908),U_1907)) ),
inference(clausify,[status(thm)],[f_544_2]) ).
fof(f_545_1,plain,
! [X_a,X_b,Z,F,A_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),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_2] :
( ti(X_a,Z) != 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)) ) )
& ( ? [X_2] :
( ti(X_a,Z) = 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),Z),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_482_image__iff]) ).
fof(f_545_2,plain,
! [U_1918,U_1917,U_1916,U_1915,U_1914] :
( ( hBOOL(hAPP(fun(U_1918,bool),bool,hAPP(U_1918,fun(fun(U_1918,bool),bool),member(U_1918),U_1916),hAPP(fun(U_1917,bool),fun(U_1918,bool),hAPP(fun(U_1917,U_1918),fun(fun(U_1917,bool),fun(U_1918,bool)),image(U_1917,U_1918),U_1915),U_1914)))
| ! [U_1913] :
( ti(U_1918,U_1916) != hAPP(U_1917,U_1918,U_1915,U_1913)
| ~ hBOOL(hAPP(fun(U_1917,bool),bool,hAPP(U_1917,fun(fun(U_1917,bool),bool),member(U_1917),U_1913),U_1914)) ) )
& ( ? [U_1912] :
( ti(U_1918,U_1916) = hAPP(U_1917,U_1918,U_1915,U_1912)
& hBOOL(hAPP(fun(U_1917,bool),bool,hAPP(U_1917,fun(fun(U_1917,bool),bool),member(U_1917),U_1912),U_1914)) )
| ~ hBOOL(hAPP(fun(U_1918,bool),bool,hAPP(U_1918,fun(fun(U_1918,bool),bool),member(U_1918),U_1916),hAPP(fun(U_1917,bool),fun(U_1918,bool),hAPP(fun(U_1917,U_1918),fun(fun(U_1917,bool),fun(U_1918,bool)),image(U_1917,U_1918),U_1915),U_1914))) ) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
fof(f_545_3,plain,
( ! [U_1928,U_1926,U_1924,U_1922,U_1920] :
( hBOOL(hAPP(fun(U_1928,bool),bool,hAPP(U_1928,fun(fun(U_1928,bool),bool),member(U_1928),U_1924),hAPP(fun(U_1926,bool),fun(U_1928,bool),hAPP(fun(U_1926,U_1928),fun(fun(U_1926,bool),fun(U_1928,bool)),image(U_1926,U_1928),U_1922),U_1920)))
| ! [U_1913] :
( ti(U_1928,U_1924) != hAPP(U_1926,U_1928,U_1922,U_1913)
| ~ hBOOL(hAPP(fun(U_1926,bool),bool,hAPP(U_1926,fun(fun(U_1926,bool),bool),member(U_1926),U_1913),U_1920)) ) )
& ! [U_1927,U_1925,U_1923,U_1921,U_1919] :
( ? [U_1912] :
( ti(U_1927,U_1923) = hAPP(U_1925,U_1927,U_1921,U_1912)
& hBOOL(hAPP(fun(U_1925,bool),bool,hAPP(U_1925,fun(fun(U_1925,bool),bool),member(U_1925),U_1912),U_1919)) )
| ~ hBOOL(hAPP(fun(U_1927,bool),bool,hAPP(U_1927,fun(fun(U_1927,bool),bool),member(U_1927),U_1923),hAPP(fun(U_1925,bool),fun(U_1927,bool),hAPP(fun(U_1925,U_1927),fun(fun(U_1925,bool),fun(U_1927,bool)),image(U_1925,U_1927),U_1921),U_1919))) ) ),
inference(miniscope,[status(thm)],[f_545_2]) ).
fof(f_545_4,plain,
( ! [U_1928,U_1926,U_1924,U_1922,U_1920] :
( hBOOL(hAPP(fun(U_1928,bool),bool,hAPP(U_1928,fun(fun(U_1928,bool),bool),member(U_1928),U_1924),hAPP(fun(U_1926,bool),fun(U_1928,bool),hAPP(fun(U_1926,U_1928),fun(fun(U_1926,bool),fun(U_1928,bool)),image(U_1926,U_1928),U_1922),U_1920)))
| ! [U_1913] :
( ti(U_1928,U_1924) != hAPP(U_1926,U_1928,U_1922,U_1913)
| ~ hBOOL(hAPP(fun(U_1926,bool),bool,hAPP(U_1926,fun(fun(U_1926,bool),bool),member(U_1926),U_1913),U_1920)) ) )
& ! [U_1927,U_1925,U_1923,U_1921,U_1919] :
( ( ti(U_1927,U_1923) = hAPP(U_1925,U_1927,U_1921,sK109(U_1927,U_1925,U_1923,U_1921,U_1919))
& hBOOL(hAPP(fun(U_1925,bool),bool,hAPP(U_1925,fun(fun(U_1925,bool),bool),member(U_1925),sK109(U_1927,U_1925,U_1923,U_1921,U_1919)),U_1919)) )
| ~ hBOOL(hAPP(fun(U_1927,bool),bool,hAPP(U_1927,fun(fun(U_1927,bool),bool),member(U_1927),U_1923),hAPP(fun(U_1925,bool),fun(U_1927,bool),hAPP(fun(U_1925,U_1927),fun(fun(U_1925,bool),fun(U_1927,bool)),image(U_1925,U_1927),U_1921),U_1919))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_1912,sK109(U_1927,U_1925,U_1923,U_1921,U_1919))],[f_545_3]) ).
cnf(f_545_5,plain,
( hBOOL(hAPP(fun(U_1925,bool),bool,hAPP(U_1925,fun(fun(U_1925,bool),bool),member(U_1925),sK109(U_1927,U_1925,U_1923,U_1921,U_1919)),U_1919))
| ~ hBOOL(hAPP(fun(U_1927,bool),bool,hAPP(U_1927,fun(fun(U_1927,bool),bool),member(U_1927),U_1923),hAPP(fun(U_1925,bool),fun(U_1927,bool),hAPP(fun(U_1925,U_1927),fun(fun(U_1925,bool),fun(U_1927,bool)),image(U_1925,U_1927),U_1921),U_1919))) ),
inference(clausify,[status(thm)],[f_545_4]) ).
cnf(f_545_6,plain,
( ti(U_1927,U_1923) = hAPP(U_1925,U_1927,U_1921,sK109(U_1927,U_1925,U_1923,U_1921,U_1919))
| ~ hBOOL(hAPP(fun(U_1927,bool),bool,hAPP(U_1927,fun(fun(U_1927,bool),bool),member(U_1927),U_1923),hAPP(fun(U_1925,bool),fun(U_1927,bool),hAPP(fun(U_1925,U_1927),fun(fun(U_1925,bool),fun(U_1927,bool)),image(U_1925,U_1927),U_1921),U_1919))) ),
inference(clausify,[status(thm)],[f_545_4]) ).
cnf(f_545_7,plain,
( hBOOL(hAPP(fun(U_1928,bool),bool,hAPP(U_1928,fun(fun(U_1928,bool),bool),member(U_1928),U_1924),hAPP(fun(U_1926,bool),fun(U_1928,bool),hAPP(fun(U_1926,U_1928),fun(fun(U_1926,bool),fun(U_1928,bool)),image(U_1926,U_1928),U_1922),U_1920)))
| ti(U_1928,U_1924) != hAPP(U_1926,U_1928,U_1922,U_1913)
| ~ hBOOL(hAPP(fun(U_1926,bool),bool,hAPP(U_1926,fun(fun(U_1926,bool),bool),member(U_1926),U_1913),U_1920)) ),
inference(clausify,[status(thm)],[f_545_4]) ).
fof(f_546_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_483_image__image]) ).
fof(f_546_2,plain,
! [U_1934,U_1933,U_1932,U_1931,U_1930,U_1929] : hAPP(fun(U_1934,bool),fun(U_1933,bool),hAPP(fun(U_1934,U_1933),fun(fun(U_1934,bool),fun(U_1933,bool)),image(U_1934,U_1933),U_1931),hAPP(fun(U_1932,bool),fun(U_1934,bool),hAPP(fun(U_1932,U_1934),fun(fun(U_1932,bool),fun(U_1934,bool)),image(U_1932,U_1934),U_1930),U_1929)) = hAPP(fun(U_1932,bool),fun(U_1933,bool),hAPP(fun(U_1932,U_1933),fun(fun(U_1932,bool),fun(U_1933,bool)),image(U_1932,U_1933),hAPP(fun(U_1932,U_1934),fun(U_1932,U_1933),hAPP(fun(U_1934,U_1933),fun(fun(U_1932,U_1934),fun(U_1932,U_1933)),combb(U_1934,U_1933,U_1932),U_1931),U_1930)),U_1929),
inference(variable_rename,[status(thm)],[f_546_1]) ).
cnf(f_546_3,plain,
hAPP(fun(U_1934,bool),fun(U_1933,bool),hAPP(fun(U_1934,U_1933),fun(fun(U_1934,bool),fun(U_1933,bool)),image(U_1934,U_1933),U_1931),hAPP(fun(U_1932,bool),fun(U_1934,bool),hAPP(fun(U_1932,U_1934),fun(fun(U_1932,bool),fun(U_1934,bool)),image(U_1932,U_1934),U_1930),U_1929)) = hAPP(fun(U_1932,bool),fun(U_1933,bool),hAPP(fun(U_1932,U_1933),fun(fun(U_1932,bool),fun(U_1933,bool)),image(U_1932,U_1933),hAPP(fun(U_1932,U_1934),fun(U_1932,U_1933),hAPP(fun(U_1934,U_1933),fun(fun(U_1932,U_1934),fun(U_1932,U_1933)),combb(U_1934,U_1933,U_1932),U_1931),U_1930)),U_1929),
inference(clausify,[status(thm)],[f_546_2]) ).
fof(f_547_1,plain,
! [X_a,Y_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),combi(X_a)),Y_1) = ti(fun(X_a,bool),Y_1),
inference(fof_nnf,[status(thm)],[fact_484_image__ident]) ).
fof(f_547_2,plain,
! [U_1936,U_1935] : hAPP(fun(U_1936,bool),fun(U_1936,bool),hAPP(fun(U_1936,U_1936),fun(fun(U_1936,bool),fun(U_1936,bool)),image(U_1936,U_1936),combi(U_1936)),U_1935) = ti(fun(U_1936,bool),U_1935),
inference(variable_rename,[status(thm)],[f_547_1]) ).
cnf(f_547_3,plain,
hAPP(fun(U_1936,bool),fun(U_1936,bool),hAPP(fun(U_1936,U_1936),fun(fun(U_1936,bool),fun(U_1936,bool)),image(U_1936,U_1936),combi(U_1936)),U_1935) = ti(fun(U_1936,bool),U_1935),
inference(clausify,[status(thm)],[f_547_2]) ).
fof(f_548_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_485_subset__image__iff]) ).
fof(f_548_2,plain,
! [U_1943,U_1942,U_1941,U_1940,U_1939] :
( ( hBOOL(hAPP(fun(U_1943,bool),bool,hAPP(fun(U_1943,bool),fun(fun(U_1943,bool),bool),ord_less_eq(fun(U_1943,bool)),U_1941),hAPP(fun(U_1942,bool),fun(U_1943,bool),hAPP(fun(U_1942,U_1943),fun(fun(U_1942,bool),fun(U_1943,bool)),image(U_1942,U_1943),U_1940),U_1939)))
| ! [U_1938] :
( ti(fun(U_1943,bool),U_1941) != hAPP(fun(U_1942,bool),fun(U_1943,bool),hAPP(fun(U_1942,U_1943),fun(fun(U_1942,bool),fun(U_1943,bool)),image(U_1942,U_1943),U_1940),U_1938)
| ~ hBOOL(hAPP(fun(U_1942,bool),bool,hAPP(fun(U_1942,bool),fun(fun(U_1942,bool),bool),ord_less_eq(fun(U_1942,bool)),U_1938),U_1939)) ) )
& ( ? [U_1937] :
( ti(fun(U_1943,bool),U_1941) = hAPP(fun(U_1942,bool),fun(U_1943,bool),hAPP(fun(U_1942,U_1943),fun(fun(U_1942,bool),fun(U_1943,bool)),image(U_1942,U_1943),U_1940),U_1937)
& hBOOL(hAPP(fun(U_1942,bool),bool,hAPP(fun(U_1942,bool),fun(fun(U_1942,bool),bool),ord_less_eq(fun(U_1942,bool)),U_1937),U_1939)) )
| ~ hBOOL(hAPP(fun(U_1943,bool),bool,hAPP(fun(U_1943,bool),fun(fun(U_1943,bool),bool),ord_less_eq(fun(U_1943,bool)),U_1941),hAPP(fun(U_1942,bool),fun(U_1943,bool),hAPP(fun(U_1942,U_1943),fun(fun(U_1942,bool),fun(U_1943,bool)),image(U_1942,U_1943),U_1940),U_1939))) ) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
fof(f_548_3,plain,
( ! [U_1953,U_1951,U_1949,U_1947,U_1945] :
( hBOOL(hAPP(fun(U_1953,bool),bool,hAPP(fun(U_1953,bool),fun(fun(U_1953,bool),bool),ord_less_eq(fun(U_1953,bool)),U_1949),hAPP(fun(U_1951,bool),fun(U_1953,bool),hAPP(fun(U_1951,U_1953),fun(fun(U_1951,bool),fun(U_1953,bool)),image(U_1951,U_1953),U_1947),U_1945)))
| ! [U_1938] :
( ti(fun(U_1953,bool),U_1949) != hAPP(fun(U_1951,bool),fun(U_1953,bool),hAPP(fun(U_1951,U_1953),fun(fun(U_1951,bool),fun(U_1953,bool)),image(U_1951,U_1953),U_1947),U_1938)
| ~ hBOOL(hAPP(fun(U_1951,bool),bool,hAPP(fun(U_1951,bool),fun(fun(U_1951,bool),bool),ord_less_eq(fun(U_1951,bool)),U_1938),U_1945)) ) )
& ! [U_1952,U_1950,U_1948,U_1946,U_1944] :
( ? [U_1937] :
( ti(fun(U_1952,bool),U_1948) = hAPP(fun(U_1950,bool),fun(U_1952,bool),hAPP(fun(U_1950,U_1952),fun(fun(U_1950,bool),fun(U_1952,bool)),image(U_1950,U_1952),U_1946),U_1937)
& hBOOL(hAPP(fun(U_1950,bool),bool,hAPP(fun(U_1950,bool),fun(fun(U_1950,bool),bool),ord_less_eq(fun(U_1950,bool)),U_1937),U_1944)) )
| ~ hBOOL(hAPP(fun(U_1952,bool),bool,hAPP(fun(U_1952,bool),fun(fun(U_1952,bool),bool),ord_less_eq(fun(U_1952,bool)),U_1948),hAPP(fun(U_1950,bool),fun(U_1952,bool),hAPP(fun(U_1950,U_1952),fun(fun(U_1950,bool),fun(U_1952,bool)),image(U_1950,U_1952),U_1946),U_1944))) ) ),
inference(miniscope,[status(thm)],[f_548_2]) ).
fof(f_548_4,plain,
( ! [U_1953,U_1951,U_1949,U_1947,U_1945] :
( hBOOL(hAPP(fun(U_1953,bool),bool,hAPP(fun(U_1953,bool),fun(fun(U_1953,bool),bool),ord_less_eq(fun(U_1953,bool)),U_1949),hAPP(fun(U_1951,bool),fun(U_1953,bool),hAPP(fun(U_1951,U_1953),fun(fun(U_1951,bool),fun(U_1953,bool)),image(U_1951,U_1953),U_1947),U_1945)))
| ! [U_1938] :
( ti(fun(U_1953,bool),U_1949) != hAPP(fun(U_1951,bool),fun(U_1953,bool),hAPP(fun(U_1951,U_1953),fun(fun(U_1951,bool),fun(U_1953,bool)),image(U_1951,U_1953),U_1947),U_1938)
| ~ hBOOL(hAPP(fun(U_1951,bool),bool,hAPP(fun(U_1951,bool),fun(fun(U_1951,bool),bool),ord_less_eq(fun(U_1951,bool)),U_1938),U_1945)) ) )
& ! [U_1952,U_1950,U_1948,U_1946,U_1944] :
( ( ti(fun(U_1952,bool),U_1948) = hAPP(fun(U_1950,bool),fun(U_1952,bool),hAPP(fun(U_1950,U_1952),fun(fun(U_1950,bool),fun(U_1952,bool)),image(U_1950,U_1952),U_1946),sK110(U_1952,U_1950,U_1948,U_1946,U_1944))
& hBOOL(hAPP(fun(U_1950,bool),bool,hAPP(fun(U_1950,bool),fun(fun(U_1950,bool),bool),ord_less_eq(fun(U_1950,bool)),sK110(U_1952,U_1950,U_1948,U_1946,U_1944)),U_1944)) )
| ~ hBOOL(hAPP(fun(U_1952,bool),bool,hAPP(fun(U_1952,bool),fun(fun(U_1952,bool),bool),ord_less_eq(fun(U_1952,bool)),U_1948),hAPP(fun(U_1950,bool),fun(U_1952,bool),hAPP(fun(U_1950,U_1952),fun(fun(U_1950,bool),fun(U_1952,bool)),image(U_1950,U_1952),U_1946),U_1944))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_1937,sK110(U_1952,U_1950,U_1948,U_1946,U_1944))],[f_548_3]) ).
cnf(f_548_5,plain,
( hBOOL(hAPP(fun(U_1950,bool),bool,hAPP(fun(U_1950,bool),fun(fun(U_1950,bool),bool),ord_less_eq(fun(U_1950,bool)),sK110(U_1952,U_1950,U_1948,U_1946,U_1944)),U_1944))
| ~ hBOOL(hAPP(fun(U_1952,bool),bool,hAPP(fun(U_1952,bool),fun(fun(U_1952,bool),bool),ord_less_eq(fun(U_1952,bool)),U_1948),hAPP(fun(U_1950,bool),fun(U_1952,bool),hAPP(fun(U_1950,U_1952),fun(fun(U_1950,bool),fun(U_1952,bool)),image(U_1950,U_1952),U_1946),U_1944))) ),
inference(clausify,[status(thm)],[f_548_4]) ).
cnf(f_548_6,plain,
( ti(fun(U_1952,bool),U_1948) = hAPP(fun(U_1950,bool),fun(U_1952,bool),hAPP(fun(U_1950,U_1952),fun(fun(U_1950,bool),fun(U_1952,bool)),image(U_1950,U_1952),U_1946),sK110(U_1952,U_1950,U_1948,U_1946,U_1944))
| ~ hBOOL(hAPP(fun(U_1952,bool),bool,hAPP(fun(U_1952,bool),fun(fun(U_1952,bool),bool),ord_less_eq(fun(U_1952,bool)),U_1948),hAPP(fun(U_1950,bool),fun(U_1952,bool),hAPP(fun(U_1950,U_1952),fun(fun(U_1950,bool),fun(U_1952,bool)),image(U_1950,U_1952),U_1946),U_1944))) ),
inference(clausify,[status(thm)],[f_548_4]) ).
cnf(f_548_7,plain,
( hBOOL(hAPP(fun(U_1953,bool),bool,hAPP(fun(U_1953,bool),fun(fun(U_1953,bool),bool),ord_less_eq(fun(U_1953,bool)),U_1949),hAPP(fun(U_1951,bool),fun(U_1953,bool),hAPP(fun(U_1951,U_1953),fun(fun(U_1951,bool),fun(U_1953,bool)),image(U_1951,U_1953),U_1947),U_1945)))
| ti(fun(U_1953,bool),U_1949) != hAPP(fun(U_1951,bool),fun(U_1953,bool),hAPP(fun(U_1951,U_1953),fun(fun(U_1951,bool),fun(U_1953,bool)),image(U_1951,U_1953),U_1947),U_1938)
| ~ hBOOL(hAPP(fun(U_1951,bool),bool,hAPP(fun(U_1951,bool),fun(fun(U_1951,bool),bool),ord_less_eq(fun(U_1951,bool)),U_1938),U_1945)) ),
inference(clausify,[status(thm)],[f_548_4]) ).
fof(f_549_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_486_image__mono]) ).
fof(f_549_2,plain,
! [U_1958,U_1957,U_1956,U_1955,U_1954] :
( hBOOL(hAPP(fun(U_1958,bool),bool,hAPP(fun(U_1958,bool),fun(fun(U_1958,bool),bool),ord_less_eq(fun(U_1958,bool)),hAPP(fun(U_1957,bool),fun(U_1958,bool),hAPP(fun(U_1957,U_1958),fun(fun(U_1957,bool),fun(U_1958,bool)),image(U_1957,U_1958),U_1956),U_1955)),hAPP(fun(U_1957,bool),fun(U_1958,bool),hAPP(fun(U_1957,U_1958),fun(fun(U_1957,bool),fun(U_1958,bool)),image(U_1957,U_1958),U_1956),U_1954)))
| ~ hBOOL(hAPP(fun(U_1957,bool),bool,hAPP(fun(U_1957,bool),fun(fun(U_1957,bool),bool),ord_less_eq(fun(U_1957,bool)),U_1955),U_1954)) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
cnf(f_549_3,plain,
( hBOOL(hAPP(fun(U_1958,bool),bool,hAPP(fun(U_1958,bool),fun(fun(U_1958,bool),bool),ord_less_eq(fun(U_1958,bool)),hAPP(fun(U_1957,bool),fun(U_1958,bool),hAPP(fun(U_1957,U_1958),fun(fun(U_1957,bool),fun(U_1958,bool)),image(U_1957,U_1958),U_1956),U_1955)),hAPP(fun(U_1957,bool),fun(U_1958,bool),hAPP(fun(U_1957,U_1958),fun(fun(U_1957,bool),fun(U_1958,bool)),image(U_1957,U_1958),U_1956),U_1954)))
| ~ hBOOL(hAPP(fun(U_1957,bool),bool,hAPP(fun(U_1957,bool),fun(fun(U_1957,bool),bool),ord_less_eq(fun(U_1957,bool)),U_1955),U_1954)) ),
inference(clausify,[status(thm)],[f_549_2]) ).
fof(f_550_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_487_atLeastLessThan__eq__iff]) ).
fof(f_550_2,plain,
! [U_1963] :
( ! [U_1962,U_1961,U_1960,U_1959] :
( ( ( hAPP(U_1963,fun(U_1963,bool),hAPP(U_1963,fun(U_1963,fun(U_1963,bool)),ord_atLeastLessThan(U_1963),U_1960),U_1959) = hAPP(U_1963,fun(U_1963,bool),hAPP(U_1963,fun(U_1963,fun(U_1963,bool)),ord_atLeastLessThan(U_1963),U_1962),U_1961)
| ti(U_1963,U_1959) != ti(U_1963,U_1961)
| ti(U_1963,U_1960) != ti(U_1963,U_1962) )
& ( ( ti(U_1963,U_1959) = ti(U_1963,U_1961)
& ti(U_1963,U_1960) = ti(U_1963,U_1962) )
| hAPP(U_1963,fun(U_1963,bool),hAPP(U_1963,fun(U_1963,fun(U_1963,bool)),ord_atLeastLessThan(U_1963),U_1960),U_1959) != hAPP(U_1963,fun(U_1963,bool),hAPP(U_1963,fun(U_1963,fun(U_1963,bool)),ord_atLeastLessThan(U_1963),U_1962),U_1961) ) )
| ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1962),U_1961))
| ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1960),U_1959)) )
| ~ linorder(U_1963) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
cnf(f_550_3,plain,
( ti(U_1963,U_1960) = ti(U_1963,U_1962)
| hAPP(U_1963,fun(U_1963,bool),hAPP(U_1963,fun(U_1963,fun(U_1963,bool)),ord_atLeastLessThan(U_1963),U_1960),U_1959) != hAPP(U_1963,fun(U_1963,bool),hAPP(U_1963,fun(U_1963,fun(U_1963,bool)),ord_atLeastLessThan(U_1963),U_1962),U_1961)
| ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1962),U_1961))
| ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1960),U_1959))
| ~ linorder(U_1963) ),
inference(clausify,[status(thm)],[f_550_2]) ).
cnf(f_550_4,plain,
( ti(U_1963,U_1959) = ti(U_1963,U_1961)
| hAPP(U_1963,fun(U_1963,bool),hAPP(U_1963,fun(U_1963,fun(U_1963,bool)),ord_atLeastLessThan(U_1963),U_1960),U_1959) != hAPP(U_1963,fun(U_1963,bool),hAPP(U_1963,fun(U_1963,fun(U_1963,bool)),ord_atLeastLessThan(U_1963),U_1962),U_1961)
| ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1962),U_1961))
| ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1960),U_1959))
| ~ linorder(U_1963) ),
inference(clausify,[status(thm)],[f_550_2]) ).
cnf(f_550_5,plain,
( hAPP(U_1963,fun(U_1963,bool),hAPP(U_1963,fun(U_1963,fun(U_1963,bool)),ord_atLeastLessThan(U_1963),U_1960),U_1959) = hAPP(U_1963,fun(U_1963,bool),hAPP(U_1963,fun(U_1963,fun(U_1963,bool)),ord_atLeastLessThan(U_1963),U_1962),U_1961)
| ti(U_1963,U_1959) != ti(U_1963,U_1961)
| ti(U_1963,U_1960) != ti(U_1963,U_1962)
| ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1962),U_1961))
| ~ hBOOL(hAPP(U_1963,bool,hAPP(U_1963,fun(U_1963,bool),ord_less(U_1963),U_1960),U_1959))
| ~ linorder(U_1963) ),
inference(clausify,[status(thm)],[f_550_2]) ).
fof(f_551_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_488_atLeastLessThan__inj_I1_J]) ).
fof(f_551_2,plain,
! [U_1968] :
( ! [U_1967,U_1966,U_1965,U_1964] :
( ti(U_1968,U_1967) = ti(U_1968,U_1965)
| ~ hBOOL(hAPP(U_1968,bool,hAPP(U_1968,fun(U_1968,bool),ord_less(U_1968),U_1965),U_1964))
| ~ hBOOL(hAPP(U_1968,bool,hAPP(U_1968,fun(U_1968,bool),ord_less(U_1968),U_1967),U_1966))
| hAPP(U_1968,fun(U_1968,bool),hAPP(U_1968,fun(U_1968,fun(U_1968,bool)),ord_atLeastLessThan(U_1968),U_1967),U_1966) != hAPP(U_1968,fun(U_1968,bool),hAPP(U_1968,fun(U_1968,fun(U_1968,bool)),ord_atLeastLessThan(U_1968),U_1965),U_1964) )
| ~ linorder(U_1968) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
cnf(f_551_3,plain,
( ti(U_1968,U_1967) = ti(U_1968,U_1965)
| ~ hBOOL(hAPP(U_1968,bool,hAPP(U_1968,fun(U_1968,bool),ord_less(U_1968),U_1965),U_1964))
| ~ hBOOL(hAPP(U_1968,bool,hAPP(U_1968,fun(U_1968,bool),ord_less(U_1968),U_1967),U_1966))
| hAPP(U_1968,fun(U_1968,bool),hAPP(U_1968,fun(U_1968,fun(U_1968,bool)),ord_atLeastLessThan(U_1968),U_1967),U_1966) != hAPP(U_1968,fun(U_1968,bool),hAPP(U_1968,fun(U_1968,fun(U_1968,bool)),ord_atLeastLessThan(U_1968),U_1965),U_1964)
| ~ linorder(U_1968) ),
inference(clausify,[status(thm)],[f_551_2]) ).
fof(f_552_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_489_atLeastLessThan__inj_I2_J]) ).
fof(f_552_2,plain,
! [U_1973] :
( ! [U_1972,U_1971,U_1970,U_1969] :
( ti(U_1973,U_1971) = ti(U_1973,U_1969)
| ~ hBOOL(hAPP(U_1973,bool,hAPP(U_1973,fun(U_1973,bool),ord_less(U_1973),U_1970),U_1969))
| ~ hBOOL(hAPP(U_1973,bool,hAPP(U_1973,fun(U_1973,bool),ord_less(U_1973),U_1972),U_1971))
| hAPP(U_1973,fun(U_1973,bool),hAPP(U_1973,fun(U_1973,fun(U_1973,bool)),ord_atLeastLessThan(U_1973),U_1972),U_1971) != hAPP(U_1973,fun(U_1973,bool),hAPP(U_1973,fun(U_1973,fun(U_1973,bool)),ord_atLeastLessThan(U_1973),U_1970),U_1969) )
| ~ linorder(U_1973) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
cnf(f_552_3,plain,
( ti(U_1973,U_1971) = ti(U_1973,U_1969)
| ~ hBOOL(hAPP(U_1973,bool,hAPP(U_1973,fun(U_1973,bool),ord_less(U_1973),U_1970),U_1969))
| ~ hBOOL(hAPP(U_1973,bool,hAPP(U_1973,fun(U_1973,bool),ord_less(U_1973),U_1972),U_1971))
| hAPP(U_1973,fun(U_1973,bool),hAPP(U_1973,fun(U_1973,fun(U_1973,bool)),ord_atLeastLessThan(U_1973),U_1972),U_1971) != hAPP(U_1973,fun(U_1973,bool),hAPP(U_1973,fun(U_1973,fun(U_1973,bool)),ord_atLeastLessThan(U_1973),U_1970),U_1969)
| ~ linorder(U_1973) ),
inference(clausify,[status(thm)],[f_552_2]) ).
fof(f_553_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_490_range__composition]) ).
fof(f_553_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_553_1]) ).
cnf(f_553_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_553_2]) ).
fof(f_554_1,plain,
! [X_a,X_b,Ba,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)))))
| ti(X_a,Ba) != hAPP(X_b,X_a,F,X_1) ),
inference(fof_nnf,[status(thm)],[fact_491_range__eqI]) ).
fof(f_554_2,plain,
! [U_1983,U_1982,U_1981,U_1980,U_1979] :
( hBOOL(hAPP(fun(U_1983,bool),bool,hAPP(U_1983,fun(fun(U_1983,bool),bool),member(U_1983),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),top_top(fun(U_1982,bool)))))
| ti(U_1983,U_1981) != hAPP(U_1982,U_1983,U_1980,U_1979) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
! [U_1983,U_1982,U_1981,U_1980] :
( ! [U_1979] : ti(U_1983,U_1981) != hAPP(U_1982,U_1983,U_1980,U_1979)
| hBOOL(hAPP(fun(U_1983,bool),bool,hAPP(U_1983,fun(fun(U_1983,bool),bool),member(U_1983),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),top_top(fun(U_1982,bool))))) ),
inference(miniscope,[status(thm)],[f_554_2]) ).
cnf(f_554_4,plain,
( ti(U_1983,U_1981) != hAPP(U_1982,U_1983,U_1980,U_1979)
| hBOOL(hAPP(fun(U_1983,bool),bool,hAPP(U_1983,fun(fun(U_1983,bool),bool),member(U_1983),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),top_top(fun(U_1982,bool))))) ),
inference(clausify,[status(thm)],[f_554_3]) ).
fof(f_555_1,plain,
! [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),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))))),
inference(fof_nnf,[status(thm)],[fact_492_rangeI]) ).
fof(f_555_2,plain,
! [U_1987,U_1986,U_1985,U_1984] : hBOOL(hAPP(fun(U_1987,bool),bool,hAPP(U_1987,fun(fun(U_1987,bool),bool),member(U_1987),hAPP(U_1986,U_1987,U_1985,U_1984)),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),top_top(fun(U_1986,bool))))),
inference(variable_rename,[status(thm)],[f_555_1]) ).
cnf(f_555_3,plain,
hBOOL(hAPP(fun(U_1987,bool),bool,hAPP(U_1987,fun(fun(U_1987,bool),bool),member(U_1987),hAPP(U_1986,U_1987,U_1985,U_1984)),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),top_top(fun(U_1986,bool))))),
inference(clausify,[status(thm)],[f_555_2]) ).
fof(f_556_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_493_finite__range__imageI]) ).
fof(f_556_2,plain,
! [U_1992,U_1991,U_1990,U_1989,U_1988] :
( hBOOL(hAPP(fun(U_1992,bool),bool,finite_finite_1(U_1992),hAPP(fun(U_1990,bool),fun(U_1992,bool),hAPP(fun(U_1990,U_1992),fun(fun(U_1990,bool),fun(U_1992,bool)),image(U_1990,U_1992),hAPP(fun(U_1990,U_1991),fun(U_1990,U_1992),hAPP(fun(U_1991,U_1992),fun(fun(U_1990,U_1991),fun(U_1990,U_1992)),combb(U_1991,U_1992,U_1990),U_1989),U_1988)),top_top(fun(U_1990,bool)))))
| ~ hBOOL(hAPP(fun(U_1991,bool),bool,finite_finite_1(U_1991),hAPP(fun(U_1990,bool),fun(U_1991,bool),hAPP(fun(U_1990,U_1991),fun(fun(U_1990,bool),fun(U_1991,bool)),image(U_1990,U_1991),U_1988),top_top(fun(U_1990,bool))))) ),
inference(variable_rename,[status(thm)],[f_556_1]) ).
cnf(f_556_3,plain,
( hBOOL(hAPP(fun(U_1992,bool),bool,finite_finite_1(U_1992),hAPP(fun(U_1990,bool),fun(U_1992,bool),hAPP(fun(U_1990,U_1992),fun(fun(U_1990,bool),fun(U_1992,bool)),image(U_1990,U_1992),hAPP(fun(U_1990,U_1991),fun(U_1990,U_1992),hAPP(fun(U_1991,U_1992),fun(fun(U_1990,U_1991),fun(U_1990,U_1992)),combb(U_1991,U_1992,U_1990),U_1989),U_1988)),top_top(fun(U_1990,bool)))))
| ~ hBOOL(hAPP(fun(U_1991,bool),bool,finite_finite_1(U_1991),hAPP(fun(U_1990,bool),fun(U_1991,bool),hAPP(fun(U_1990,U_1991),fun(fun(U_1990,bool),fun(U_1991,bool)),image(U_1990,U_1991),U_1988),top_top(fun(U_1990,bool))))) ),
inference(clausify,[status(thm)],[f_556_2]) ).
fof(f_557_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_494_subset__card__intvl__is__intvl]) ).
fof(f_557_2,plain,
! [U_1994,U_1993] :
( U_1994 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_1993),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1993),hAPP(fun(nat,bool),nat,finite_card(nat),U_1994)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_1994),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_1993),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1993),hAPP(fun(nat,bool),nat,finite_card(nat),U_1994))))) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
cnf(f_557_3,plain,
( U_1994 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_1993),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1993),hAPP(fun(nat,bool),nat,finite_card(nat),U_1994)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),U_1994),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),U_1993),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1993),hAPP(fun(nat,bool),nat,finite_card(nat),U_1994))))) ),
inference(clausify,[status(thm)],[f_557_2]) ).
fof(f_558_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_495_inj__on__strict__subset]) ).
fof(f_558_2,plain,
! [U_1999,U_1998,U_1997,U_1996,U_1995] :
( hBOOL(hAPP(fun(U_1998,bool),bool,hAPP(fun(U_1998,bool),fun(fun(U_1998,bool),bool),ord_less(fun(U_1998,bool)),hAPP(fun(U_1999,bool),fun(U_1998,bool),hAPP(fun(U_1999,U_1998),fun(fun(U_1999,bool),fun(U_1998,bool)),image(U_1999,U_1998),U_1996),U_1997)),hAPP(fun(U_1999,bool),fun(U_1998,bool),hAPP(fun(U_1999,U_1998),fun(fun(U_1999,bool),fun(U_1998,bool)),image(U_1999,U_1998),U_1996),U_1995)))
| ~ hBOOL(hAPP(fun(U_1999,bool),bool,hAPP(fun(U_1999,bool),fun(fun(U_1999,bool),bool),ord_less(fun(U_1999,bool)),U_1997),U_1995))
| ~ hBOOL(hAPP(fun(U_1999,bool),bool,hAPP(fun(U_1999,U_1998),fun(fun(U_1999,bool),bool),inj_on(U_1999,U_1998),U_1996),U_1995)) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
cnf(f_558_3,plain,
( hBOOL(hAPP(fun(U_1998,bool),bool,hAPP(fun(U_1998,bool),fun(fun(U_1998,bool),bool),ord_less(fun(U_1998,bool)),hAPP(fun(U_1999,bool),fun(U_1998,bool),hAPP(fun(U_1999,U_1998),fun(fun(U_1999,bool),fun(U_1998,bool)),image(U_1999,U_1998),U_1996),U_1997)),hAPP(fun(U_1999,bool),fun(U_1998,bool),hAPP(fun(U_1999,U_1998),fun(fun(U_1999,bool),fun(U_1998,bool)),image(U_1999,U_1998),U_1996),U_1995)))
| ~ hBOOL(hAPP(fun(U_1999,bool),bool,hAPP(fun(U_1999,bool),fun(fun(U_1999,bool),bool),ord_less(fun(U_1999,bool)),U_1997),U_1995))
| ~ hBOOL(hAPP(fun(U_1999,bool),bool,hAPP(fun(U_1999,U_1998),fun(fun(U_1999,bool),bool),inj_on(U_1999,U_1998),U_1996),U_1995)) ),
inference(clausify,[status(thm)],[f_558_2]) ).
fof(f_559_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_496_image__surj__f__inv__f]) ).
fof(f_559_2,plain,
! [U_2003,U_2002,U_2001,U_2000] :
( hAPP(fun(U_2003,bool),fun(U_2002,bool),hAPP(fun(U_2003,U_2002),fun(fun(U_2003,bool),fun(U_2002,bool)),image(U_2003,U_2002),U_2000),hAPP(fun(U_2002,bool),fun(U_2003,bool),hAPP(fun(U_2002,U_2003),fun(fun(U_2002,bool),fun(U_2003,bool)),image(U_2002,U_2003),hAPP(fun(U_2003,U_2002),fun(U_2002,U_2003),hAPP(fun(U_2003,bool),fun(fun(U_2003,U_2002),fun(U_2002,U_2003)),hilbert_inv_into(U_2003,U_2002),top_top(fun(U_2003,bool))),U_2000)),U_2001)) = ti(fun(U_2002,bool),U_2001)
| hAPP(fun(U_2003,bool),fun(U_2002,bool),hAPP(fun(U_2003,U_2002),fun(fun(U_2003,bool),fun(U_2002,bool)),image(U_2003,U_2002),U_2000),top_top(fun(U_2003,bool))) != top_top(fun(U_2002,bool)) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
cnf(f_559_3,plain,
( hAPP(fun(U_2003,bool),fun(U_2002,bool),hAPP(fun(U_2003,U_2002),fun(fun(U_2003,bool),fun(U_2002,bool)),image(U_2003,U_2002),U_2000),hAPP(fun(U_2002,bool),fun(U_2003,bool),hAPP(fun(U_2002,U_2003),fun(fun(U_2002,bool),fun(U_2003,bool)),image(U_2002,U_2003),hAPP(fun(U_2003,U_2002),fun(U_2002,U_2003),hAPP(fun(U_2003,bool),fun(fun(U_2003,U_2002),fun(U_2002,U_2003)),hilbert_inv_into(U_2003,U_2002),top_top(fun(U_2003,bool))),U_2000)),U_2001)) = ti(fun(U_2002,bool),U_2001)
| hAPP(fun(U_2003,bool),fun(U_2002,bool),hAPP(fun(U_2003,U_2002),fun(fun(U_2003,bool),fun(U_2002,bool)),image(U_2003,U_2002),U_2000),top_top(fun(U_2003,bool))) != top_top(fun(U_2002,bool)) ),
inference(clausify,[status(thm)],[f_559_2]) ).
fof(f_560_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_560_2,plain,
! [U_2005,U_2004] :
( preorder(fun(U_2005,U_2004))
| ~ preorder(U_2004) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
cnf(f_560_3,plain,
( preorder(fun(U_2005,U_2004))
| ~ preorder(U_2004) ),
inference(clausify,[status(thm)],[f_560_2]) ).
fof(f_561_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_561_2,plain,
! [U_2007,U_2006] :
( finite_finite(fun(U_2007,U_2006))
| ~ finite_finite(U_2007)
| ~ finite_finite(U_2006) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
cnf(f_561_3,plain,
( finite_finite(fun(U_2007,U_2006))
| ~ finite_finite(U_2007)
| ~ finite_finite(U_2006) ),
inference(clausify,[status(thm)],[f_561_2]) ).
fof(f_562_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_562_2,plain,
! [U_2009,U_2008] :
( order(fun(U_2009,U_2008))
| ~ order(U_2008) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
cnf(f_562_3,plain,
( order(fun(U_2009,U_2008))
| ~ order(U_2008) ),
inference(clausify,[status(thm)],[f_562_2]) ).
fof(f_563_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_563_2,plain,
! [U_2011,U_2010] :
( top(fun(U_2011,U_2010))
| ~ top(U_2010) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
cnf(f_563_3,plain,
( top(fun(U_2011,U_2010))
| ~ top(U_2010) ),
inference(clausify,[status(thm)],[f_563_2]) ).
fof(f_564_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_564_2,plain,
! [U_2013,U_2012] :
( ord(fun(U_2013,U_2012))
| ~ ord(U_2012) ),
inference(variable_rename,[status(thm)],[f_564_1]) ).
cnf(f_564_3,plain,
( ord(fun(U_2013,U_2012))
| ~ ord(U_2012) ),
inference(clausify,[status(thm)],[f_564_2]) ).
fof(f_565_1,plain,
semiri456707255roduct(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc]) ).
cnf(f_565_2,plain,
semiri456707255roduct(nat),
inference(clausify,[status(thm)],[f_565_1]) ).
fof(f_566_1,plain,
ordere223160158up_add(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add]) ).
cnf(f_566_2,plain,
ordere223160158up_add(nat),
inference(clausify,[status(thm)],[f_566_1]) ).
fof(f_567_1,plain,
ordere236663937imp_le(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(f_567_2,plain,
ordere236663937imp_le(nat),
inference(clausify,[status(thm)],[f_567_1]) ).
fof(f_568_1,plain,
ordere779506340up_add(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add]) ).
cnf(f_568_2,plain,
ordere779506340up_add(nat),
inference(clausify,[status(thm)],[f_568_1]) ).
fof(f_569_1,plain,
ordere216010020id_add(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__comm__monoid__add]) ).
cnf(f_569_2,plain,
ordere216010020id_add(nat),
inference(clausify,[status(thm)],[f_569_1]) ).
fof(f_570_1,plain,
cancel146912293up_add(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_570_2,plain,
cancel146912293up_add(nat),
inference(clausify,[status(thm)],[f_570_1]) ).
fof(f_571_1,plain,
cancel_semigroup_add(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__semigroup__add]) ).
cnf(f_571_2,plain,
cancel_semigroup_add(nat),
inference(clausify,[status(thm)],[f_571_1]) ).
fof(f_572_1,plain,
linordered_semidom(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semidom]) ).
cnf(f_572_2,plain,
linordered_semidom(nat),
inference(clausify,[status(thm)],[f_572_1]) ).
fof(f_573_1,plain,
ab_semigroup_add(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__add]) ).
cnf(f_573_2,plain,
ab_semigroup_add(nat),
inference(clausify,[status(thm)],[f_573_1]) ).
fof(f_574_1,plain,
comm_monoid_add(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__add]) ).
cnf(f_574_2,plain,
comm_monoid_add(nat),
inference(clausify,[status(thm)],[f_574_1]) ).
fof(f_575_1,plain,
comm_semiring_1(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring__1]) ).
cnf(f_575_2,plain,
comm_semiring_1(nat),
inference(clausify,[status(thm)],[f_575_1]) ).
fof(f_576_1,plain,
zero_neq_one(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ozero__neq__one]) ).
cnf(f_576_2,plain,
zero_neq_one(nat),
inference(clausify,[status(thm)],[f_576_1]) ).
fof(f_577_1,plain,
preorder(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]) ).
cnf(f_577_2,plain,
preorder(nat),
inference(clausify,[status(thm)],[f_577_1]) ).
fof(f_578_1,plain,
linorder(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Olinorder]) ).
cnf(f_578_2,plain,
linorder(nat),
inference(clausify,[status(thm)],[f_578_1]) ).
fof(f_579_1,plain,
monoid_add(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__add]) ).
cnf(f_579_2,plain,
monoid_add(nat),
inference(clausify,[status(thm)],[f_579_1]) ).
fof(f_580_1,plain,
order(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]) ).
cnf(f_580_2,plain,
order(nat),
inference(clausify,[status(thm)],[f_580_1]) ).
fof(f_581_1,plain,
ord(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oord]) ).
cnf(f_581_2,plain,
ord(nat),
inference(clausify,[status(thm)],[f_581_1]) ).
fof(f_582_1,plain,
zero(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ozero]) ).
cnf(f_582_2,plain,
zero(nat),
inference(clausify,[status(thm)],[f_582_1]) ).
fof(f_583_1,plain,
one(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oone]) ).
cnf(f_583_2,plain,
one(nat),
inference(clausify,[status(thm)],[f_583_1]) ).
fof(f_584_1,plain,
preorder(bool),
inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]) ).
cnf(f_584_2,plain,
preorder(bool),
inference(clausify,[status(thm)],[f_584_1]) ).
fof(f_585_1,plain,
finite_finite(bool),
inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]) ).
cnf(f_585_2,plain,
finite_finite(bool),
inference(clausify,[status(thm)],[f_585_1]) ).
fof(f_586_1,plain,
order(bool),
inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]) ).
cnf(f_586_2,plain,
order(bool),
inference(clausify,[status(thm)],[f_586_1]) ).
fof(f_587_1,plain,
top(bool),
inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Otop]) ).
cnf(f_587_2,plain,
top(bool),
inference(clausify,[status(thm)],[f_587_1]) ).
fof(f_588_1,plain,
ord(bool),
inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oord]) ).
cnf(f_588_2,plain,
ord(bool),
inference(clausify,[status(thm)],[f_588_1]) ).
fof(f_589_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_589_2,plain,
! [U_2015,U_2014] :
( finite_finite(sum_sum(U_2015,U_2014))
| ~ finite_finite(U_2015)
| ~ finite_finite(U_2014) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
cnf(f_589_3,plain,
( finite_finite(sum_sum(U_2015,U_2014))
| ~ finite_finite(U_2015)
| ~ finite_finite(U_2014) ),
inference(clausify,[status(thm)],[f_589_2]) ).
fof(f_590_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_590_2,plain,
! [U_2016] :
( finite_finite(option(U_2016))
| ~ finite_finite(U_2016) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
cnf(f_590_3,plain,
( finite_finite(option(U_2016))
| ~ finite_finite(U_2016) ),
inference(clausify,[status(thm)],[f_590_2]) ).
fof(f_591_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_591_2,plain,
! [U_2018,U_2017] :
( finite_finite(product_prod(U_2018,U_2017))
| ~ finite_finite(U_2018)
| ~ finite_finite(U_2017) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
cnf(f_591_3,plain,
( finite_finite(product_prod(U_2018,U_2017))
| ~ finite_finite(U_2018)
| ~ finite_finite(U_2017) ),
inference(clausify,[status(thm)],[f_591_2]) ).
fof(f_592_1,plain,
finite_finite(product_unit),
inference(fof_nnf,[status(thm)],[arity_Product__Type_Ounit___Finite__Set_Ofinite]) ).
cnf(f_592_2,plain,
finite_finite(product_unit),
inference(clausify,[status(thm)],[f_592_1]) ).
fof(f_593_1,plain,
! [T,A] : ti(T,ti(T,A)) = ti(T,A),
inference(fof_nnf,[status(thm)],[help_ti_idem]) ).
fof(f_593_2,plain,
! [U_2020,U_2019] : ti(U_2020,ti(U_2020,U_2019)) = ti(U_2020,U_2019),
inference(variable_rename,[status(thm)],[f_593_1]) ).
cnf(f_593_3,plain,
ti(U_2020,ti(U_2020,U_2019)) = ti(U_2020,U_2019),
inference(clausify,[status(thm)],[f_593_2]) ).
fof(f_594_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_594_2,plain,
! [U_2023,U_2022,U_2021] : hAPP(U_2023,U_2023,hAPP(U_2023,fun(U_2023,U_2023),hAPP(bool,fun(U_2023,fun(U_2023,U_2023)),if(U_2023),fTrue),U_2022),U_2021) = ti(U_2023,U_2022),
inference(variable_rename,[status(thm)],[f_594_1]) ).
cnf(f_594_3,plain,
hAPP(U_2023,U_2023,hAPP(U_2023,fun(U_2023,U_2023),hAPP(bool,fun(U_2023,fun(U_2023,U_2023)),if(U_2023),fTrue),U_2022),U_2021) = ti(U_2023,U_2022),
inference(clausify,[status(thm)],[f_594_2]) ).
fof(f_595_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_595_2,plain,
! [U_2026,U_2025,U_2024] : hAPP(U_2026,U_2026,hAPP(U_2026,fun(U_2026,U_2026),hAPP(bool,fun(U_2026,fun(U_2026,U_2026)),if(U_2026),fFalse),U_2025),U_2024) = ti(U_2026,U_2024),
inference(variable_rename,[status(thm)],[f_595_1]) ).
cnf(f_595_3,plain,
hAPP(U_2026,U_2026,hAPP(U_2026,fun(U_2026,U_2026),hAPP(bool,fun(U_2026,fun(U_2026,U_2026)),if(U_2026),fFalse),U_2025),U_2024) = ti(U_2026,U_2024),
inference(clausify,[status(thm)],[f_595_2]) ).
fof(f_596_1,plain,
! [P] :
( ti(bool,P) = fFalse
| ti(bool,P) = fTrue ),
inference(fof_nnf,[status(thm)],[help_If_3_1_T]) ).
fof(f_596_2,plain,
! [U_2027] :
( ti(bool,U_2027) = fFalse
| ti(bool,U_2027) = fTrue ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
cnf(f_596_3,plain,
( ti(bool,U_2027) = fFalse
| ti(bool,U_2027) = fTrue ),
inference(clausify,[status(thm)],[f_596_2]) ).
fof(f_597_1,plain,
! [P] :
( ~ hBOOL(P)
| ~ hBOOL(hAPP(bool,bool,fNot,P)) ),
inference(fof_nnf,[status(thm)],[help_fNot_1_1_U]) ).
fof(f_597_2,plain,
! [U_2028] :
( ~ hBOOL(U_2028)
| ~ hBOOL(hAPP(bool,bool,fNot,U_2028)) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
cnf(f_597_3,plain,
( ~ hBOOL(U_2028)
| ~ hBOOL(hAPP(bool,bool,fNot,U_2028)) ),
inference(clausify,[status(thm)],[f_597_2]) ).
fof(f_598_1,plain,
! [P] :
( hBOOL(hAPP(bool,bool,fNot,P))
| hBOOL(P) ),
inference(fof_nnf,[status(thm)],[help_fNot_2_1_U]) ).
fof(f_598_2,plain,
! [U_2029] :
( hBOOL(hAPP(bool,bool,fNot,U_2029))
| hBOOL(U_2029) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
cnf(f_598_3,plain,
( hBOOL(hAPP(bool,bool,fNot,U_2029))
| hBOOL(U_2029) ),
inference(clausify,[status(thm)],[f_598_2]) ).
fof(f_599_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_599_2,plain,
! [U_2035,U_2034,U_2033,U_2032,U_2031,U_2030] : hAPP(U_2035,U_2034,hAPP(fun(U_2035,U_2033),fun(U_2035,U_2034),hAPP(fun(U_2033,U_2034),fun(fun(U_2035,U_2033),fun(U_2035,U_2034)),combb(U_2033,U_2034,U_2035),U_2032),U_2031),U_2030) = hAPP(U_2033,U_2034,U_2032,hAPP(U_2035,U_2033,U_2031,U_2030)),
inference(variable_rename,[status(thm)],[f_599_1]) ).
cnf(f_599_3,plain,
hAPP(U_2035,U_2034,hAPP(fun(U_2035,U_2033),fun(U_2035,U_2034),hAPP(fun(U_2033,U_2034),fun(fun(U_2035,U_2033),fun(U_2035,U_2034)),combb(U_2033,U_2034,U_2035),U_2032),U_2031),U_2030) = hAPP(U_2033,U_2034,U_2032,hAPP(U_2035,U_2033,U_2031,U_2030)),
inference(clausify,[status(thm)],[f_599_2]) ).
fof(f_600_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_600_2,plain,
! [U_2041,U_2040,U_2039,U_2038,U_2037,U_2036] : hAPP(U_2041,U_2040,hAPP(U_2039,fun(U_2041,U_2040),hAPP(fun(U_2041,fun(U_2039,U_2040)),fun(U_2039,fun(U_2041,U_2040)),combc(U_2041,U_2039,U_2040),U_2038),U_2037),U_2036) = hAPP(U_2039,U_2040,hAPP(U_2041,fun(U_2039,U_2040),U_2038,U_2036),U_2037),
inference(variable_rename,[status(thm)],[f_600_1]) ).
cnf(f_600_3,plain,
hAPP(U_2041,U_2040,hAPP(U_2039,fun(U_2041,U_2040),hAPP(fun(U_2041,fun(U_2039,U_2040)),fun(U_2039,fun(U_2041,U_2040)),combc(U_2041,U_2039,U_2040),U_2038),U_2037),U_2036) = hAPP(U_2039,U_2040,hAPP(U_2041,fun(U_2039,U_2040),U_2038,U_2036),U_2037),
inference(clausify,[status(thm)],[f_600_2]) ).
fof(f_601_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_601_2,plain,
! [U_2043,U_2042] : hAPP(U_2043,U_2043,combi(U_2043),U_2042) = ti(U_2043,U_2042),
inference(variable_rename,[status(thm)],[f_601_1]) ).
cnf(f_601_3,plain,
hAPP(U_2043,U_2043,combi(U_2043),U_2042) = ti(U_2043,U_2042),
inference(clausify,[status(thm)],[f_601_2]) ).
fof(f_602_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_602_2,plain,
! [U_2047,U_2046,U_2045,U_2044] : hAPP(U_2047,U_2046,hAPP(U_2046,fun(U_2047,U_2046),combk(U_2046,U_2047),U_2045),U_2044) = ti(U_2046,U_2045),
inference(variable_rename,[status(thm)],[f_602_1]) ).
cnf(f_602_3,plain,
hAPP(U_2047,U_2046,hAPP(U_2046,fun(U_2047,U_2046),combk(U_2046,U_2047),U_2045),U_2044) = ti(U_2046,U_2045),
inference(clausify,[status(thm)],[f_602_2]) ).
fof(f_603_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_603_2,plain,
! [U_2053,U_2052,U_2051,U_2050,U_2049,U_2048] : hAPP(U_2053,U_2052,hAPP(fun(U_2053,U_2051),fun(U_2053,U_2052),hAPP(fun(U_2053,fun(U_2051,U_2052)),fun(fun(U_2053,U_2051),fun(U_2053,U_2052)),combs(U_2053,U_2051,U_2052),U_2050),U_2049),U_2048) = hAPP(U_2051,U_2052,hAPP(U_2053,fun(U_2051,U_2052),U_2050,U_2048),hAPP(U_2053,U_2051,U_2049,U_2048)),
inference(variable_rename,[status(thm)],[f_603_1]) ).
cnf(f_603_3,plain,
hAPP(U_2053,U_2052,hAPP(fun(U_2053,U_2051),fun(U_2053,U_2052),hAPP(fun(U_2053,fun(U_2051,U_2052)),fun(fun(U_2053,U_2051),fun(U_2053,U_2052)),combs(U_2053,U_2051,U_2052),U_2050),U_2049),U_2048) = hAPP(U_2051,U_2052,hAPP(U_2053,fun(U_2051,U_2052),U_2050,U_2048),hAPP(U_2053,U_2051,U_2049,U_2048)),
inference(clausify,[status(thm)],[f_603_2]) ).
fof(f_604_1,plain,
hBOOL(fTrue),
inference(fof_nnf,[status(thm)],[help_fTrue_1_1_U]) ).
cnf(f_604_2,plain,
hBOOL(fTrue),
inference(clausify,[status(thm)],[f_604_1]) ).
fof(f_605_1,plain,
! [P] :
( ti(bool,P) = fFalse
| ti(bool,P) = fTrue ),
inference(fof_nnf,[status(thm)],[help_fTrue_1_1_T]) ).
fof(f_605_2,plain,
! [U_2054] :
( ti(bool,U_2054) = fFalse
| ti(bool,U_2054) = fTrue ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
cnf(f_605_3,plain,
( ti(bool,U_2054) = fFalse
| ti(bool,U_2054) = fTrue ),
inference(clausify,[status(thm)],[f_605_2]) ).
fof(f_606_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_606_2,plain,
! [U_2056,U_2055] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2055),U_2056))
| ~ hBOOL(U_2056)
| ~ hBOOL(U_2055) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
fof(f_606_3,plain,
! [U_2056] :
( ! [U_2055] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2055),U_2056))
| ~ hBOOL(U_2055) )
| ~ hBOOL(U_2056) ),
inference(miniscope,[status(thm)],[f_606_2]) ).
cnf(f_606_4,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2055),U_2056))
| ~ hBOOL(U_2055)
| ~ hBOOL(U_2056) ),
inference(clausify,[status(thm)],[f_606_3]) ).
fof(f_607_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_607_2,plain,
! [U_2058,U_2057] :
( hBOOL(U_2058)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2058),U_2057)) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
fof(f_607_3,plain,
! [U_2058] :
( ! [U_2057] : ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2058),U_2057))
| hBOOL(U_2058) ),
inference(miniscope,[status(thm)],[f_607_2]) ).
cnf(f_607_4,plain,
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2058),U_2057))
| hBOOL(U_2058) ),
inference(clausify,[status(thm)],[f_607_3]) ).
fof(f_608_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_608_2,plain,
! [U_2060,U_2059] :
( hBOOL(U_2059)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2060),U_2059)) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
cnf(f_608_3,plain,
( hBOOL(U_2059)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2060),U_2059)) ),
inference(clausify,[status(thm)],[f_608_2]) ).
fof(f_609_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_609_2,plain,
! [U_2062,U_2061] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2061),U_2062))
| ~ hBOOL(U_2061) ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
cnf(f_609_3,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2061),U_2062))
| ~ hBOOL(U_2061) ),
inference(clausify,[status(thm)],[f_609_2]) ).
fof(f_610_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_610_2,plain,
! [U_2064,U_2063] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2064),U_2063))
| ~ hBOOL(U_2063) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
cnf(f_610_3,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2064),U_2063))
| ~ hBOOL(U_2063) ),
inference(clausify,[status(thm)],[f_610_2]) ).
fof(f_611_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_611_2,plain,
! [U_2066,U_2065] :
( hBOOL(U_2065)
| hBOOL(U_2066)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2066),U_2065)) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
fof(f_611_3,plain,
! [U_2066] :
( ! [U_2065] :
( hBOOL(U_2065)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2066),U_2065)) )
| hBOOL(U_2066) ),
inference(miniscope,[status(thm)],[f_611_2]) ).
cnf(f_611_4,plain,
( hBOOL(U_2065)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2066),U_2065))
| hBOOL(U_2066) ),
inference(clausify,[status(thm)],[f_611_3]) ).
fof(f_612_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_612_2,plain,
! [U_2069,U_2068,U_2067] :
( ti(U_2069,U_2068) = ti(U_2069,U_2067)
| ~ hBOOL(hAPP(U_2069,bool,hAPP(U_2069,fun(U_2069,bool),fequal(U_2069),U_2068),U_2067)) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
cnf(f_612_3,plain,
( ti(U_2069,U_2068) = ti(U_2069,U_2067)
| ~ hBOOL(hAPP(U_2069,bool,hAPP(U_2069,fun(U_2069,bool),fequal(U_2069),U_2068),U_2067)) ),
inference(clausify,[status(thm)],[f_612_2]) ).
fof(f_613_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_613_2,plain,
! [U_2072,U_2071,U_2070] :
( hBOOL(hAPP(U_2072,bool,hAPP(U_2072,fun(U_2072,bool),fequal(U_2072),U_2071),U_2070))
| ti(U_2072,U_2071) != ti(U_2072,U_2070) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
cnf(f_613_3,plain,
( hBOOL(hAPP(U_2072,bool,hAPP(U_2072,fun(U_2072,bool),fequal(U_2072),U_2071),U_2070))
| ti(U_2072,U_2071) != ti(U_2072,U_2070) ),
inference(clausify,[status(thm)],[f_613_2]) ).
fof(f_614_1,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_614_2,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
inference(definitional_conversion,[status(esa)],[f_614_1]) ).
cnf(f_614_3,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
inference(clausify,[status(thm)],[f_614_2]) ).
cnf(f_67_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_67_7]) ).
cnf(f_68_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_68_7]) ).
cnf(f_74_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_74_7]) ).
cnf(f_74_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_74_8]) ).
cnf(f_74_13_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_74_13]) ).
cnf(f_86_23_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_86_23]) ).
cnf(f_86_24_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_86_24]) ).
cnf(f_107_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_4]) ).
cnf(f_107_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_5]) ).
cnf(f_107_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_6]) ).
cnf(f_107_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_7]) ).
cnf(f_107_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_8]) ).
cnf(f_107_9_simplified,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ),
inference(simplify_clause,[status(thm)],[f_107_9]) ).
cnf(f_107_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_10]) ).
cnf(f_107_14_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_14]) ).
cnf(f_107_15_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_15]) ).
cnf(f_107_16_simplified,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_225) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
inference(simplify_clause,[status(thm)],[f_107_16]) ).
cnf(f_107_17_simplified,plain,
( hAPP(arrow_660593299e_indi,nat,h,U_225) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
inference(simplify_clause,[status(thm)],[f_107_17]) ).
cnf(f_107_18_simplified,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_225)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_225)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
inference(simplify_clause,[status(thm)],[f_107_18]) ).
cnf(f_107_19_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_19]) ).
cnf(f_107_20_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_20]) ).
cnf(f_107_24_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_24]) ).
cnf(f_107_25_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_25]) ).
cnf(f_107_26_simplified,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e))) ),
inference(simplify_clause,[status(thm)],[f_107_26]) ).
cnf(f_107_28_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_28]) ).
cnf(f_107_29_simplified,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),c),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) != n ),
inference(simplify_clause,[status(thm)],[f_107_29]) ).
cnf(f_107_30_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_30]) ).
cnf(f_107_31_simplified,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,U_226)),n))
| hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,U_226)),e)))
| hAPP(arrow_660593299e_indi,nat,h,U_226) = n ),
inference(simplify_clause,[status(thm)],[f_107_31]) ).
cnf(f_107_32_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_32]) ).
cnf(f_107_34_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_34]) ).
cnf(f_141_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_141_7]) ).
cnf(f_141_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_141_8]) ).
cnf(f_141_15_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_141_15]) ).
cnf(f_145_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_145_4]) ).
cnf(f_145_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_145_5]) ).
cnf(f_145_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_145_10]) ).
cnf(f_145_14_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_145_14]) ).
cnf(f_145_15_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_145_15]) ).
cnf(f_145_20_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_145_20]) ).
cnf(f_145_24_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_145_24]) ).
cnf(f_145_28_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_145_28]) ).
cnf(f_145_30_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_145_30]) ).
cnf(f_280_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_280_7]) ).
cnf(f_280_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_280_8]) ).
cnf(f_280_15_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_280_15]) ).
cnf(f_290_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_290_4]) ).
cnf(f_290_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_290_5]) ).
cnf(f_290_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_290_6]) ).
cnf(f_290_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_290_7]) ).
cnf(f_290_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_290_8]) ).
cnf(f_290_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_290_9]) ).
cnf(f_290_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_290_10]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( 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,
( 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_8,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_9,axiom,
( combi(Eq_x_0) = combi(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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_11,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_12,axiom,
( finite_card(Eq_x_0) = finite_card(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,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_15,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_16,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_17,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_18,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_19,axiom,
( one_one(Eq_x_0) = one_one(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( plus_plus(Eq_x_0) = plus_plus(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( zero_zero(Eq_x_0) = zero_zero(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( undefined(Eq_x_0) = undefined(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,axiom,
( if(Eq_x_0) = if(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,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_26,axiom,
( ord_less(Eq_x_0) = ord_less(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,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_28,axiom,
( top_top(Eq_x_0) = top_top(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,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_30,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_31,axiom,
( ord_atLeastLessThan(Eq_x_0) = ord_atLeastLessThan(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( collect(Eq_x_0) = collect(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,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_34,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_35,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_36,axiom,
( fequal(Eq_x_0) = fequal(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,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_38,axiom,
( member(Eq_x_0) = member(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( option(Eq_x_0) = option(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,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_41,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_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,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_55,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,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_60,axiom,
( sK21(Eq_x_0) = sK21(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK22(Eq_x_0) = sK22(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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,
( 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_65,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_66,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_67,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_68,axiom,
( sK31(Eq_x_0,Eq_x_1) = sK31(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,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_70,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_71,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_72,axiom,
( sK37(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK37(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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,
( 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_74,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_75,axiom,
( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,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_77,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_78,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_79,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_80,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_81,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_82,axiom,
( sK47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,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_84,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_85,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_86,axiom,
( sK51(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK51(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_87,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_88,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_89,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_90,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_91,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_92,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_93,axiom,
( sK58(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK58(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK59(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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,
( sK60(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK60(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_96,axiom,
( sK61(Eq_x_0,Eq_x_1,Eq_x_2) = sK61(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,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_98,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_99,axiom,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK64(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_100,axiom,
( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK65(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_101,axiom,
( sK66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK66(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_102,axiom,
( sK67(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK67(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_103,axiom,
( sK68(Eq_x_0,Eq_x_1) = sK68(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_104,axiom,
( 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_105,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_106,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_107,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_108,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_109,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_110,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_111,axiom,
( sK77(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK77(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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,
( sK78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,axiom,
( sK79(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK79(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_114,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_115,axiom,
( sK81(Eq_x_0) = sK81(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,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_117,axiom,
( sK83(Eq_x_0) = sK83(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,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_119,axiom,
( sK85(Eq_x_0,Eq_x_1) = sK85(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK86(Eq_x_0,Eq_x_1) = sK86(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,
( sK87(Eq_x_0,Eq_x_1) = sK87(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,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_123,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_124,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_125,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_126,axiom,
( sK92(Eq_x_0) = sK92(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_127,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_128,axiom,
( sK94(Eq_x_0,Eq_x_1,Eq_x_2) = sK94(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,
( sK95(Eq_x_0,Eq_x_1) = sK95(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_130,axiom,
( sK96(Eq_x_0) = sK96(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_131,axiom,
( sK97(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK97(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,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_133,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_134,axiom,
( sK100(Eq_x_0,Eq_x_1) = sK100(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_135,axiom,
( 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_136,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_137,axiom,
( sK103(Eq_x_0) = sK103(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( sK104(Eq_x_0) = sK104(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_139,axiom,
( sK105(Eq_x_0) = sK105(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( sK106(Eq_x_0,Eq_x_1) = sK106(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( sK107(Eq_x_0,Eq_x_1,Eq_x_2) = sK107(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_142,axiom,
( sK109(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK109(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,
( 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_144,axiom,
( one(Eq_y_0)
| ~ one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_145,axiom,
( monoid_add(Eq_y_0)
| ~ monoid_add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_146,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_147,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_148,axiom,
( zero(Eq_y_0)
| ~ zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_149,axiom,
( ring_1(Eq_y_0)
| ~ ring_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_150,axiom,
( ord(Eq_y_0)
| ~ ord(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_151,axiom,
( top(Eq_y_0)
| ~ top(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_152,axiom,
( linorder(Eq_y_0)
| ~ linorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_153,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_154,axiom,
( preorder(Eq_y_0)
| ~ preorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_155,axiom,
( order(Eq_y_0)
| ~ order(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_156,axiom,
( linordered_semidom(Eq_y_0)
| ~ linordered_semidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_157,axiom,
( ordere223160158up_add(Eq_y_0)
| ~ ordere223160158up_add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_158,axiom,
( dense_linorder(Eq_y_0)
| ~ dense_linorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_159,axiom,
( linordered_idom(Eq_y_0)
| ~ linordered_idom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_160,axiom,
( cancel146912293up_add(Eq_y_0)
| ~ cancel146912293up_add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_161,axiom,
( ordere236663937imp_le(Eq_y_0)
| ~ ordere236663937imp_le(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_162,axiom,
( ordere779506340up_add(Eq_y_0)
| ~ ordere779506340up_add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_163,axiom,
( finite_finite(Eq_y_0)
| ~ finite_finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_164,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_165,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_166,axiom,
( linord219039673up_add(Eq_y_0)
| ~ linord219039673up_add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_167,axiom,
( ordere216010020id_add(Eq_y_0)
| ~ ordere216010020id_add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_168,axiom,
( semiri456707255roduct(Eq_y_0)
| ~ semiri456707255roduct(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_169,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_170,axiom,
( linordered_field(Eq_y_0)
| ~ linordered_field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_171,axiom,
( ring_char_0(Eq_y_0)
| ~ ring_char_0(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+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 21:27:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 5.35/5.66 % SZS status Theorem for theBenchmark
% 5.35/5.66 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------